While continuing my quest into the world of linear data analysis and signal processing, I came to a point where I wanted to emphasize variations in FFT traces. While I am keeping my original data for scientific reference, visually I want to represent it emphasizing variations rather than concentrating on trends. I wrote a detrending function which I’m sure will be useful for many applications:detrend_fft

def detrend(data,degree=10):
	detrended=[None]*degree
	for i in range(degree,len(data)-degree):
		chunk=data[i-degree:i+degree]
		chunk=sum(chunk)/len(chunk)
		detrended.append(data[i]-chunk)
	return detrended+[None]*degree

However, this method is extremely slow. I need to think of a way to accomplish this same thing much faster. [ponders]

UPDATE: It looks like I’ve once again re-invented the wheel. All of this has been done already, and FAR more efficiently I might add. Simply:

import scipy.signal
ffty=scipy.signal.detrend(ffty)

Now I’m looking into scipy.signal.triang()





Additional Resources

I’m attempting to thoroughly re-write the data assessment portions of my QRSS VD software, and rather than rushing to code it (like I did last time) I’m working hard on every step trying to optimize the code. I came across some notes I made about Fast Fourier Transformations from the first time I coded the software, and though I’d post some code I found helpful. Of particular satisfaction is an email I received from Alberto, I2PHD, the creator of Argo (the “gold standard” QRSS spectrograph software for Windows). In it he notes:

I think that [it is a mistake to] throw away the imaginary part of the FFT. What I do in Argo, in Spectran, in Winrad, in SDRadio and in all of my other programs is compute the magnitude of the [FFT] signal, then compute the logarithm of it, and only then I do a mapping of the colors on the screen with the result of this last computation.

These concepts are simple to visualize when graphed. Here I’ve written a short Python script to listen to the microphone (which is being fed a 2kHz sine wave), perform the FFT, and graph the real FFT component, imaginary FFT component, and their sum. The output is:real_imaginary_fft_pcm

Of particular interest to me is the beautiful complementarity of the two curves. It makes me wonder what types of data can be extracted by the individual curves (or perhaps their difference?) down the road. I wonder if phase measurements would be useful in extracting weak carries from beneath the noise floor?

Here’s the code I used to generate the image above. Note that my microphone device was set to listen to my stereo output, and I generated a 2kHz sine wave using the command speaker-test -t sine -f 2000 on a PC running Linux. I hope you find it useful!

import numpy
import pyaudio
import pylab
import numpy

### RECORD AUDIO FROM MICROPHONE ###
rate=44100
soundcard=1 #CUSTOMIZE THIS!!!
p=pyaudio.PyAudio()
strm=p.open(format=pyaudio.paInt16,channels=1,rate=rate,
			input_device_index=soundcard,input=True)
strm.read(1024) #prime the sound card this way
pcm=numpy.fromstring(strm.read(1024), dtype=numpy.int16)

### DO THE FFT ANALYSIS ###
fft=numpy.fft.fft(pcm)
fftr=10*numpy.log10(abs(fft.real))[:len(pcm)/2]
ffti=10*numpy.log10(abs(fft.imag))[:len(pcm)/2]
fftb=10*numpy.log10(numpy.sqrt(fft.imag**2+fft.real**2))[:len(pcm)/2]
freq=numpy.fft.fftfreq(numpy.arange(len(pcm)).shape[-1])[:len(pcm)/2]
freq=freq*rate/1000 #make the frequency scale

### GRAPH THIS STUFF ###
pylab.subplot(411)
pylab.title("Original Data")
pylab.grid()
pylab.plot(numpy.arange(len(pcm))/float(rate)*1000,pcm,'r-',alpha=1)
pylab.xlabel("Time (milliseconds)")
pylab.ylabel("Amplitude")
pylab.subplot(412)
pylab.title("Real FFT")
pylab.xlabel("Frequency (kHz)")
pylab.ylabel("Power")
pylab.grid()
pylab.plot(freq,fftr,'b-',alpha=1)
pylab.subplot(413)
pylab.title("Imaginary FFT")
pylab.xlabel("Frequency (kHz)")
pylab.ylabel("Power")
pylab.grid()
pylab.plot(freq,ffti,'g-',alpha=1)
pylab.subplot(414)
pylab.title("Real+Imaginary FFT")
pylab.xlabel("Frequency (kHz)")
pylab.ylabel("Power")
pylab.grid()
pylab.plot(freq,fftb,'k-',alpha=1)
pylab.show()

After fighting for a while long with a “shifty baseline” of the FFT, I came to another understanding. Let me first address the problem. Taking the FFT of different regions of the 2kHz wave I got traces with the peak in the identical location, but the “baselines” completely different. fft_base2

Like many things, I re-invented the wheel. Since I knew the PCM values weren’t changing, the only variable was the starting/stopping point of the linear sample. “Hard edges”, I imagined, must be the problem. I then wrote the following function to shape the PCM audio like a triangle, silencing the edges and sweeping the volume up toward the middle of the sample:

def shapeTriangle(data):
	triangle=numpy.array(range(len(data)/2)+range(len(data)/2)[::-1])+1
	return data*triangle

After shaping the data BEFORE I applied the FFT, I made the subsequent traces MUCH more acceptable. Observe:fft_base3

Now that I’ve done all this experimentation/thinking, I remembered that this is nothing new! Everyone talks about shaping the wave to minimize hard edges before taking the FFT. BAH! Another case of me re-inventing the wheel because I’m too lazy to read others’ work. However, in my defense, I learned a lot by trying all this stuff — far more than I would have learned simply by copying someone else’s code into my script. Experimentation is the key to discovery!





Additional Resources

Additional Resources

I completed work on my first RF receiver, and for what it is it seems to work decently. It should be self-explanatory from the photos. It’s based around an SA602. As with everything, I don’t plan on posting schematics until the project is complete because I don’t want people re-creating junky circuits! It’s stationed at the University of Florida’s club station W4DFU and its spectrograph can be viewed in real time from the QRSS VD – Web Grabber – W4DFU page. Back to work!IMG_3475IMG_3482IMG_34792dc_qrsscapture

And some music to complete the day!





Additional Resources

Now that my minimalist QRSS transmitter is mostly functional, I’m shifting gears toward building a minimalist receiver. These are some early tests, but I’m amazed I managed to hack something together that actually works! Once it’s finished I’ll post schematics. For now, here are some photos. This receiver is based upon an SA602 and although there *IS* an op-amp on the board, I actually bypassed it completely! The SA602 seems to put out enough juice to make my PC microphone jack happy, and those cheap op-amps are noisy anyway, so awesome! Go minimalism!

Here it’s pictured with its power supply:DSCN0833

Here’s a close-up. Remember, the op-amp is there but NOT used!DSCN0832

Here’s the output from 7.040 MHz. Conditions are pretty bad right now, and I’m at my apartment using my crazy indoor antenna [pic1] [pic2]recvbig