So every element of the resulting vector will hold the intensity of a 1Hz bit
of spectrum? Also, you mentioned what would be in X, but what should vector W
contain?
Sent from Windows Mail
From: Marcus Müller
Sent: Sunday, March 20, 2016 1:57 PM
To: discuss-gnuradio@gnu.org
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
Sent: Sunday, March 20, 2016 12:22 PM
To: 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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