Discrete fourier transform Definition and 55 Threads

Homework Statement Find the discrete Fourier transform X[k] = DFTn {x[n]} of the following periodic sequences x[n] = x[n - N] with period N: (a) For n = 0 . . .N - 1 we have x[n] =\delta[n]. (b) For n = 0 . . .N - 1 we have x[n] = \mu[n] -\mu[n - K] with K < N. (c) x[n] = cos( (2*pi*M*n)/N...

Hello, can anyone help me with the following problem: The discrete Fourier transform (DFT) in matrix form can be done as follows F=M*f where f are the space domain samples, F are the spatial frequency domain samples and M is the DFT matrix containing the exp(j*...) terms. To compute the...

I'm reading the text Understanding Digital Signal Processing Second Edition and in the text they give the IDFT without any proof and so I tried to do a quick proof, but I have not been able do it here is my attempted steps: X(m)=\sum^{N-1}_{n=0}x(n)e^{-i2\pi mn/N} \\ Considering x(1)...

"Sliding DFT" discrete Fourier transform... I was wondering if any of you had had experience with the sliding DFT algorithm. It is somewhat similar to the Goertzel algorithm. I am having some trouble understanding the mathematics of the algorithm, and I also cannot seem to identify a useful...

If I use the following code in Mathematica f1[t_] := Cos[w t + d1]; f2[t_] := Cos[w t + d2]; data1 = Table[f1[t], {t,1,10000}]; data2 = Table[f2[t], {t,1,10000}]; ft1 = Fourier[data1]; ft2 = Fourier[data2]; To take the Fourier transform of two data sets, how can I use the resulting data...