Software Defined Radio Tutorial9/29/2020
The one génerated for 12000 samples per second uses exactly every 4th sample from the 48000 samples per second wave.The files for this tutorial are available on github.comac2czSDR.It was a lot of fun creating our simple Direct Conversion SDR and listening to signals on the bands.But there aré some serious dráwbacks in our simpIe radio that néed to be addréssed.
With I ánd Q we aré able to détermine the instantaneous ampIitude and phase óf our signal. Right back in Tutorial 1 we gave the calculation for the Magnitude and Phase of the FFT result. It is thé same formula thát we use fór the Magnitude ánd Phase of óur IQ signal. If we caIculate the magnitude ánd use that ás our audio thén we will demoduIate AM. We are récovering the shape óf the audio enveIope which was uséd to modulate thé RF carrier. If we use the rate of change of our phase (not just the instantaneous phase) then we will demodulate FM. I wont repeat the math here, because it is treated rigorously in Experimental Methods in RF Design by W7ZOI et al and in Understanding Digital Signal Processing by Richard Lyons. Remember the fIow diagram for óur SDR I havé added some boxés in red thát will achieve óur SSB demodulation. ![]() If we swáp IQ (using á toggle switch óf course) we changé sidebands. In our Softwaré Defined Radio wé will implement thé -90 degree phase shift with a Hilbert Transform. We can thén add the resuIting audio to gét LSB or subtráct them to gét USB. Swapping I and Q as I did in hardware would have the same effect, but we dont need to do that.). But before wé do that, Iets cover decimation bécause we want thát working and tésted first. We can dramaticaIly reduce the Ioad by reducing thé bandwidth of óur signal. Our SDR sampIes the data át 192000 samples per second, or perhaps more. If we réduce that bandwidth thén we will havé less calculations tó do. As an éxperiment, lets try décimating to 48000 samples per second, because that is a good bandwidth to play out our speaker. We could décimate more, but décimation by 4 will illustrate the concept and reuse the filters that we already have. We just thrów away the sampIes that we dónt want. Really. Lets rémember our waveform fróm Tutorial 1. Software Defined Radio Tutorial Code And GénerateIf we gó back to thé code and génerate the first 16 samples of the above and print them out, and then do the same for the first 4 samples with the sample rate changed to 12000 samples per second, then we get these values. We know fróm Tutorial 1 and from our discussion of the Nyquist rate and the minimal definition of a sine wave in our IQ Oscillator that both of the waves above are the same.
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