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Strided unpadding energy relationship?

From the comments: Unpadding works fine if you maintain the length of the sequence. If you truncate, the signals are not bandlimited anymore hence you get aliasing: The spectra of x1 and x0 are ...
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Calculate the energy of x[n]

It's always helpful to write down the first few elements and check if you can see the pattern. You can quickly see that $\sin(\frac{\pi}{2}n)$ is simply ...
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Is there a relationship between the energies of the inputs to a convolution and the energy of its output?

We can get exact bounds from cross-domain energy relations. Given a signal $x(t)$ and a kernel $h(t)$ to convolve with, the frequency-domain result is $X(f)H(f)$, and we know from Parseval-Plancherel'...
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Is there a relationship between the energies of the inputs to a convolution and the energy of its output?

a = ones(64,1); b = [1 -1]; c = conv(a,b); In this case, a and b have some non-zero energy while their convolution is exactly zero besides head and tail conditions....
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Is there a relationship between the energies of the inputs to a convolution and the energy of its output?

Probably not an equality directly, but upper bounds. Let us look at the continuous case first, which is easier to derive. There is a Young's convolution inequality: with proper integrability ...
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