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The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

8 votes
5 answers
34k views

Difference between DC component and zero frequency component of signal

We know that Fourier Transform of a signal exists if it is absolutely integrable and it exists for periodic signals if impulse functions are allowed. If we consider the fourier transform of $\text{r …
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1 vote

Why are the basis functions for DFT so?

If you look at the idea of Continuous Time Fourier Series (CTFT), it says any periodic signal can be constructed by summation of infinite number of complex exponentials. But in descrete case , only 'N …
spectre's user avatar
  • 585
3 votes
2 answers
6k views

Relation between the DTFT and the spectrum of a sampled signal

In the $\rm DTFT$ (Discrete Time Fourier Transform) the spectrum is periodic with a period of $2\pi$ . A continuous signal when sampled has a spectrum which is a repeated version of its original spect …
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