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2 votes

Understanding the Conditions for Recovering a Discrete Time Signal Through Sampling

If we assume the signal has limited bandwidth, namely from a given frequency and above it vanishes in the Fourier domain then the Nyquist Shannon Sampling Theorem states a simple rule, sample the signal …
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Nyquist Rate (Sampling Frequency) for $ {f}^{2} \left( x, y \right) $

By the Convolution Theorem multiplication in Time / Spatial domain is equivalent of Convolution in the Frequency Domain. The sampling rate (In its classic interpretation) is proportional to the suppo …
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4 votes
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Downsampling and Gaussian Filtering in the Context of Scale Space Pyramids

You're correct, it has to do with the Cut Off frequency of the Gaussian Blur Filter in its Frequency Domain. In order to see it, just apply a DFT (Using MATLAB it can be achieved by fft / fft2) and …
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Derivation of Nyquist Frequency and Sampling Theorem

Approaching The Sampling Theorem as Inner Product Space Preface There are many ways to derive the Nyquist Shannon Sampling Theorem with the constraint on the sampling frequency being 2 times the Nyquist
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4 votes

Proving Nyquist Sampling Theorem for Strictly Band Limited Signals (Whittaker Shannon Interp...

Approaching The Sampling Theorem as Inner Product Space Preface There are many ways to derive the Nyquist Shannon Sampling Theorem with the constraint on the sampling frequency being 2 times the Nyquist
Royi's user avatar
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