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Re: [Discuss-gnuradio] Goertzel vs FIR bandpass

From: Gregory Maxwell
Subject: Re: [Discuss-gnuradio] Goertzel vs FIR bandpass
Date: Tue, 28 Dec 2010 00:18:43 -0500

On Mon, Dec 27, 2010 at 10:12 PM, Marcus D. Leech <address@hidden> wrote:
> I tried an experiment this evening with my 6-channel VLF receiver, which
> uses a sound-card (sampled at 96KHz or 192KHz) to sample
>  a VLF loop antenna and amplifier, and then do power detection (and other
> things) over six discrete channels, arbitrarily spaced.
> The version that I've been using up until now uses a FIR bandpass filter for
> each channel, followed by an utterly-uninteresting
>  power-detector chain.
> I didn't know anything about the Goertzel transform until a couple of days
> ago, and decided to substitute an equivalent Goertzel
>  transform for each channel, to see if I could save any CPU by doing so. The
> result was that I can save about 15% by going  to
>  the Goertzel transform, instead of an FIR filter with roughly-equivalent
> bandwidth.
> I'm going to let it run for a couple of days to compare sensitivity.
> For equally-spaced channels (which isn't the case here), an FFT might also
> be useful and slightly cheaper than a discrete FIR filter
>  for each channel.

For non-equally space subband filters you can use lifting to generate
transforms with performance compariable to the FFT if you're willing
to accept some limitations on the shape of the responses.

I've mostly been working on this in the area of video coding, — where
the filterbanks are small enough that I can find the coefficients via
straight numerical optimization, so I don't know a whole lot about
constructing them in the general case.  But it's certainly an area
that someone interested in building faster filterbanks should look

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