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Results tagged with fourier-transform
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user 8336
The Fourier transform decomposes a signal (a function of time) into frequencies, giving the energy at each frequency.
31
votes
From a statistical perspective: Fourier transform vs regression with Fourier basis
They're the same. Here's how...
Doing a Regression
Say you fit the model
$$
y_t = \sum_{j=1}^n A_j \cos(2 \pi t [j/N] + \phi_j)
$$
where $t=1,\ldots,N$ and $n = \text{floor}(N/2)$. This isn't suita …
- 21.5k
1
vote
Spectral Analysis in R - the periodogram
The periodogram function $P(\cdot)$ has the property that
$$
P(j/n) = P(1 - j/n)
$$
for $j=0,\ldots,n-1$. The frequency $.5$ is a folding frequency. This all can be verified by the definition of a per …
- 21.5k
3
votes
Accepted
Why is spectral density only defined for stationary processes?
To quote Brockwell and Davis:
"[t]he summability of $|\gamma(\cdot)|$ implies that the series converges absolutely..."
When you look at the definition of the spectral density
$$
f(\lambda) = \frac{1} …
- 21.5k