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1

What's labeled $(1)$ in your question is a special case, the flat channel. It can be represented as a single coefficient. In general, channels aren't flat, and we then need to apply $(2)$ instead. That's no different from acoustics. So, your claim that $(1)$ generally applies to SISO channels is plain wrong. However, when naming something "SISO", one ...


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Why normalized filters Last question first, "Why $1/\sqrt2$": Because it makes the (Euclidean) norm of the filter $1$, so that the whole wavelet filter bank operation (if done right, that is, the decimated version) is orthogonal/isometric. It is a design choice, there is nothing wrong in staying with the integer values and correct the combined factor during ...


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staying faithful to the subject "removing window effect in freq domain via convolution" (despite the OP perhaps wanted to achieve something else or something similar), I feel to add my comment having personal experience with this specific topic. Often I have the necessity to remove a Hann window in frequency domain, working in a STFT framework which uses ...


0

Dechirping is a bit different than matched filtering, but perhaps that not important here. The code you have looks like it should work if the variables are as you describe. Here is a hypothetical example that range compresses an LFM pulse. The reflected signal from an actual target in the scene is a just a delayed version of the waveform, so it will just be ...


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It looks like your choice is based on whether (approx) 5*NLogN (IFFTs+FFTs) is greater or lesser than N^2 (linear convolution). You could use coarser interpolation methods (cubic, spline, etc.) to upsample the spectra but the error would likely be audible as a clear loss in quality.


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The correlation is used to find the time shift between signsls while convolution represents system response to predefined input. Since the system response depends on previous input, rether then future input, the sign of the time distance is negative.


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I figured out my problem. The kernel needs to be shifted so the 'center' is on the corner of the image (which acts as the origin in an FFT). The built-in ifftshift function works just fine for this. (Note, there are some subtleties here depending on whether you have even or odd shapes or differences in shape that can result in one row or column shifts. I ...


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The idea here is to build the problem in its Matrix Form. We have the filter $ h $ which is represented by the matrix $ H $ to represent Linear Convolution operation: $$ H = \begin{bmatrix} {h}_{1} & 0 & 0 & \ldots & & 0 \\ {h}_{2} & {h}_{1} & 0 & \ldots & & 0 \\ \vdots & & \ddots & & & \...


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Check LMS in Wikipedia, it is an iterative way, works for any size.


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What format is your input data in? It sounds like you have a phase history signal as it's often called. Assuming that the transmitted waveform was a linear FM chirp, has it already been deramped? Some receivers perform deramp-on-receive processing, which removes the chirped nature of the waveform. In that case, range compression is as simple as performing a ...


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