This is an AI Generated Summary
Many of the blog posts I wrote when I was young are no longer available on this website.
However, AI was used to summarize the content of the original post into a single sentence
as described in my 2003 article,
Summarizing Blog Posts with AI.
Summary:
The author is using a new method to analyze an EEG signal that does not involve Fourier transformation, and they are able to determine heart rate from the signal using peak detection and integration.
This summary was generated in 57.79 seconds
from an original post containing 368 words.
This is an AI Generated Summary
Many of the blog posts I wrote when I was young are no longer available on this website.
However, AI was used to summarize the content of the original post into a single sentence
as described in my 2003 article,
Summarizing Blog Posts with AI.
Summary:
The author of the blog post is expressing their love for Inkscape, a free and open-source vector graphics editor that they used to create diagrams for their master's thesis or possibly for publication.
This summary was generated in 57.98 seconds
from an original post containing 551 words.
This is an AI Generated Summary
Many of the blog posts I wrote when I was young are no longer available on this website.
However, AI was used to summarize the content of the original post into a single sentence
as described in my 2003 article,
Summarizing Blog Posts with AI.
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.
⚠️ WARNING: This page is obsolete
Articles typically receive this designation when the technology they describe is no longer relevant, code
provided is later deemed to be of poor quality, or the topics discussed are better presented in future
articles. Articles like this are retained for the sake of preservation, but their content should be
critically assessed.
⚠️ 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.
-
(A) The original signal we want to isolate. (IE: our actual heart signal)
-
(B) Some electrical noise. (3 sine waves of different amplitudes and periods)
-
(C) Electrical noise (what happens when you add those 3 sine waves together)
-
(D) Static (random noise generated by a random number generator)
-
(E) Signal (A) plus static (D)
-
(F) Signal (A) plus static (D) plus electrical noise (C)
-
(G) Total FFT trace of (F). Note the low frequency peak due to the signal and electrical noise (near 0) and the high frequency peak due to static (near 10,000)
-
(H) This is a zoomed-in region of (F) showing 4 peaks (one for the original signal and 3 for high frequency noise). By blocking-out (set it to 0) everything above 10Hz (red), we isolate the peak we want (signal). This is a low-pass filter.
-
(I) Performing an inverse FFT (iFFT) on the low-pass iFFT, we get a nice trace which is our original signal!
-
(J) Comparison of our iFFT with our original signal shows that the amplitude is kinda messed up. If we normalize each of these (set minimum to 0, maximum to 1) they line up. Awesome!
-
(K) How close were we? Graphing the difference of iFFT and the original signal shows that usually we’re not far off. The ends are a problem though, but if our data analysis trims off these ends then our center looks great.
-
Note: these ends can be fixed by applying a windowing function to the original data. The FFT works best if the input data starts and ends at zero.
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()
This is an AI Generated Summary
Many of the blog posts I wrote when I was young are no longer available on this website.
However, AI was used to summarize the content of the original post into a single sentence
as described in my 2003 article,
Summarizing Blog Posts with AI.
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.
⚠️ WARNING: This page is obsolete
Articles typically receive this designation when the technology they describe is no longer relevant, code
provided is later deemed to be of poor quality, or the topics discussed are better presented in future
articles. Articles like this are retained for the sake of preservation, but their content should be
critically assessed.
⚠️ 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.
⚠️ 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.
