Alberto, >I hope to have dissipated some of your doubts on how a SDR works. Yes it is perfectly clear now. TKS again.
73 Patrick ----- Original Message ----- From: i2phd To: [email protected] Sent: Sunday, August 26, 2007 10:54 PM Subject: [soft_radio] Re: Mix the time domain Q & I signal with a NCO to make a near to zero signal --- In [email protected], "Patrick Lindecker" <[EMAIL PROTECTED]> wrote: > > TKS Leon and Alberto for the help. > > So the working must be something close to: > * analytic mixing of I (with cos(wt) and sin(wt)) > * analytic mixing of Q (with cos(wt) and sin(wt)), > At this level there are 4 components. > * sum et difference of components (I don't go into details) will give two new components in quadrature I' and Q', with > two major frequencies (the base band (around w=0) and the image band (around -2w). > > At this level, either you do a FFT or you do a decimation. In the second case, you must apply two low pass filters (one for I' and for Q') before the decimation and the FFT. Patrick, what is done in Winrad is to combine the signals I and Q into a single complex value, which is then multiplied (using the rules of the complex multiplication) by the complex NCO signal. The result is a shifting in frequency of the signal, without generation of any image components, as otherwise would have been the case, should complex quadrature signals had not been used. Now the wanted signal is centered around zero frequency, and there is no need to keep a high sampling rate, as the voice information (in case of SSB or AM) requires no more than, let's say, 8 or 11 kHz of sampling rate. So a decimation is performed, but of course we must keep Nyquist happy, so a complex low pass FIR filter is applied to the complex signal before the resampling. At this point you have many choices. If you want to do bandpass filtering, you can operate in the time domain with another FIR filter working at the new sampling frequency, or better yet, you can use a fast convolution filter in the frequency domain with an FFT, an overlap-and-save, then an IFFT. If you operated in the time domain, it comes natural at this point to recover the USB or the LSB using the Hilbert transformer to delay by 90 degrees one of the components before adding it with the other. Or you can continue to work in the frequency domain (as I do in Winrad), taking the upper or the lower half of the FFT around zero, mirroring it in a complex conjugate way, then do an IFFT with produces a real signal, which is the demodulated audio. I hope to have dissipated some of your doubts on how a SDR works. 73 Alberto I2PHD
