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Results tagged with dft
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user 32888
The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.
3
votes
1
answer
2k
views
Proving that the IDTFT is the inverse of the DTFT?
The DTFT is given by:
$$X(e^{j\omega}) = \sum_{n=-\infty}^{\infty}x[n]e^{-j\omega n}$$
The IDTFT is given by:
$$x[n]=\frac{1}{2\pi}\int_{0}^{2\pi}X(e^{j\omega})e^{j\omega n}d\omega$$
I have been a …
- 143
1
vote
0
answers
142
views
Equivalence of the Power Spectral Density definitions
I am trying to show the equivalence of the following Power Spectral Density definitions in Matlab:
Definition 1:
$$ P(\omega) = \sum_{k=-\infty}^{\infty} r(k)e^{-j\omega k} $$
Definition 2:
$$ P(\ …
- 143