SWHarden.com

The personal website of Scott W Harden

Using PHP to Create Apache-Style Access.log

Summary: The author is using PHP to create Apache-style access logs and demonstrates how to turn the log data into useful information once a good volume of log data has been collected.
This summary was generated in 71.68 seconds from an original post containing 485 words.

Signal Filtering with Python

⚠️ SEE UPDATED POST: Signal Filtering in Python

I’ve been spending a lot of time creating a DIY ECGs which produce fairly noisy signals. I have researched the ways to clean-up these signals, and the results are very useful! I document some of these findings here.

This example shows how I take __a noisy recording and turn it into a smooth trace. __This is achieved by eliminating excess high-frequency components which are in the original recording due to electromagnetic noise. A major source of noise can be from the AC passing through wires traveling through the walls of my apartment. My original ECG circuit was highly susceptible to this kind of interference, but my improved ECG circuit eliminates much of this noise. However, noise is still in the trace and it needs to be removed.

One method of reducing noise uses the FFT (Fast Fourier Transformation) and its inverse (iFFT) algorithm. Let’s say you have a trace with repeating sine-wave noise. The output of the FFT is the breakdown of the signal by frequency. Check out this FFT trace of a noisy signal from a few posts ago. High peaks represent frequencies which are common. See the enormous peak around 60 Hz? That’s noise from AC power lines. Other peaks (shown in colored bands) are other electromagnetic noise sources, such as wireless networks, TVs, telephones, and maybe my computer. The heart produces changes in electricity that are very slow (a heartbeat is about 1 Hz), so if we can eliminate higher-frequency sine waves we can get a pretty clear trace. This is called a band-stop filter (we block-out certain bands of frequencies). A band-pass filter is the opposite, where we only allow frequencies which are below (low-pass) or above (high-pass) a given frequency. By eliminating each of the peaks in the colored regions (setting each value to 0), then performing an inverse fast Fourier transformation (going backwards from frequency back to time), the result is the signal trace (seen as light gray on the bottom graph) with those high-frequency sine waves removed! (the gray trace on the bottom graph). A little touch-up smoothing makes a great trace (black trace on the bottom graph).

Here’s some Python code you may find useful. The image below is the output of the Python code at the bottom of this entry. This python file requires that ecg.wav (an actual ECG recording of my heartbeat) exist in the same folder.

import numpy, scipy, pylab, random

# This script demonstrates how to use band-pass (low-pass)
# filtering to eliminate electrical noise and static
# from signal data!

##################
### PROCESSING ###
##################

xs=numpy.arange(1,100,.01) #generate Xs (0.00,0.01,0.02,0.03,...,100.0)
signal = sin1=numpy.sin(xs*.3) #(A)
sin1=numpy.sin(xs) # (B) sin1
sin2=numpy.sin(xs*2.33)*.333 # (B) sin2
sin3=numpy.sin(xs*2.77)*.777 # (B) sin3
noise=sin1+sin2+sin3 # (C)
static = (numpy.random.random_sample((len(xs)))-.5)*.2 # (D)
sigstat=static+signal # (E)
rawsignal=sigstat+noise # (F)
fft=scipy.fft(rawsignal) # (G) and (H)
bp=fft[:]
for i in range(len(bp)): # (H-red)
    if i>=10:bp[i]=0
ibp=scipy.ifft(bp) # (I), (J), (K) and (L)

################
### GRAPHING ###
################

h,w=6,2
pylab.figure(figsize=(12,9))
pylab.subplots_adjust(hspace=.7)

pylab.subplot(h,w,1);pylab.title("(A) Original Signal")
pylab.plot(xs,signal)

pylab.subplot(h,w,3);pylab.title("(B) Electrical Noise Sources (3 Sine Waves)")
pylab.plot(xs,sin1,label="sin1")
pylab.plot(xs,sin2,label="sin2")
pylab.plot(xs,sin3,label="sin3")
pylab.legend()

pylab.subplot(h,w,5);pylab.title("(C) Electrical Noise (3 sine waves added together)")
pylab.plot(xs,noise)

pylab.subplot(h,w,7);pylab.title("(D) Static (random noise)")
pylab.plot(xs,static)
pylab.axis([None,None,-1,1])

pylab.subplot(h,w,9);pylab.title("(E) Signal + Static")
pylab.plot(xs,sigstat)

pylab.subplot(h,w,11);pylab.title("(F) Recording (Signal + Static + Electrical Noise)")
pylab.plot(xs,rawsignal)

pylab.subplot(h,w,2);pylab.title("(G) FFT of Recording")
fft=scipy.fft(rawsignal)
pylab.plot(abs(fft))
pylab.text(200,3000,"signals",verticalalignment='top')
pylab.text(9500,3000,"static",verticalalignment='top',
        horizontalalignment='right')

pylab.subplot(h,w,4);pylab.title("(H) Low-Pass FFT")
pylab.plot(abs(fft))
pylab.text(17,3000,"sin1",verticalalignment='top',horizontalalignment='left')
pylab.text(37,2000,"sin2",verticalalignment='top',horizontalalignment='center')
pylab.text(45,3000,"sin3",verticalalignment='top',horizontalalignment='left')
pylab.text(6,3000,"signal",verticalalignment='top',horizontalalignment='left')
pylab.axvspan(10,10000,fc='r',alpha='.5')
pylab.axis([0,60,None,None])

pylab.subplot(h,w,6);pylab.title("(I) Inverse FFT")
pylab.plot(ibp)

pylab.subplot(h,w,8);pylab.title("(J) Signal vs. iFFT")
pylab.plot(signal,'k',label="signal",alpha=.5)
pylab.plot(ibp,'b',label="ifft",alpha=.5)

pylab.subplot(h,w,10);pylab.title("(K) Normalized Signal vs. iFFT")
pylab.plot(signal/max(signal),'k',label="signal",alpha=.5)
pylab.plot(ibp/max(ibp),'b',label="ifft",alpha=.5)

pylab.subplot(h,w,12);pylab.title("(L) Difference / Error")
pylab.plot(signal/max(signal)-ibp/max(ibp),'k')

pylab.savefig("SIG.png",dpi=200)
pylab.show()

DIY ECG Detected an Irregular Heartbeat

Summary: The author of the blog post does not know how to analyze blood flow using an ECG and suggests that it is not worth the time, hassle or expense of building such a system.
This summary was generated in 55.17 seconds from an original post containing 276 words.

DIY ECG Detected an Irregular Heartbeat

⚠️ Check out my newer ECG designs:

Am I going to die? It’s unlikely. Upon analyzing ~20 minutes of heartbeat data (some of which is depicted in the previous entry) I found a peculiarity. Technically this could be some kind of noise (a ‘pop’ in the microphone signal due to the shuffling of wires or a momentary disconnect from the electrodes or perhaps even a static shock to my body from something), but because this peculiarity happened only once in 20 minutes I’m not ruling out the possibility that this is the first irregular heartbeat I captured with my DIY ECG. Note that single-beat irregularities are common, and that this does not alarm me so much as fascinates me. Below is the section of the data which contains this irregular beat.

In the spirit of improvement I wonder how much more interesting this project would be if I were to combine the already-designed ECG machine with a sensor to detect the physical effect of the heart’s beating on my vasculature. in other words, can I combine my electrical traces with physical traces? (Blood pressure or blood flow) I found an interesting site that shows how someone built a DIY blood flow meter using a piezo film pulse sensor. Pretty clever I must say… but I think I draw my limit at what I’ve done. Although blood flow would be interesting to analyze (does the murmur depicted above produce an alteration in normal blood flow?), it’s not worth the time, hassle or expense of building.


DIY ECG Improvements

⚠️ Check out my newer ECG designs:

Instead of using a single op-amp circuit like the previous entries which gave me decent but staticky traces, I decided to build a more advanced ECG circuit documented by Jason Nguyen which used 6 op amps! (I’d only been using one). Luckily I got a few couple LM324 quad op-amps from radioshack ($1.40 each), so I had everything I needed.

The results look great! Noise is almost zero, so true details of the trace are visible. I can now clearly see the PQRST features in the wave. I’ll detail how I did this in a later entry. For now, here are some photos of the little device.

UPDATE: After analyzing ~20 minutes of heartbeat data I found a peculiarity. Technically this could be some kind of noise (a ‘pop’ in the microphone signal), but because this peculiarity happened only once in 20 minutes I’m not ruling out the possibility that this is the first irregular heartbeat I captured with my DIY ECG. Note that single-beat irregularities are common in healthy people, and that this does not alarm me so much as fascinate me.