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In the context of wireless communications, the channel impulse response (CIR) is often estimated indirectly via the time-varying transfer function (TVTF) $H(t, f)$, defined by: $$H(t, f) = \mathcal F_\tau [ h(t, \tau)]$$ where $\mathcal F_\tau [ \cdot ]$ denotes the Fourier transform with respect to the $\tau$ (lag) variable. For example, the air interface ...

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All the operations are commutative, the order in which you employ them is irrelevant. EDIT As Robert pointed out in the the comments, this is not true. The operations are not commutative. Thus, the order of reversal operations can only be guessed.

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Although I cannot directly provide a solution to your problem I think I can point you towards the "most well established" approach. To the best of my knowledge, non-uniform sampling (both in time and space if this is of interest to you in some generic way) is related to uniform sampling via interpolation. I believe that the "simplest" and ...

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An asynchronous resampler should do the trick. Basically positioning a continuous time windowed sinc at the desired (uniform) output time instants, sampling it by a neighbourhood of input time instants, choosing sinc width (inverse of bandwidth) either as a function of the largest input inter sample spacing, or locally as a function of sample density. Unless ...

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I think the way to go here is oversampling, lowpass filtering and, optional, consecutive downsampling. This process will yield equidistant audiodata. 1. Oversampling Choose a target oversampling period $T_{os}$ and correspondig oversampling frequency $f_{os}=1/T_{os}$ that is well below $T_{\text{min}}$, the shortest time distance occuring in your data. The ...

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The second derivative of a ramp function is a delta function. So essentially, you can construct a new signal by taking the second derivative of the original signal. Approach: If the original signal $\mathbf{x}$ is given as $x(0), \ldots, x(N-1)$, then the second derivative is given as \begin{align} y[t] = x[t] - 2 x[t-1] + x[t-2], \quad 2 \le t < N \end{...

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