New answers tagged dft
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Showing analytically that sampling exactly 1 period of a sinusoid yields a spectrum with no lobes in the DFT
To solve the roots, set:
$$e^{-j(\Omega-\omega_o)M/2}\frac{\sin \bigg(\frac{M+1}{2} (\Omega - \omega_o))\bigg)}{\sin((\Omega-\omega_0)/2)} = -e^{-j(\Omega+\omega_o)M/2}\frac{\sin \bigg(\frac{M+1}{2} (\...
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Frequency resolution in STFT
The $N$ defining the full signal length is not the same as the $N$ in the STFT equation, which defines the DFT length.
The STFT is a sliding DFT so the only value that matters is the latter.
Without ...
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What is the Wrap-Around Phenomenon in FFT?
Just like the reciprocal case of padding a time domain signal with zeros, but padding in frequency domain, you effectively interpolate.
You can think of it as if you’ve at a higher rate, and had no ...
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32-point DFT computation of a sampled sinusoidal signal
Hint: The DFT of a complex sine wave that has an integer number of periods in the DFT window is simply a Kronecker Delta at that frequency. We can write the time domain signal as
$$x[n] = e^{j2\pi\...
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