Hi Henry,
Look up the Discrete Fourier Transform in its Matrix form: You take a
vector of samples $x$ and multiply it with a matrix $W$ to get the
discrete Fourier transform of $x$, which I shall denote $X$:
$X=Wx$, with
$W \in \mathbb N ^{N\times N}$ (i.e. a square matrix, representing the
N-point DFT)
$x,X \in \mathbb N ^N$ (i.e. column vectors).
Remember how you do matrix-vector multiplication:
To get the result's element in its $n$-th result row and the $m$-th
result column, you take row $n$ from the left factor (i.e. a row of $W$,
which has $N$ rows, so $n\in\{1,\dots,N\}$), and multiply it point-wise
with $m$-th column of the right factor ($x$, which only has 1 column, so
$m\equiv 1$) and calculate the sum.
On 20.03.2016 17:45, Henry Barton wrote:
> So correlating is digitally mixing something with a predetermined
> sequence? I’ve been struggling to figure out what correlation means
> and this seems right. I guess, then, if you have a PSK waveform you
> might multiply it by something, starting at various offsets in the
> signal, to try and decode it?
>
> Sent from Windows Mail
>
> *From:* madengr <mailto:rfeng...@me.com>
> *Sent:* Sunday, March 20, 2016 12:22 PM
> *To:* discuss-gnuradio@gnu.org <mailto:Discuss-gnuradio@gnu.org>
>
> Yes, pretty much. With the DFT (and the continuous one) you are
> correlating
> the input waveform with harmonically related, complex sinusoids;
> essentially
> for each harmonic you mix it down to DC then sum (integrate). The FFT is
> different (I actually don't know how it works, other than it operates
> on 2^n
> samples), but the output is the same.
> Lou
>
>
> Henry Barton wrote
> > I’ve read up on the FFT and DSP and I must say I’m impressed that
> > multiplying two waveforms is the digital equivalent of heterodyning.
> Am I
> > right in my understanding that finding frequency components (FFT-ing) is
> > simply multiplying a series of known sine waves by your input waveform?
>
>
>
>
>
> --
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>
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