engineering recuitment GATE ECE 2023-24 Test Series Signals and Systems Discrete Fourier Transform (DFT) and Discrete Fourier Series (DFS) Definition of Discrete Fourier Transform (DFT)
For the sequence x[n] = {1, -1, 1, -1}, with n = 0, 1, 2, 3, the DFT is computed as \(X\left( k \right) = \mathop \sum \limits_{n = 0}^3 x\left[ n \right]{e^{ - j\frac{{2\pi }}{4}nk}}\), for k = 0, 1, 2, 3. The value of k for which X(k) is not zero is
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