Re: [Discuss-gnuradio] Bandswitch and rf gain added to HF Explorer

[Lamar Owen]

On Wednesday 29 June 2005 19:44, John Ackermann N8UR wrote:
> I meant to mention earlier in reference to the filter and the tradeoff
> between skirts and CPU usage -- have you looked at the filtering scheme
> used in the Flex-Radio SDR-1000 software?  I don't recall the exact
> details right now, but it works something along the lines of doing an
> FFT to convert the baseband signal back into the frequency domain, and
> implementing the filter as a mask against the FFT bins, and then an
> inverse FFT back to the time domain.  

There are no brick wall filters.  Basically all digital filters have ripple in 
the stopband due to the basis in the sinc (sin(x)/x) function.  FFT's also 
have aliased ripple out past their 'stop' band; this is controlled with the 
windowing function used.  The less the stopband ripple, the wider (in terms 
of bins) the passband is (for any given bin).  The reason this is so is due 
to the way discrete Fourier transforms (including the FFT) assume that the 
data being transformed is periodic; the problem occurs when the signal period 
doesn't end exactly on the DFT's boundaries.  The response of the default 
rectangular window for all frequencies except multiples of the FFT frequency 
(sampling rate divided by number of points) is the sinc function, and the 
ripple out of band (out of each bin's band) is 12dB down for the first 
sidelobe, and the sidelobes roll off at the leisurely rate of 6dB per octave.  
This is the 'tail' you see on narrow spectral features in FFT's.

So, since there is spectral leakage from bin to bin, if you zero out the bins 
you don't want and do an inverse FFT, you will get spectral leakage from the 
bins you want into the frequencies whose bins you zeroed, and the leakage is 
defined by the window (which just happens to have the same shape as a filter 
kernel, but I digress).  Adding points on an FFT is basically the same thing 
as adding taps on a filter, both computationally (in terms of CPU load) and 
spectrally.
-- 
Lamar Owen
Director of Information Technology
Pisgah Astronomical Research Institute
1 PARI Drive
Rosman, NC  28772
(828)862-5554
www.pari.edu