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From: | Marcus Müller |
Subject: | Re: [Discuss-gnuradio] Continuously Write FFT Samples to a File |
Date: | Thu, 12 Jan 2017 10:30:10 +0100 |
User-agent: | Mozilla/5.0 (X11; Linux x86_64; rv:45.0) Gecko/20100101 Thunderbird/45.3.0 |
But if you do a single 1024-FFT, you'd only operate on 1024 of the input samples! And: the FFT doesn't just give you power values, but complex values; mathematically, the FFT is a DFT, and the DFT is an invertible linear operator : which maps complex vectors to complex vectors of size . It is, in fact, representable as square
matrix with column (and row) vectors being samples of the
orthogonal complex sinusoids $e^{j\frac{2\pi}N nk},\,
k=0,\ldots,N-1$; that is, it can also be understood as a base
change matrix, that just represents the "input vector"
according to a different base, orthogonal base. The Fourier transforms are not magical by any means. What
they do is represent the same signal from a different
point of view. It can be interpreted as transform between
time and frequency domain (or space and impulse, or...). The DFT
is still just a boring, old, square, orthogonal, invertible matrix
that produces output of the same dimensionality as it takes input.
As you can see, the DFT/FFT itself never reduces the amount of
data. What you might be referring to is some kind PSD estimate done by
first |·|² a lot of DFTed vectors and then averaging them. The
data reduction here lies in the magnitude square operation and the
average, not in the DFT. Best regards, Marcus On 12.01.2017 05:54, Mallesham Dasari
wrote:
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