20 votes
Accepted

Why is the time domain low-pass filter the "sinc" shape?

It is a good way to understand the lowpass behavior of sinc function (as well as the convolution) through visualization. I've made some modification on this animated convolution project and here are ...
ZR Han's user avatar
  • 3,228
14 votes

What is the name of a low-pass filter that tracks rate of change?

I was able to remember how the filter works. The idea is very simple, a second low-pass filter tracks the steady-state error in the result of the first one, and it is then added to the output: Based ...
jpa's user avatar
  • 703
7 votes

What is the explanation that filter EQ changes "Ah" to "O"?

Expanding a bit on Tim Wescott's answer: Vowels are made by a combination of an excitation and a resonant filter. The excitation comes from the glottis in your throat. The speed of that vibration ...
Hilmar's user avatar
  • 44.7k
6 votes

What is the name of a low-pass filter that tracks rate of change?

I do not think that there's a specific name for this type of lowpass filter. There are indeed similarities between the cascade of two lowpass filters as suggested in the OP's answer, and a combination ...
Matt L.'s user avatar
  • 90k
6 votes
Accepted

FIR filter design with nonlinear phase from measured amplitude and phase responses

The algorithm gives you the best least squares approximation possible for a causal filter with the specified filter order and the given desired frequency response. The problem with your specification ...
Matt L.'s user avatar
  • 90k
6 votes

Why is the time domain low-pass filter the "sinc" shape?

One way to think about it is the requirement of what a filter does, and what is the relation between the time domain and frequency domain plots of the signal or the filter. This also requires to know ...
Justme's user avatar
  • 2,303
5 votes
Accepted

Gaussian filter: Plotting DTFT and DFT (by hand) from the continuous-time impulsive response

Before anything, let me just rewrite your TF from linear frequency ($f$, in Hertz) to angular frequency ($\Omega = 2\pi f$, in rad/sec). The notation $\Omega$ is usually adopted in the field of DSP to ...
Rubem Pacelli's user avatar
5 votes

How to estimate the local trend in a signal?

Start simple: just use a 1-D median filter of an appropriate length. If I do that with a length of 100 samples, I get the following for your first signal. The top plot shows the original signal (blue)...
Peter K.'s user avatar
  • 25.7k
5 votes
Accepted

removing spikes from spectrum

These spikes look like harmonics of some sort of line noise at $250 \texttt{MHz}$. To get rid of these, what you need is a comb notch filter. There are a few ways to build one. If the fundamental (...
Jdip's user avatar
  • 6,055
5 votes
Accepted

Why does causality imply that the system function is analytic?

New answer: I provide a new answer because I believe that this is a clearer and more direct way of explaining the relation between causality of the impulse response and analyticity of the ...
Matt L.'s user avatar
  • 90k
5 votes

Why is the time domain low-pass filter the "sinc" shape?

Perhaps one way to see the sinc is as a special moving average filter. As you noted, the lower the cutoff frequency (filtering out higher frequencies), the wider the sinc mainlobe. This corresponds to ...
Gillespie's user avatar
  • 1,767
4 votes
Accepted

What is the explanation that filter EQ changes "Ah" to "O"?

What is the explanation of this phenomenon? Your vocal cords have a very raspy sort of vibration -- they generate spectral components at the fundamental, and at many many harmonics going up from ...
TimWescott's user avatar
  • 12.7k
4 votes

Why does convolution give the output of a passing a signal through a filter?

You can describe the system with an operator acting over an input $x(t)$ transforming it into $z(t)$. If $L$ is the operator, $z(t)=L[x(t)]$. Remember that the system and the operator are linear and ...
Andy R's user avatar
  • 81
4 votes
Accepted

Unexpected frequency components after applying bandpass filter in python

When you "turn on" filtering at time zero, the filtered output starts with a transient plt.figure('signal filtered') plt.plot(t, samples_filt) To make ...
V.V.T's user avatar
  • 1,729
4 votes
Accepted

Intuitive explanation of magnitude-phase-relationship for minimum phase filters

Let's start with a causal impulse response $h[n]$. We know that the $\mathcal{Z}$-transform of a causal and stable sequence converges outside (and on) the unit circle, i.e., all singularities (poles ...
Matt L.'s user avatar
  • 90k
4 votes

Applying Lowpass filter on a signal in time domain gives ringing artifacts - how to get rid of them

Why do I see the ringing artifacts after the decay of the impulse response and why are they pronounced at the end of the signal? DFT based frequency domain multiplication corresponds to circular (not ...
Hilmar's user avatar
  • 44.7k
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

How to estimate the local trend in a signal?

In A Self Supervised Learning for a Signal Denoising I wrote: You may have a look at the method called JOT: A Variational Signal Decomposition Into Jump, Oscillation and Trend (You may access it in A ...
Royi's user avatar
  • 19.6k
3 votes
Accepted

What are the tradeoffs between shifting a lowpass FIR filter vs using a bandpass FIR filter?

If you need several bandpass filters with the same bandwidth, it's advantageous to derive them all from the same prototype lowpass filter (e.g., modulated filter banks). You only need to store one set ...
Matt L.'s user avatar
  • 90k
3 votes

IIR/FIR equations for custom frequency response

Here is one way to do this: You can implement a more or less constant slope by cascading high-shelf filters as described in the Audio EQ Cookbook. Create a list of frequencies. Start with a frequency ...
Hilmar's user avatar
  • 44.7k
3 votes
Accepted

What is the difference between STFT and Gabor filter?

The Gabor transform is just a special case of the STFT, the main difference is, like you said, the Gaussian window. One characteristics of window functions is that they are $0$ outside a specific ...
Jdip's user avatar
  • 6,055
3 votes

Total delay of cascade FIR filters

No, this is not correct. The actual delay that you describe depends on the signal component's frequency and on the actual filters implemented using these delays! The technical term you need to ...
Marcus Müller's user avatar
3 votes

Time-varying shot noise generation

You have two simple cases: Input is 0: then $\sigma^2_{I_{\text{shot}}} =0$, which means it is a constant value. So, in Python, that just means you set the result to ...
Marcus Müller's user avatar
3 votes
Accepted

How does function c2d in MATLAB manage fractional delay?

The zero-order hold (ZOH) discretization is the same as the step-invariant method, which means that the step response of the discrete-time system equals the continuous-time step response at the sample ...
Matt L.'s user avatar
  • 90k
3 votes
Accepted

How to derive matched filters for PPM modulation?

Your approach looks correct to me. but your results seem wrong: for example, the output of the second matched filter (g1) starts at 3000; also, the output of both filters goes to zero when the input ...
MBaz's user avatar
  • 15.3k
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
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
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
2 votes

What are the advantages and disadvantages of Kalman filter compared with FIR, IIR and low pass filter to filter data with noise?

The accepted reply is correct (and very funny). But there is one other point worth mentioning that differentiates the Kalman Filter from an IIR or FIR filter: At its core sits a probabilistic model ...
means-to-meaning's user avatar
2 votes
Accepted

A self-supervised learning technique to denoise my specific signal

You may have a look at the method called JOT: A Variational Signal Decomposition Into Jump, Oscillation and Trend (You may access it in A Two Stage Signal Decomposition into Jump, Oscillation and ...
Royi's user avatar
  • 19.6k

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