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Divide 10 MHz to 1PPS with a Microcontroller

How to use a microcontroller to inexpensively scale down a 10 MHz reference clock into a one pulse per second (1pps) signal
December 17, 2022
circuit microcontroller

I often find it useful to gate frequency counters using a 1 pulse per second (1PPS) signal derived from a 10 MHz precision frequency reference. However, a divide-by-10-million circuit isn’t trivial to implement. Counter ICs exist which enable divide-by-100 by combining multiple divide-by-2 and divide-by-5 stages (e.g., MC74HC390A around $0.85 each), but dividing 10 MHz all the way down to 1Hz would require at least 4 of these chips and a lot of wiring.

You can clock a microcontroller at 10 MHz and use its timer and interrupt systems to generate 1PPS. For example, an ATTiny202 in an 8-pin SOIC package is available from Mouser (>50k stocked) for $0.51 each. Note that modern series AVRs require a special UDPI programmer.

ATTiny202 ($0.51) ATTint826 ($0.95)

This page documents a divide-by-10-million circuit achieved with a single microcontroller to scale a 10MHz frequency reference down to 1PPS. I’m using an ATTiny826 because that is what I have on hand, but these concepts apply to any microcontroller with a 16-bit timer.

ATTiny Breakout Board

Some AVRs come in DIP packages but their pin numbers may be different than the same chip in a SMT package. To facilitate prototyping using designs and code that will work identically across a breadboard prototype and a PCB containing SMT chips, I prefer to build DIP breakout boards using whatever SMT package I intend to include in my final builds. In this case it’s ATTint826 in a SOIC-20 package, and I can easily use this in a breadboard by soldering them onto SOIC-to-DIP breakout boards.

I assembled the breakout board by hand using a regular soldering iron. When working with small packages it helps so much to coat the pins with a little tack flux to facilitate wetting and prevent solder bridges. I’m presently using Chip Quik NC191. Even if flux is advertized as “no-clean”, it’s good practice and makes the boards look much nicer to remove remaining flux with acetone and Q-tips or brushes.

Circuit

Configuration Change Protection (CCP)

Traditional AVR microcontrollers used fuse bits to set the clock source, but modern series chips can change the clock source from within code. However, modifying the clock source requires temporarily disabling the configuration change protection (CCP) system.

Disabling the CCP only lasts four clock cycles, so the immediate next statement must be assignment of the new value. I use the following function to facilitate this action.

/* Write a value to a CCP-protected register */
void ccp_write(volatile register8_t* address, uint8_t value){
	CCP = CCP_IOREG_gc;
	*address = value;
}

// Use internal 20 MHz clock with CKOUT pin enabled
ccp_write(&CLKCTRL.MCLKCTRLA, CLKCTRL.MCLKCTRLA | CLKCTRL_CLKOUT_bm);

Do not use compound statements when writing to the CCP register. The code below fails to change clock as one may expect by looking at the code, presumably because the combined OR operation with the assignment exceeds four clock cycles. Instead of direct assignment, use the ccp_write function described above.

// WARNING: This code does not actually change the clock source
CCP = CCP_IOREG_gc;
CLKCTRL.MCLKCTRLA = CLKCTRL.MCLKCTRLA | CLKCTRL_CLKOUT_bm;

Configuring the Clock Source

Internal 10 MHz clock

This is the configuration I use to achieve a 10 CPU clock using the built-in 20 MHz oscillator.

void configure_clock_internal_10mhz(){
	ccp_write(&CLKCTRL.MCLKCTRLA, CLKCTRL.MCLKCTRLA | CLKCTRL_CLKOUT_bm); // 20 MHz internal clock, enable CKOUT
	ccp_write(&CLKCTRL.MCLKCTRLB, CLKCTRL_PEN_bm); // enable divide-by-2 clock prescaler
}

External 10 MHz clock

This is the configuration I use to clock the CPU from an external 10 MHz clock source applied to the EXTCLK pin.

void configure_clock_external(){
	ccp_write(&CLKCTRL.MCLKCTRLA, CLKCTRL_CLKSEL_EXTCLK_gc | CLKCTRL_CLKOUT_bm); // external clock, enable CKOUT
	ccp_write(&CLKCTRL.MCLKCTRLB, 0); // disable prescaler
}

Configuring the 16-Bit Timer

This is how I configured my ATTiny826’s TCA0 16-bit timer to fire an interrupt every 200 ms.

void configure_1pps(){
	// 10 MHz system clock with div64 prescaler is 156,250 Hz.
	// Setting a 16-bit timer's top to 31,250 means 5 overflows per second.
	TCA0.SINGLE.INTCTRL = TCA_SINGLE_OVF_bm; // overflow interrupt
	TCA0.SINGLE.CTRLB = TCA_SINGLE_WGMODE_NORMAL_gc; // normal mode
	TCA0.SINGLE.PER = 31249UL; // control timer period by setting timer top
	TCA0.SINGLE.CTRLA |= TCA_SINGLE_CLKSEL_DIV64_gc; // set clock source
	TCA0.SINGLE.CTRLA |= TCA_SINGLE_ENABLE_bm; // start timer
}

Alternatively, multiple timers could be cascaded to achieve a similar effect. Modern AVR series microcontrollers have sections in their datasheet describing considerations for cascading two 16-bit timers to create a single 32-bit timer. Using this strategy one could set the top of the counter to 5 million and arrange an interrupt to toggle an LED, resulting in a 1Hz signal with 50% duty.

Configuring the Interrupt System

This method is called whenever the timer’s overflow interrupt is triggered. Since it’s called 5 times per second, I just need a global counter to count the number of times it was called, and set an output pin to high on every 5th invocation.

uint8_t overflow_count;

ISR(TCA0_OVF_vect)
{
	overflow_count++;
	if (overflow_count == 5){
		overflow_count = 0;
		PORTB.OUT = PIN1_bm;
    } else {
		PORTB.OUT = 0;
	}
    
	TCA0.SINGLE.INTFLAGS = TCA_SINGLE_OVF_bm; // indicate interrupt was handled
}

Do not forget to enable global interrupts in your start-up sequence! This is an easy mistake to make, and without calling this function the overflow function will never be invoked.

sei(); // enable global interrupts

Results

We have achieved a light that blinks exactly once per second with roughly the same precision as the 10 MHz frequency reference used to clock the microcontroller. This output signal is ready to use for precision measurement purposes, such as toggling the gate of a discrete frequency counter.

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Programming Modern AVR Microcontrollers

How to program modern AVR chips using Atmel ICE, MPLAB Snap, or Serial Port UPDI programmers
December 9, 2022
circuit microcontroller

This page describes how to program Microchip’s newest series of AVR microcontrollers using official programming gear and software. I spent many years programming the traditional series of Atmel chips, but now several years after Microchip acquired Atmel I am interested in exploring the capabilities of the latest series of AVR microcontrollers (especially the new AVR DD family). Currently the global chip shortage makes it difficult to source traditional ATMega and STM32 chips, but the newest series of AVR microcontrollers feature an impressive set of peripherals for the price and are available from all the major vendors. pressive set of peripherals for the price and are available from all the major vendors.

TLDR

Blinking a LED is the “Hello, World” of microcontroller programming. Let’s take a look at the code necessary to blink a LED on pin 2 of an ATTiny286. It is compiled and programmed onto the chip using Microchip Studio.

#define F_CPU 3333333UL
#include <avr/io.h>
#include <util/delay.h>

int main(void)
{
	PORTA.DIR = 0xFF;
	while (1)
	{
		PORTA.OUT = 255;
		_delay_ms(500);
		PORTA.OUT = 0;
		_delay_ms(500);
	}
}

ATTiny826 Pinout

From page 14 of the ATTiny826 datasheet

SMT ATTiny Breakout Board

Many of the newer AVR series microcontrollers are not available in breadboard-friendly DIP packages. I find SOIC-to-DIP breakout boards (available on Amazon and eBay) to be useful for experimenting with chips in SOIC packages. Here I added extra power and PA4 (pin 2) LEDs and 10 kΩ current limiting resistors.

I power the device from the 3.3V or 5V pins on a FT232 USB breakout board. Although the topic is out of scope for this article, I find it convenient to use FTDI chips to exchange small amounts of data or debug messages between a microcontroller and a modern PC over USB without requiring special drivers.

Why is programming modern AVRs so difficult?

I’m surprised how little information there is online about how to reliably program modern AVR series microcontrollers. In late 2022 there is a surprisingly large amount of “advice” on this topic which leads to dead ends and broken or abandoned projects. After looking into it for a while, here is my opinionated assessment. Mouser and Digikey have links to expensive programmers, and Amazon has links to similar items but reviews are littered with comments like “arrived bricked” and “can not program AVR series chips”. DIY options typically involve abandoned (or soon-to-be abandoned?) GitHub repositories, or instructions for Arduino-related programming. I seek to consolidate and distill the most useful information onto this page, and I hope others will find it useful.

Atmel-ICE: Expensive but Effective

After using $5 ICSP programmers for the last decade I almost fell out of my chair when I saw Microchip’s recommended entry-level programmer is over $180! Digikey sells a “basic” version without cables for $130, but that still seems crazy to me. Also, $50 for a ribbon cable?

I found a kit on Amazon that sells the programmer with a cable for $126. It was hard for me to press that buy button, but I figured the time I would save by having access to modern and exotic chips during the present global chip shortage would make it worth it. After a couple days of free Prime shipping, it arrived. It was smaller than I thought it would be from the product photos.

The cable that came with the device seemed a bit hacky at first, but I’m happy to have it. The female 2.54 mm socket is easy to insert breadboard jumpers into.

I’m glad this thing is idiot proof. The very first thing I did after unboxing this programmer was hook it up to my power supply rails using reverse polarity. I misread the pin diagram and confused the socket with the connector (they are mirror images of one another). This is an easy mistake to make though, so here’s a picture of the correct orientation. Note the location of the tab on the side of the connector.

Atmel ICE Pinout Programming Connection

You can break-out power and programming pins so you can power your device with this programmer and also not need the stupid ribbon cable for programming it! See my article Hack an Atmel ICE to Deliver Power for more information.

The Atmel ICE was easy to use with Microchip Studio. My programmer was detected immediately, a window popped-up and walked me through updating the firmware, and my LED was blinking in no time.

MPLAB Snap: Cheap and Convoluted

Did I really need to spend $126 for an AVR programmer? Amazon carries the MPLAB Snap for $34, but lots of reviews say it doesn’t work. After easily getting the Atmel-ICE programmer up and running I thought it would be a similarly easy experience setting-up the MPLAB Snap for AVR UPDI programming, but boy was I wrong. Now that I know the steps to get this thing working it’s not so bad, but the information here was only gathered after hours of frustration.

Here are the steps you can take to program modern AVR microcontrollers with UPDI using a MPLAB Snap:

Step 1: Setup MPLAB

Step 2: Re-Flash the Programmer

Step 3: Acknowledge Your Programmer is Defective

Defective may be a strong word, but let’s just say the hardware was not designed to enable programming AVR chips using UPDI. Microchip Studio will detect the programmer but if you try to program an AVR you’ll get a pop-up error message that provides surprisingly little useful information.

Atmel Studio was unable to start your debug session. Please verify device selection, interface settings, target power and connections to the target device. Look in the details section for more information. StatusCode: 131107 ModuleName: TCF (TCF command: Processes:launch failed.) An illegal configuration parameter was used. Debugger command Activate physical failed.

Step 4: Fix Your Programmer

The reason MPLAB Snap cannot program AVR microcontrollers is because the UPDI pin should be pulled high, but the MPLAB Snap comes from the factory with its UPDI pin pulled low with a 4.7 kΩ resistor to ground. You can try to overpower this resistor by adding a low value pull-up resistor to Vcc (1 kΩ worked for me on a breadboard), but the actual fix is to fire-up the soldering iron and remove that tiny surface-mount pull-down resistor labeled R48.

Have your glasses? R48 is here:

These photos were taken after I removed the resistor. I didn’t use hot air. I just touched it a for a few seconds with a soldering iron and wiped it off then threw it away.

You don’t need a microscope, but I’m glad I had one.

Step 5: Reflect

You can now program AVR microcontrollers using UPDI with your MPLAB Snap! Blink, LED, blink.

Can you believe this is the officially recommended action? According to the official Microchip Engineering Technical Note ETN #36: MPLAB Snap AVR Interface Modification

I feel genuinely sorry for the Amazon sellers who are getting poor reviews because they sell this product. It really isn’t their fault. I hope Google directs people here so that they can get their boards working and leave positive reviews that point more people to this issue.

UPDI Programming with a Serial Adapter

There is no official support for UPDI programming using a serial adapter, but it seems some people have figured out how to do it in some capacity. There was a promising pyupdi project, but it is now deprecated. At the time of writing the leading project aiming to enable UPDI programming without official hardware is pymcuprog, but its repository has a single commit dated two months ago and no activity since. Interestingly, that commit was made by buildmaster@microchip.com (an unverified email address), so it may not be fair to refer to it as an “unofficial” solution. The long term support of the pymcuprog project remains uncertain, but regardless let’s take a closer look at how it works.

To build a programmer you just need a TTL USB serial adapter and a 1kΩ resistor. These are the steps I used to program a LED blink program using this strategy:

Ping the Microcontroller

This command returns the device ID (1E9328 for my ATtiny826) indicating the UPDI connection is working successfully

pymcuprog ping -d attiny826 -t uart -u com12

Connecting to SerialUPDI
Pinging device...
Ping response: 1E9328

Write a Hex File

I used Microchip Studio to compile my C code and generate the hex file. Now I can use pymcuprog to load those hex files onto the chip. It’s slower to program and inconvenient to drop to a terminal whenever I want to program a chip, but it works.

pymcuprog write -f LedBlink.hex -d attiny826 -t uart -u com12

Connecting to SerialUPDI
Pinging device...
Ping response: 1E9328
Writing from hex file...
Writing flash...

Conclusions

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Interfacing HX710 Differential ADC with Arduino

How to read differential voltage from a HX710 ADC using Arduino
November 15, 2022
circuit microcontroller

This page demonstrates how to read differential voltage from a HX710 ADC using Arduino. I recently obtained some pressure sensor boards from Amazon for less than $3 each under names like 6pcs 3.3-5V Digital Barometric Air Pressure Sensor Module Liquid Water Level Controller Board 0-40KPa that use this ADC. Several years ago I worked on a precision pressure meter project based on an I2C temperature and pressure sensor (MS5611), and now that I see new inexpensive SPI pressure sensor modules on the consumer market I’m interested to learn more about their capabilities.

Analog-to-Digital Converter IC

The ADC chip is easily identified as a HX710B 24-Bit Analog-to-Digital Converter (ADC) with Built-in Temperature Sensor. According to the datasheet it can be powered by a 3.3V or 5V supply, and the value it reports is the differential voltage between two input pins.

The datasheet indicates this device can be run from a 3.3V or 5V supply, it uses a built-in fixed-gain (128x) differential amplifier, and it can read up to 40 samples per second. The datasheet provides an example circuit demonstrating how this ADC can be used to measure weight from a scale sensor:

Pressure Sensor

To get a better idea of how this sensor works it would be helpful to locate its product number. I had a hunch it was beneath the part so I desoldered it, and indeed I found part identification information.

The pressure sensor is labeled as a PSG010S but unfortunately I struggled to find a quality datasheet for it. I did find some now-deleted images from an AliExpress listing showing the differences between the base model and the R and S variants. I found this PSG010R datasheet (curiously written in Comic Sans) indicating that maximum voltage is 5V and that the gauge pressure is 0 - 40KPa (0 - 5.8 PSI). This seems to be a fairly standard differential pressure sensor design using a pair of voltage dividers where the pressure is a function of the difference in voltage at the two mid-points (a Wheatstone bridge).

I used a multimeter to determine the resistor network inside this pressure sensor. Interestingly I found that pin 4 was not connected, which is opposite of many other designs I find online (where pin 5 is not connected). It is critically important to get this right if your goal is to design a PCB around this component. I guess connecting pins 1 & 6 and also 3 & 4 could be an option for covering all your bases? I also question if people are getting confused and reporting the mirror image pinout because they mistake the vent hole for the registration marker. Either way, I made the following diagram which I found helpful:

Update (2022-12-23): I received an email from somebody offering additional information about this component:

The PSG010 reports positive and negative pressures and can easily have its range shifted to almost double in one direction with almost none in the other. All that is needed is to lift the VCC or GND pin and insert a surface mount 75R ±15R under it. Lifting the ground side by 75R makes it double positive, while pushing the applied +V down makes it double negative (vacuum).
– bruceg

Read HX710B with Arduino

This code demonstrates how to measure HX710B values using Arduino and display the readings in the serial terminal sufficient to graph in real time using the serial plotter. The animated plot is what it looks like when I blow puffs of air on the sensor.

void setup() {
  pinMode(2, INPUT);   // Connect HX710 OUT to Arduino pin 2
  pinMode(3, OUTPUT);  // Connect HX710 SCK to Arduino pin 3
  Serial.begin(9600);
}

void loop() {
  // wait for the current reading to finish
  while (digitalRead(2)) {}

  // read 24 bits
  long result = 0;
  for (int i = 0; i < 24; i++) {
    digitalWrite(3, HIGH);
    digitalWrite(3, LOW);
    result = result << 1;
    if (digitalRead(2)) {
      result++;
    }
  }

  // get the 2s compliment
  result = result ^ 0x800000;

  // pulse the clock line 3 times to start the next pressure reading
  for (char i = 0; i < 3; i++) {
    digitalWrite(3, HIGH);
    digitalWrite(3, LOW);
  }

  // display pressure
  Serial.println(result);
}

Open-Source HX710B Libraries

Although some libraries are available which facilitate interacting with the HX710, here I engage with it discretely to convey each step of the conversion and measurement process. I found that many libraries use the 10 Hz mode by default, whereas I certainly prefer the 40 Hz mode. More frustratingly, code in many libraries refer to this as gain, which is incorrect. The datasheet indicates gain is fixed at 128 and cannot be changed in software.

Update (2022-12-23): I received an email explaining why people often use “gain” and “mode” when referring to the HX710:

The HX711 is similar to the HX710 but it has user selectable gain AND user selectable sample rates BUT only certain combinations are allowed, so setting mode WILL also select its matched gain value. The HX710 uses most of the same internals, but with just 3 modes - reading the Wheatstone Bridge always using 128 gain at 10 or 40Hz while swapping to Avolt (HX710A) or internal Temperature (HX710B) uses a lower gain and less digits. So for people familiar with the HX711 there is no ambiguity in mixing mode and gain.
– bruceg

Update (2024-12-26): I received an email that provided additional information regarding biasing:

Note, your suggestion to attempt to bias the sensor range by inserting resistors does not work. I tested it.

I think this is because the ADC is differential input so it is insensitive to common mode changes. One way to bias the output down is to put a 330k resistor between Vneg and VCC. Similarly you could put a large resistor between GND and VPOS. This introduces a bias to the difference between Vpos and Vneg. To bias the output values higher for vacuum operation put a resistor between VCC and Vpos or VNeg and GND.

A 330k resistor between Vneg and VCC changed my sensor output from 10M to 2M, but this asymmetrical arrangement compromises the thermal balance of the bridge, so it will be more temp sensitive.
– Dan

Update (2026-04-26): I received an email that provided additional information regarding PSG010 pin names and tips for zeroing:

I suggest that the original design intent for the pin names on the diagram of the sensor could be:

  • 4 - GND
  • 2 & 5 - bridge arms
  • 1 & 6 - bridge excitation via a balance potentiometer (e.g., 100 ohm) with ends connected to 1 & 6 and the wiper to VCC

This would allow the bridge to be zeroed.

– Peter

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Creating Bitmaps from Scratch in C#

How to create a bitmap and set pixel colors in memory and save the result to disk or convert it to a traditional image format
November 7, 2022
csharp graphics

This project how to represent bitmap data in a plain old C object (POCO) to create images from scratch using C# and no dependencies. Common graphics libraries like SkiaSharp, ImageSharp, System.Drawing, and Maui.Graphics can read and write bitmaps in memory, so a POCO that stores image data and converts it to a bitmap byte allows creation of platform-agnostic APIs that can be interfaced from any graphics library.

This page demonstrates how to use C# (.NET 6.0) to create bitmap images from scratch. Bitmap images can then be saved to disk and viewed with any image editing program, or they can consumed as a byte array in memory by a graphics library. There are various bitmap image formats (grayscale, indexed colors, 16-bit, 32-bit, transparent, etc.) but code here demonstrates the simplest common case (8-bit RGB color).

Representing Color

The following struct represents RGB color as 3 byte values and has helper methods for creating new colors.

public struct RawColor
{
    public readonly byte R, G, B;

    public RawColor(byte r, byte g, byte b)
    {
        (R, G, B) = (r, g, b);
    }

    public static RawColor Random(Random rand)
    {
        byte r = (byte)rand.Next(256);
        byte g = (byte)rand.Next(256);
        byte b = (byte)rand.Next(256);
        return new RawColor(r, g, b);
    }

    public static RawColor Gray(byte value)
    {
        return new RawColor(value, value, value);
    }
}

A color class like this could be extended to support additional niceties. Refer to SkiaSharp’s SKColor.cs, System.Drawing’s Color.cs, and Maui.Graphics’ Color.cs for examples and implementation details. I commonly find the following features useful include when writing a color class:

Representing the Bitmap Image

This is the entire image class and it serves a few specific roles:

public class RawBitmap
{
    public readonly int Width;
    public readonly int Height;
    private readonly byte[] ImageBytes;

    public RawBitmap(int width, int height)
    {
        Width = width;
        Height = height;
        ImageBytes = new byte[width * height * 4];
    }

    public void SetPixel(int x, int y, RawColor color)
    {
        int offset = ((Height - y - 1) * Width + x) * 4;
        ImageBytes[offset + 0] = color.B;
        ImageBytes[offset + 1] = color.G;
        ImageBytes[offset + 2] = color.R;
    }

    public byte[] GetBitmapBytes()
    {
        const int imageHeaderSize = 54;
        byte[] bmpBytes = new byte[ImageBytes.Length + imageHeaderSize];
        bmpBytes[0] = (byte)'B';
        bmpBytes[1] = (byte)'M';
        bmpBytes[14] = 40;
        Array.Copy(BitConverter.GetBytes(bmpBytes.Length), 0, bmpBytes, 2, 4);
        Array.Copy(BitConverter.GetBytes(imageHeaderSize), 0, bmpBytes, 10, 4);
        Array.Copy(BitConverter.GetBytes(Width), 0, bmpBytes, 18, 4);
        Array.Copy(BitConverter.GetBytes(Height), 0, bmpBytes, 22, 4);
        Array.Copy(BitConverter.GetBytes(32), 0, bmpBytes, 28, 2);
        Array.Copy(BitConverter.GetBytes(ImageBytes.Length), 0, bmpBytes, 34, 4);
        Array.Copy(ImageBytes, 0, bmpBytes, imageHeaderSize, ImageBytes.Length);
        return bmpBytes;
    }

    public void Save(string filename)
    {
        byte[] bytes = GetBitmapBytes();
        File.WriteAllBytes(filename, bytes);
    }
}

Generate Images from Scratch

The following code uses the bitmap class and color struct above to create test images

Random Colors

RawBitmap bmp = new(400, 300);
Random rand = new();
for (int x = 0; x < bmp.Width; x++)
    for (int y = 0; y < bmp.Height; y++)
        bmp.SetPixel(x, y, RawColor.Random(rand));
bmp.Save("random-rgb.bmp");

Rainbow

RawBitmap bmp = new(400, 300);
Random rand = new();
for (int x = 0; x < bmp.Width; x++)
{
    for (int y = 0; y < bmp.Height; y++)
    {
        byte r = (byte)(255.0 * x / bmp.Width);
        byte g = (byte)(255.0 * y / bmp.Height);
        byte b = (byte)(255 - 255.0 * x / bmp.Width);
        RawColor color = new(r, g, b);
        bmp.SetPixel(x, y, color);
    }
}
bmp.Save("rainbow.bmp");

Rectangles

RawBitmap bmp = new(400, 300);
Random rand = new();
for (int i = 0; i < 1000; i++)
{
    int rectX = rand.Next(bmp.Width);
    int rectY = rand.Next(bmp.Height);
    int rectWidth = rand.Next(50);
    int rectHeight = rand.Next(50);
    RawColor color = RawColor.Random(rand);

    for (int x = rectX; x < rectX + rectWidth; x++)
    {
        for (int y = rectY; y < rectY + rectHeight; y++)
        {
            if (x < 0 || x >= bmp.Width) continue;
            if (y < 0 || y >= bmp.Height) continue;
            bmp.SetPixel(x, y, color);
        }
    }
}
bmp.Save("rectangles.bmp");

Drawing Operations

The following functions can be added to the RawBitmap class to add drawing common operations

Draw Line

Here’s a simple (not optimized) method for drawing lines. Users interested in high quality drawing methods will find Bresenham’s line algorithm and Bresenham’s circle algorithm useful. There’s also A Rasterizing Algorithm for Drawing Curves which has extensive information about anti-aliasing and drawing Bézier splines.

public void DrawLine(int x1, int y1, int x2, int y2, Color color)
{
    int xMin = Math.Min(x1, x2);
    int xMax = Math.Max(x1, x2);
    int yMin = Math.Min(y1, y2);
    int yMax = Math.Max(y1, y2);

    int xSpan = xMax - xMin;
    int ySpan = yMax - yMin;

    if (xSpan == 0)
    {
        for (int y = yMin; y <= yMax; y++)
            SetPixel(xMin, y, color);
    }
    else if (ySpan == 0)
    {
        for (int x = xMin; x <= xMax; x++)
            SetPixel(x, yMin, color);
    }
    else if (ySpan > xSpan)
    {
        for (int y = yMin; y <= yMax; y++)
        {
            double frac = (y - yMin) / (double)ySpan;
            if (y2 < y1)
                frac = 1 - frac;
            int x = (int)(frac * xSpan + xMin);
            SetPixel(x, y, color);
        }
    }
    else
    {
        for (int x = xMin; x <= xMax; x++)
        {
            double frac = (x - xMin) / (double)xSpan;
            if (x2 < x1)
                frac = 1 - frac;
            int y = (int)(frac * ySpan + yMin);
            SetPixel(x, y, color);
        }
    }
}

Draw Rectangle

public void DrawRect(Rectangle rect, Color color)
{
    DrawLine(rect.Left, rect.Top, rect.Right, rect.Top, color);
    DrawLine(rect.Right, rect.Top, rect.Right, rect.Bottom, color);
    DrawLine(rect.Right, rect.Bottom, rect.Left, rect.Bottom, color);
    DrawLine(rect.Left, rect.Bottom, rect.Left, rect.Top, color);
}

Fill Rectangle

public void FillRect(Rectangle rect, Color color)
{
    for (int y = rect.YMin; y < rect.YMax; y++)
    {
        for (int x = rect.XMin; x < rect.XMax; x++)
        {
            SetPixel(x, y, color);
        }
    }
}

Interfacing Graphics Libraries

The following code demonstrates how to load the bitmap byte arrays generated above into common graphics libraries and save the result as a JPEG file. Although the bitmap byte array can be written directly to disk as a .bmp file, these third-party libraries are required to encode images in additional formats like JPEG.

System.Drawing

using System.Drawing;

static void SaveBitmap(byte[] bytes, string filename = "demo.jpg")
{
    using MemoryStream ms = new(bytes);
    using Image img = Bitmap.FromStream(ms);
    img.Save(filename);
}

SkiaSharp

using SkiaSharp;

static void SaveBitmap(byte[] bytes, string filename = "demo.jpg")
{
    using SKBitmap bmp = SKBitmap.Decode(bytes);
    using SKFileWStream fs = new(filename);
    bmp.Encode(fs, SKEncodedImageFormat.Jpeg, quality: 95);
}

ImageSharp

using SixLabors.ImageSharp;
using SixLabors.ImageSharp.Formats.Jpeg;

static void SaveBitmap(byte[] bytes, string filename = "demo.jpg")
{
    using Image img = Image.Load(bytes);
    JpegEncoder encoder = new() { Quality = 95 };
    img.Save(filename, encoder);
}

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Experiments in PSK-31 Synthesis

How to encode and decode PSK-31 messages using C#
October 16, 2022
amateur radio csharp

PSK-31 is a narrow-bandwidth digital mode which encodes text as an audio tone that varies phase at a known rate. To learn more about this digital mode and solve a challenging programming problem, I’m going to write a PSK-31 encoder and decoder from scratch using the C# programming language. All code created for this project is open-source, available from my PSK Experiments GitHub Repository, and released under the permissive MIT license. This page documents my progress and notes things I learn along the way.

Encoding Bits as Phase Shifts

Amplitude Modulation Silences Phase Transitions

Although a continuous phase-shifting tone of constant amplitude can successfully transmit PSK31 data, the abrupt phase transitions will cause splatter. If you transmit this you will be heard, but those trying to communicate using adjacent frequencies will be highly disappointed.

Hard phase transitions (splatter) Soft phase transitions (cleaner)

To reduce spectral artifacts that result from abruptly changing phase, phase transitions are silenced by shaping the waveform envelope as a sine wave so it is silent at the transition. This way the maximum rate of phase shifts is a sine wave with a period of half the baud rate. This is why the opening of a PSK31 message (a series of logical 0 bits) sounds like two tones: It’s the carrier sine wave with an envelope shaped like a sine wave with a period of 31.25/2 Hz. These two tones separated by approximately 15 Hz are visible in the spectrogram (waterfall).

Encoding Text as Bits

Unlike ASCII (8 bits per character) and RTTY (5 bits per character), BPSK uses Varicode (1-10 bits per character) to encode text. Consecutive zeros 00 separate characters, so character codes must not contain 00 and they must start ane end with a 1 bit. Messages are flanked by a preamble (repeated 0 bits) and a postamble (repeated 1 bits).

NUL 1010101011
SOH 1011011011
STX 1011101101
ETX 1101110111
EOT 1011101011
ENQ 1101011111
ACK 1011101111
BEL 1011111101
BS  1011111111
HT  11101111
LF  11101
VT  1101101111
FF  1011011101
CR  11111
SO  1101110101
SI  1110101011
DLE 1011110111
DC1 1011110101
DC2 1110101101
DC3 1110101111
DC4 1101011011
NAK 1101101011
SYN 1101101101
ETB 1101010111
CAN 1101111011
EM  1101111101
SUB 1110110111
ESC 1101010101
FS  1101011101
GS  1110111011
RS  1011111011
US  1101111111
SP  1
!   111111111
"   101011111
#   111110101
$   111011011
%   1011010101
&   1010111011
'   101111111
(   11111011
)   11110111
*   101101111 		+   111011111
,   1110101
-   110101
.   1010111
/   110101111
0   10110111
1   10111101
2   11101101
3   11111111
4   101110111
5   101011011
6   101101011
7   110101101
8   110101011
9   110110111
:   11110101
;   110111101
<   111101101
=   1010101
>   111010111
?   1010101111
@   1010111101
A   1111101
B   11101011
C   10101101
D   10110101
E   1110111
F   11011011
G   11111101
H   101010101
I   1111111
J   111111101
K   101111101
L   11010111
M   10111011
N   11011101
O   10101011
P   11010101
Q   111011101
R   10101111
S   1101111
T   1101101
U   101010111 		V   110110101
X   101011101
Y   101110101
Z   101111011
[   1010101101
\   111110111
]   111101111
^   111111011
_   1010111111
.   101101101
/   1011011111
a   1011
b   1011111
c   101111
d   101101
e   11
f   111101
g   1011011
h   101011
i   1101
j   111101011
k   10111111
l   11011
m   111011
n   1111
o   111
p   111111
q   110111111
r   10101
s   10111
t   101
u   110111
v   1111011
w   1101011
x   11011111
y   1011101
z   111010101
{   1010110111
|   110111011
}   1010110101
~   1011010111
DEL 1110110101

How to Generate a PSK Waveform

Now that we’ve covered the major steps of PSK31 message composition and modulation, let’s go through the steps ot generate a PSK31 message in code.

Step 1: Convert a Message to Varicode

Here’s the gist of how I store my varicode table in code. Note that the struct has an additional Description field which is useful for decoding and debugging.

public struct VaricodeSymbol
{
    public readonly string Symbol;
    public string BitString;
    public int[] Bits;
    public readonly string Description;

    public VaricodeSymbol(string symbol, string bitString, string? description = null)
    {
        Symbol = symbol;
        BitString = bitString;
        Bits = bitString.ToCharArray().Select(x => x == '1' ? 1 : 0).ToArray();
        Description = description ?? string.Empty;
    }
}

static VaricodeSymbol[] GetAllSymbols() => new VaricodeSymbol[]
{
    new("NUL", "1010101011", "Null character"),
    new("LF", "11101", "Line feed"),
    new("CR", "11111", "Carriage return"),
    new("SP", "1", "Space"),
    new("a", "1011"),
    new("b", "1011111"),
    new("c", "101111"),
    // etc...
};

I won’t show how I do the message-to-varicode lookup, but it’s trivial. Here’s the final function I use to generate Varicode bits from a string:

static int[] GetVaricodeBits(string message)
{
    List<int> bits = new();

    // add a preamble of repeated zeros
    for (int i=0; i<20; i++)
        bits.Add(0);

    // encode each character of a message
    foreach (char character in message)
    {
        VaricodeSymbol symbol = Lookup(character);
        bits.AddRange(symbol.Bits);
        bits.AddRange(CharacterSeparator);
    }

    // add a postamble of repeated ones
    for (int i=0; i<20; i++)
        bits.Add(1);

    return bits.ToArray();
}

Step 2: Determine Phase Shifts

Now that we have our Varicode bits, we need to generate an array to indicate phase transitions. A transition occurs every time a bit changes value form the previous bit. This code returns phase as an array of double given the bits from a Varicode message.

public static double[] GetPhaseShifts(int[] bits, double phase1 = 0, double phase2 = Math.PI)
{
    double[] phases = new double[bits.Length];
    for (int i = 0; i < bits.Length; i++)
    {
        double previousPhase = i > 0 ? phases[i - 1] : phase1;
        double oppositePhase = previousPhase == phase1 ? phase2 : phase1;
        phases[i] = bits[i] == 1 ? previousPhase : oppositePhase;
    }
    return phases;
}

Step 3: Generate the Waveform

These constants will be used to define the shape of the waveform:

public const int SampleRate = 8000;
public const double Frequency = 1000;
public const double BaudRate = 31.25;

This minimal code generates a decipherable PSK-31 message, but it does not silence the phase transitions so it produces a lot of splatter. This function must be refined to shape the waveform such that phase transitions are silenced.

public double[] GetWaveformBPSK(double[] phases)
{
    int totalSamples = (int)(phases.Length * SampleRate / BaudRate);
    double[] wave = new double[totalSamples];
    for (int i = 0; i < wave.Length; i++)
    {
        double time = (double)i / SampleRate;
        int frame = (int)(time * BaudRate);
        double phaseShift = phases[frame];
        wave[i] = Math.Cos(2 * Math.PI * Frequency * time + phaseShift);
    }
    return wave;
}

Step 4: Generate the Waveform with Amplitude Modulation

This is the same function as above, but with extra logic for amplitude-modulating the waveform in the shape of a sine wave to silence phase transitions.

public double[] GetWaveformBPSK(double[] phases)
{
    int baudSamples = (int)(SampleRate / BaudRate);
    double samplesPerBit = SampleRate / BaudRate;
    int totalSamples = (int)(phases.Length * SampleRate / BaudRate);
    double[] wave = new double[totalSamples];

    // create the amplitude envelope sized for a single bit
    double[] envelope = new double[(int)samplesPerBit];
    for (int i = 0; i < envelope.Length; i++)
        envelope[i] = Math.Sin((i + .5) * Math.PI / envelope.Length);

    for (int i = 0; i < wave.Length; i++)
    {
        // phase modulated carrier
        double time = (double)i / SampleRate;
        int frame = (int)(time * BaudRate);
        double phaseShift = phases[frame];
        wave[i] = Math.Cos(2 * Math.PI * Frequency * time + phaseShift);

        // envelope at phase transitions
        int firstSample = (int)(frame * SampleRate / BaudRate);
        int distanceFromFrameStart = i - firstSample;
        int distanceFromFrameEnd = baudSamples - distanceFromFrameStart + 1;
        bool isFirstHalfOfFrame = distanceFromFrameStart < distanceFromFrameEnd;
        bool samePhaseAsLast = frame == 0 ? false : phases[frame - 1] == phases[frame];
        bool samePhaseAsNext = frame == phases.Length - 1 ? false : phases[frame + 1] == phases[frame];
        bool rampUp = isFirstHalfOfFrame && !samePhaseAsLast;
        bool rampDown = !isFirstHalfOfFrame && !samePhaseAsNext;

        if (rampUp)
            wave[i] *= envelope[distanceFromFrameStart];

        if (rampDown)
            wave[i] *= envelope[distanceFromFrameEnd];
    }

    return wave;
}

PSK31 Encoder Program

I wrapped the functionality above in a Windows Forms GUI that allows the user to type a message, specify frequency, baud rate, and whether or not to refine the envelope to reduce splatter, then either play or save the result. An interactive ScottPlot Chart allows the user to inspect the waveform.

Sample PSK-31 Transmissions

These audio files encode the text The Quick Brown Fox Jumped Over The Lazy Dog 1234567890 Times! in 1kHz BPSK at various baud rates.

Non-Standard Baud Rates

Let’s see what PSK-3 sounds like. This mode encodes data at a rate of 3 bits per second. Note that Varicode characters may require up to ten bits, so this is pretty slow. On the other hand the side tones are closer to the carrier and the total bandwidth is much smaller. The message here has been shortened to just my callsign, AJ4VD.

Encode PSK-31 In Your Browser

After implementing the C# encoder described above I created a JavaScript version (as per Atwood’s Law).

Decoding PSK-31

Considering all the steps for encoding PSK-31 transmissions are already described on this page, it doesn’t require too much additional effort to create a decoder using basic software techniques. Once symbol phases are detected it’s easy to work backwards: detect phase transitions (logical 0s) or repeats (logical 1s), treat consecutive zeros as a character separator, then look-up characters according to the Varicode table. The tricky bit is analyzing the source audio to generate the array of phase offsets.

The simplest way to decode PSK-31 transmissions leans on the fact that we already know the baud rate: 31.25 symbols per second, or one symbol every 256 samples at 8kHz sample rate. The audio signal can be segregated into many 256-sample bins, and processed by FFT. Once the center frequency is determined, the FFT power at this frequency can be calculated for each bin. Signal offset can be adjusted to minimize the imaginary component of the FFTs at the carrier frequency, then the real component will be strongly positive or negative, allowing phase transitions to be easily detected.

There are more advanced techniques to improve BPSK decoding, such as continuously adjusting frequency and phase alignment (synchronization). A Costas loop can help lock onto the carrier frequency while preserving its phase. Visit Simple BPSK31 Decoding with Python for an excellent demonstration of how to decode BPSK31 using these advanced techniques.

A crude C# implementation of a BPSK decoded is available on GitHub in the PSK Experiments repository

Encoding PSK-31 in Hardware

Since BPSK is just a carrier that applies periodic 180º phase-shifts, it’s easy to generate in hardware by directly modulating the signal source. A good example of this is KA7OEI’s PSK31 transmitter which feeds the output of an oscillator through an even or odd number of NAND gates (from a 74HC00) to produce two signals of opposite phase.

Quadrature Phase Shift Keying (QPSK)

Unlike the 0º and 180º phases of binary phase shift keying (BPSK), quadrature phase shift keying (QPSK) encodes extra data into each symbol by uses a larger number of phases. When QPSK-31 is used in amateur radio these extra bits aren’t used to send messages faster but instead send them more reliably using convolutional coding and error correction. These additional features come at a cost (an extra 3 dB SNR is required), and in practice QPSK is not used as much by amateur radio operators.

QPSK encoding/decoding and convolutional encoding/decoding are outside the scope of this page, but excellent information exists on the Wikipedia: QPSK and in the US Naval Academy’s EC314 Lesson 23: Digital Modulation document.

PSK-31 in 2022

After all that, it turns out PSK-31 isn’t that popular anymore. These days it seems the FT-8 digital mode with WSJT-X software is orders of magnitude more popular ??

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Resample Time Series Data using Cubic Spline Interpolation

Signal resampling with spline interpolation in pure C#
June 23, 2022
csharp graphics

Cubic spline interpolation can be used to modify the sample rate of time series data. This page describes how I achieve signal resampling with spline interpolation in pure C# without any external dependencies. This technique can be used to:

Simulating Data Samples

To simulate unevenly-sampled data I create a theoretical signal then sample it at 20 random time points.

// this function represents the signal being measured
static double f(double x) => Math.Sin(x * 10) + Math.Sin(x * 13f);

// randomly sample values from 20 time points
Random rand = new(123);
double[] sampleXs = Enumerable.Range(0, 20)
    .Select(x => rand.NextDouble())
    .OrderBy(x => x)
    .ToArray();
double[] sampleYs = sampleXs.Select(x => f(x)).ToArray();

Resample for Evenly-Spaced Data

I then generate an interpolated spline using my sampled data points as the input.

(double[] xs, double[] ys) = Cubic.Interpolate1D(sampleXs, sampleYs, count: 50);

The generated points line-up perfectly with the sampled data.

There is slight deviation from the theoretical signal (and it’s larger where there is more missing data) but this is an unsurprising result considering the original samples had large gaps of missing data.

Source Code

Interpolation.cs

public static class Interpolation
{
    public static (double[] xs, double[] ys) Interpolate1D(double[] xs, double[] ys, int count)
    {
        if (xs is null || ys is null || xs.Length != ys.Length)
            throw new ArgumentException($"{nameof(xs)} and {nameof(ys)} must have same length");

        int inputPointCount = xs.Length;
        double[] inputDistances = new double[inputPointCount];
        for (int i = 1; i < inputPointCount; i++)
            inputDistances[i] = inputDistances[i - 1] + xs[i] - xs[i - 1];

        double meanDistance = inputDistances.Last() / (count - 1);
        double[] evenDistances = Enumerable.Range(0, count).Select(x => x * meanDistance).ToArray();
        double[] xsOut = Interpolate(inputDistances, xs, evenDistances);
        double[] ysOut = Interpolate(inputDistances, ys, evenDistances);
        return (xsOut, ysOut);
    }

    private static double[] Interpolate(double[] xOrig, double[] yOrig, double[] xInterp)
    {
        (double[] a, double[] b) = FitMatrix(xOrig, yOrig);

        double[] yInterp = new double[xInterp.Length];
        for (int i = 0; i < yInterp.Length; i++)
        {
            int j;
            for (j = 0; j < xOrig.Length - 2; j++)
                if (xInterp[i] <= xOrig[j + 1])
                    break;

            double dx = xOrig[j + 1] - xOrig[j];
            double t = (xInterp[i] - xOrig[j]) / dx;
            double y = (1 - t) * yOrig[j] + t * yOrig[j + 1] +
                t * (1 - t) * (a[j] * (1 - t) + b[j] * t);
            yInterp[i] = y;
        }

        return yInterp;
    }

    private static (double[] a, double[] b) FitMatrix(double[] x, double[] y)
    {
        int n = x.Length;
        double[] a = new double[n - 1];
        double[] b = new double[n - 1];
        double[] r = new double[n];
        double[] A = new double[n];
        double[] B = new double[n];
        double[] C = new double[n];

        double dx1, dx2, dy1, dy2;

        dx1 = x[1] - x[0];
        C[0] = 1.0f / dx1;
        B[0] = 2.0f * C[0];
        r[0] = 3 * (y[1] - y[0]) / (dx1 * dx1);

        for (int i = 1; i < n - 1; i++)
        {
            dx1 = x[i] - x[i - 1];
            dx2 = x[i + 1] - x[i];
            A[i] = 1.0f / dx1;
            C[i] = 1.0f / dx2;
            B[i] = 2.0f * (A[i] + C[i]);
            dy1 = y[i] - y[i - 1];
            dy2 = y[i + 1] - y[i];
            r[i] = 3 * (dy1 / (dx1 * dx1) + dy2 / (dx2 * dx2));
        }

        dx1 = x[n - 1] - x[n - 2];
        dy1 = y[n - 1] - y[n - 2];
        A[n - 1] = 1.0f / dx1;
        B[n - 1] = 2.0f * A[n - 1];
        r[n - 1] = 3 * (dy1 / (dx1 * dx1));

        double[] cPrime = new double[n];
        cPrime[0] = C[0] / B[0];
        for (int i = 1; i < n; i++)
            cPrime[i] = C[i] / (B[i] - cPrime[i - 1] * A[i]);

        double[] dPrime = new double[n];
        dPrime[0] = r[0] / B[0];
        for (int i = 1; i < n; i++)
            dPrime[i] = (r[i] - dPrime[i - 1] * A[i]) / (B[i] - cPrime[i - 1] * A[i]);

        double[] k = new double[n];
        k[n - 1] = dPrime[n - 1];
        for (int i = n - 2; i >= 0; i--)
            k[i] = dPrime[i] - cPrime[i] * k[i + 1];

        for (int i = 1; i < n; i++)
        {
            dx1 = x[i] - x[i - 1];
            dy1 = y[i] - y[i - 1];
            a[i - 1] = k[i - 1] * dx1 - dy1;
            b[i - 1] = -k[i] * dx1 + dy1;
        }

        return (a, b);
    }
}

Program.cs

This is the source code I used to generate the figures on this page.

Plots were generated using ScottPlot.NET.

// this function represents the signal being measured
static double f(double x) => Math.Sin(x * 10) + Math.Sin(x * 13f);

// create points representing randomly sampled time points of a smooth curve
Random rand = new(123);
double[] sampleXs = Enumerable.Range(0, 20)
    .Select(x => rand.NextDouble())
    .OrderBy(x => x)
    .ToArray();
double[] sampleYs = sampleXs.Select(x => f(x)).ToArray();

// use 1D interpolation to create an evenly sampled curve from unevenly sampled data
(double[] xs, double[] ys) = Interpolation.Interpolate1D(sampleXs, sampleYs, count: 50);

var plt = new ScottPlot.Plot(600, 400);

double[] theoreticalXs = ScottPlot.DataGen.Range(xs.Min(), xs.Max(), .01);
double[] theoreticalYs = theoreticalXs.Select(x => f(x)).ToArray();
var perfectPlot = plt.AddScatterLines(theoreticalXs, theoreticalYs);
perfectPlot.Label = "theoretical signal";
perfectPlot.Color = plt.Palette.GetColor(2);
perfectPlot.LineStyle = ScottPlot.LineStyle.Dash;

var samplePlot = plt.AddScatterPoints(sampleXs, sampleYs);
samplePlot.Label = "sampled points";
samplePlot.Color = plt.Palette.GetColor(0);
samplePlot.MarkerSize = 10;
samplePlot.MarkerShape = ScottPlot.MarkerShape.openCircle;
samplePlot.MarkerLineWidth = 2;

var smoothPlot = plt.AddScatter(xs, ys);
smoothPlot.Label = "interpolated points";
smoothPlot.Color = plt.Palette.GetColor(3);
smoothPlot.MarkerShape = ScottPlot.MarkerShape.filledCircle;

plt.Legend();
plt.SaveFig("output.png");

2D and 3D Spline Interpolation

The interpolation method described above only considered the horizontal axis when generating evenly-spaced time points (1D interpolation). For information and code examples regarding 2D and 3D cubic spline interpolation, see my previous blog post: Spline Interpolation with C#

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Show A Progress Bar as your Blazor App Loads

How to add a progress bar to your client-side Blazor WebAssembly app to indicate page load progress.
May 29, 2022
blazor csharp

Today I created a Blazor WebAssembly app that shows a progress bar while the page loads. This is especially useful for users on slow connections because Blazor apps typically require several megabytes of DLL and DAT files to be downloaded before meaningful content appears on the page.

Live Demo: LJPcalc (source code)

Step 1: Add a progress bar

Edit index.html and identify your app’s main div:

<div id="app">Loading...</div>

Add a progress bar inside it:

<div id="app">
	<h2>Loading...</h2>
	<div class="progress mt-2" style="height: 2em;">
		<div id="progressbar" class="progress-bar progress-bar-striped progress-bar-animated"
			style="width: 10%; background-color: #204066;"></div>
	</div>
	<div>
		<span id="progressLabel" class="text-muted">Downloading file list</span>
	</div>
</div>

See Bootstrap’s progressbar page for extensive customization and animation options and best practices when working with progress indicators. Also ensure the version of Bootstrap in your Blazor app is consistent with the documentation/HTML you are referencing.

Step 2: Disable Blazor AutoStart

Edit index.html and identify where your app loads Blazor resources:

<script src="https://swharden.com/static/2022/05/29/_framework/blazor.webassembly.js"></script>

Update that script so it does not download automatically:

<script src="https://swharden.com/static/2022/05/29/_framework/blazor.webassembly.js" autostart="false"></script>

Step 3: Create a Blazor Startup Script

Add a script to the bottom of the page to start Blazor manually, identifying all the resources needed and incrementally downloading them while updating the progressbar along the way.

<script>
	function StartBlazor() {
		let loadedCount = 0;
		const resourcesToLoad = [];
		Blazor.start({
			loadBootResource:
				function (type, filename, defaultUri, integrity) {
					if (type == "dotnetjs")
						return defaultUri;

					const fetchResources = fetch(defaultUri, {
						cache: 'no-cache',
						integrity: integrity,
						headers: { 'MyCustomHeader': 'My custom value' }
					});

					resourcesToLoad.push(fetchResources);

					fetchResources.then((r) => {
						loadedCount += 1;
						if (filename == "blazor.boot.json")
							return;
						const totalCount = resourcesToLoad.length;
						const percentLoaded = 10 + parseInt((loadedCount * 90.0) / totalCount);
						const progressbar = document.getElementById('progressbar');
						progressbar.style.width = percentLoaded + '%';
						const progressLabel = document.getElementById('progressLabel');
						progressLabel.innerText = `Downloading ${loadedCount}/${totalCount}: ${filename}`;
					});

					return fetchResources;
				}
		});
	}

	StartBlazor();
</script>

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