4 votes
Accepted

Linear Phase in equiripple filters

Your filter is a linear-phase filter. There are two ways you can define the phase: \begin{align*} H(e^{j\omega}) &= \big|H(e^{j\omega})\big|e^{j\phi_a(\omega)} \\ H(e^{j\omega}) &= A(\omega)e^{...
Matt L.'s user avatar
  • 90k
3 votes
Accepted

First order filters in Direct Form I (RBJ Cookbook)

Okay, I'm gonna try to toss out here my first guess of general 1st-order filters done in the style of the Audio EQ Cookbook. The cookbook assumes the same EE definition of resonant frequency and ...
robert bristow-johnson's user avatar
3 votes

First order filters in Direct Form I (RBJ Cookbook)

A solution with the DC or Nyquist bin zeroed for a high pass or low pass respectively with real coefficients is: LOW PASS $b_0 = \frac{1+a_1}{2}$ $b_1 = b_0$ $b_2 = 0$ $a_0 = 1$ $a_1 = -\frac{\cos(\...
Dan Boschen's user avatar
  • 51.3k
3 votes

Deconvolution with unknown impulse response

What methods are there for such deconvolution problems, None for the general case (without additional information). We can easily see this by looking at the frequency domain $$y(t) = h(t)*x(t) \...
Hilmar's user avatar
  • 44.7k
2 votes

Filter secondary bounces of a pulse signal

No, probably not. If your convolutional model was based on the system being excited by your input being a linear one, it is almost certain you'd see negative amplitudes on the output. Your graph doesn'...
Marcus Müller's user avatar
2 votes

Cross-correlation of two processes generated from the same signal through different LTI systems

You have to work through the calculation once and you'll remember forever. I hope you can fill in the details yourself. First, from the definition of cross-correlation (assuming real-valued filters ...
Matt L.'s user avatar
  • 90k
1 vote

Linear Phase in equiripple filters

but do not posses linear phase Incorrect: they do posses linear phase. The problem is most likely with your plotting/visualization code. In order to get a good graph, you often need to zero-pad and ...
Hilmar's user avatar
  • 44.7k
1 vote

Filtering of sampling effects

With some more researching I looked into how a polynomial can be fitted into the data and used for filtering. Asking this questions to ChatGPT resulted in using a Savitzky–Golay_filter. While the ...
Alexander Jasper's user avatar
1 vote

Filter secondary bounces of a pulse signal

With the uncertainties involved, no, deconvolution is not something you could apply here. two factors: mismatch of physics and model uncertainty larger than information to the first factor: your ...
Marcus Müller's user avatar

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