[hpsdr] new architecture - FFT front-end

[Erik Anderson]

Please let me know if my vision is off-base here, but...

In my mind the "buckets" in a DFT represent a sine wave with a different
frequency, the act of doing a DFT (not an FFT here, although the results
are the same) is to take that sine wave and determine the average intensity
of that frequency over the duration of the sample.  The sample represents a
certain block of time; the longer the time period the more buckets you get
and the more frequency information you have about the sample.  The results
of the operation do not take time into account; that axis has been lost.

When doing an iDFT, it involves taking the number in each bucket, using
that as an amplitude for a sine wave of a specific frequency, and adding
the waves together.  A single (complicated) tone is produced over the
duration of the sample; an iDFT is a tone generator.  I figure that a
significant chunk of the sample could be described by nothing but the
component frequencies, but any components that cannot be described solely
by frequency will not be present.

To take an extreme example, someone talking for 5sec is not going to show
up well after an FFT (the voice frequencies are too transient to show up in
the average) and the resulting frequency information does not carry enough
data to be able to reproduce the contents of the speech in an iFFT
operation.

On Tue, Sep 9, 2014 at 1:24 PM, David Bridgham <dab at froghouse.org> wrote:

> On 9/4/14, 10:40, Erik Anderson wrote:
> > (*) An FFT is fundamentally calculating an approximation (average
> > intensity of a frequency over the frame) so there is some information
> > loss when calculating an FFT.
>
> I've been considering this since I read it, trying to figure out where
> the loss of information is with an FFT.  Obviously it's only looking at
> a window of the much larger set of input samples but I think an Inverse
> FFT really ought to return the samples in that window accurately.  I
> suppose there's always a little loss due to the finite precision
> arithmetic from fixed sized numbers but beyond that, where is the
> information loss?
>
> One DSP course I took described DFT as a change of basis in Hilbert
> space.  Changing bases should always be a reversible function, I would
> think.
>
>
>
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