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Re: [Discuss-gnuradio] Bandswitch and rf gain added to HF Explorer
From: |
Lamar Owen |
Subject: |
Re: [Discuss-gnuradio] Bandswitch and rf gain added to HF Explorer |
Date: |
Thu, 30 Jun 2005 11:29:07 -0400 |
User-agent: |
KMail/1.8.1 |
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