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HINT: Magnitude $M(\omega)\ge 0$ and phase $\phi(\omega)$ are defined by $$X(\omega)=M(\omega)e^{j\phi(\omega)}\tag{1}$$ Note that $(1)$ is generally complex-valued. In your example, the Fourier transform $X(\omega)$ is clearly real-valued. This restricts the possible values of the phase $\phi(\omega)$. What are those two values of $\phi(\omega)$ for ...


Zero-padding does not affect DFT magnitude of the original N-DFT Samples. Overall energy does increase in the longer DFT and that is because we have introduced non-zero samples in between N-point DFT. Zero-padding does not add noise to the DFT. The side-lobes appearing are as a consequence of polynomial interpolation which happens when we take DFT of a zero-...


Check this video on Frequency resolution using Zero Padding.

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