--- 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
