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# Questions tagged [fourier-transform]

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

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### why is the DFS of a delta function equal to 1

I have a x[n] = $\delta$[n]. By formula is should be $$X[k]= \sum_{n=0}^{N-1} \delta[n]W_N^{kn} X[k]= \sum_{n=0}^{N-1} e^{-j2*pi*kn/N}$$ The formulae isn't showing for some reason. I took a ...
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### How do I take the real part of this bandpass filter system's output?

I'm stuck on a final step in this problem. Essentially, there are the two systems above, which we'll call System 1 (Fig. 4.26, with ideal lowpass $H(jw)$) and System 2 (with $H_1(jw)$). The question ...
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### Derivation of Nyquist Frequency and Sampling Theorem [closed]

I have been looking through different sites and questions over the internet about Sampling theory, but couldn’t find the clear definition of how nyquist frequency condition is derived? It would be ...
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### Is it mathematically possible to compute Fourier transform without comparing the signal?

If I'm correct, Fourier transform lets me know the magnitude and phase of any given frequency in a signal. I have a sampled signal and I want to compute its Fourier transform (any frequency) without ...
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### Cepstrum analysis - Cut off frequencies displayed

My inquiry is regarding the so called cepstrum analysis. By conducting some experiments, i have real time data at my disposal. The acquisition rate is 1600Hz. I wanted to try cepstrum analysis just ...
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### Calculating phase only component of a signal in MATLAB

I am working in the field of digital signal processing. Recently I read a paper that tells about phase only component of a Signal. It is given that the phase only component is calculated as \$r_{phase}=...