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6

The problem lies in the formulation of the desired response, and especially in the "don't care" region, which is extremely wide for the chosen filter length. Even though I can't give any exact relation between transition band width and filter length, I know that in the case of a least squares design, the matrix of the system of linear equations ...


4

Modeling real analog components with their non-linear behavior can be a challenge to do digitally. I suggest starting with wave digital filters. Quoting from the linked source: A Wave Digital Filter (WDF)is a particular kind of digital filter based on physical modeling principles. Unlike most digital filter types, every delay element in a WDF can be ...


4

Like @MattL. and @aconcernedcitizen say, the issue is numerical. Python's scipy.signal.firls uses internally the solver scipy.linalg.solve. For your input, the solver throws a "matrix singular" error, but firls suppresses the error and falls back to another solver scipy.linalg.lstsq which doesn't throw an error but also doesn't get the problem ...


2

Because of the comment, I obviously must have seen this question nearly 5 years ago, but I don't remember it really. But one advantage that windowed-sinc has over P-McC or LS for a brick-wall interpolating filter is that the windowed-sinc can be guaranteed to pass through zero at all integer values except 0. That means the interpolated signal always goes ...


2

This approach is covered extensively in the literature, so the short answer is to get a book on DSP*, read up through the chapter on implementing a DSP filter from an analog prototype, then do what it says. There's several different methods, each of which is good in its way. Use the bilinear transform, possibly with frequency warping. This is covered in ...


1

I try to describe the linear filter aspects of the 4-pole Moog. The 4-pole Moog filter is a cascade of four 1-pole LPF filters that have resonant frequency adjustable and a feedback path that has the feedback gain adjustable (on the patchboard Moog synths, this feedback gain knob was labeled "Regeneration"). The resonant frequency filters is ...


1

To align the samples (and realigning with different filter implementations) consider implementing actual timing and carrier recovery loops, or using those discriminators and approaches to manually correcting the offsets as would be done in those acquisition and tracking loops. This will put you on the road toward an actual implementation when the transmitter ...


1

This is a well-known result with no specific name. In signal processing, we usually call the kernel impulse response (as correctly mentioned in a comment by Marcus Müller). The response to a unit step signal is called step response. So what you've found is how to compute the impulse response from the step response. If $h(t)$ denotes the impulse response of a ...


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