Last call to make your voice heard! Our 2022 Developer Survey closes in less than a week. Take survey.
19 votes
Accepted

Transfer function of second order notch filter

For digital notch filters, I like to use the following form for a notch filter at DC ( $ \omega $=0): $$ H(z) = \frac{1+a}{2}\frac{(z-1)}{(z-a)} $$ where $a$ is a real positive number < 1. The ...
user avatar
  • 36.2k
16 votes
Accepted

Single-pole IIR low-pass filter - which is the correct formula for the decay coefficient?

The given single-pole IIR filter is also called exponentially weighted moving average (EWMA) filter, and it is defined by the following difference equation: $$y[n]=\alpha x[n]+(1-\alpha)y[n-1],\qquad ...
user avatar
  • 79.3k
13 votes
Accepted

Why would one use a Hann or Bartlett window?

In reviewing Fred Harris Figures of Merit for various windows (Table 1 in this link) the Hamming is compared to the Hanning (Hann) at various values of $\alpha$ and from that it is clear that the Hann ...
user avatar
  • 36.2k
12 votes

Where do RBJ's analog shelving filters come from?

If you remove (for the time being) that leading factor $A$ as a constant gain factor: $$H(s)=\frac{s^2+\left(\frac{\sqrt{A}}{Q}\right)s + A}{As^2 + \left(\frac{\sqrt{A}}{Q}\right)s + 1}$$ what you get ...
user avatar
11 votes

Can you turn a square wave into a sine wave using a low pass filter?

To be able to analyze what a low pass filter does first you would need to understand what a Fourier transform is, hence some theory first. The Fourier transform essentially represents the time-domain ...
user avatar
10 votes
Accepted

How to produce a high-pass filter from a low-pass one?

The result will indeed be a high pass filter. From your difference equation, the transfer function of the low pass filter is $$H_l(z)=\frac{\beta}{1-(1-\beta)z^{-1}}\tag{1}$$ with $\beta=1/\alpha$. ...
user avatar
  • 79.3k
10 votes
Accepted

Apply Low pass Butterworth filter in Python

You should not be using the analog filter - use a digital filter instead. You want the filter to be defined in Z-domain, not S-domain. Also, you should define the ...
user avatar
  • 10.4k
9 votes
Accepted

Is a high-passed signal the same as a signal minus a low-passed signal?

In general you can't simply subtract a low-pass filtered version of a signal from the original one to obtain a high-pass filtered signal. The reason is as follows. What you're actually doing is ...
user avatar
  • 79.3k
9 votes

Fast Integer 8 Hz 2nd Order LP for Microcontroller

This answer provides a quick introduction to decimation concepts and CIC filters which I would consider as one solution given the description. Bottom Line First Given your use of a microcontroller, (...
user avatar
  • 36.2k
9 votes
Accepted

Shannon interpolation formula for downsampled data with an "almost ideal" low pass filter

I don't get your downsample step when you downsampled by factor $M$. Let me go from scratch with the spectrum visualization below, with time domain, continuous frequency domain and discrete frequency ...
user avatar
  • 5,720
9 votes
Accepted

What is the name of this digital low pass filter?

I'm new, so I can't add this comment to Matt L.'s answer. It is not an exponential filter, the equation is actually: $$ y[n] \ = \ \alpha \, x[n] \ + \ ( 1 - \alpha ) \, x[n-1] $$ So it is a very ...
user avatar
  • 6,875
8 votes
Accepted

Smoothed Square Wave

Yes. This looks like it's a typical first order low pass. The time constant can be determined by looking at the time it takes for the falling edge to drop to 37% of the max amplitude ($e^{-1}$). The ...
user avatar
  • 31k
8 votes
Accepted

Kalman filter after lowpass filter: bad idea?

The Kalman filter is the optimal filter under various assumptions. You need to check whether those assumptions hold in your case: a) the model perfectly matches the real system, b) the entering noise ...
user avatar
  • 21.8k
8 votes
Accepted

Cutoff frequency of a first order recursive filter

That formula for the cut-off frequency is a very inaccurate approximation. In this answer I derived the exact relation between the coefficient of a first order recursive averaging filter and its 3-dB ...
user avatar
  • 79.3k
8 votes

What is the intuition of "averaging is a low pass filter"?

Consider a sequence of numbers x = [1, 100, 1, 100, 1, 100] If we send this sequence through an averaging transformation ...
user avatar
  • 231
7 votes
Accepted

once again,confusion between phase and group delay

If you are looking for a frequency-independent delay applied to any given input signal by the filter (apart from amplifying and attenuating certain frequency components), then you won't be able to ...
user avatar
  • 79.3k
7 votes
Accepted

FIR vs IIR filter

Typically the advantages of an FIR filter are that it is easy to obtain a linear phase response, and numerical stability is not normally a problem. An IIR filter typically requires fewer taps (as you ...
user avatar
  • 3,282
7 votes
Accepted

How is the lowpass to bandpass transformation derived?

In the $s$-domain, the LPF-to-BPF transformation doubles the order of the filter. that is because the LPF has one transition from passband to stopband, but the BPF has two such transitions. Remember ...
user avatar
7 votes
Accepted

Complex low pass filters

A low pass filter has a frequency response that satisfies $$|H(\omega)|\approx 0,\quad |\omega|>\omega_c\tag{1}$$ where $\omega_c$ is the cut-off frequency. A complex low pass filter must also ...
user avatar
  • 79.3k
7 votes
Accepted

How to Get Rid of Ripples from a Gradient Image of a Smoothed Image?

I think it happens due to 2 things: Quantization You are working using UINT8 Image, try convert it into floating Point Image. You may do this by ...
user avatar
  • 39.6k
7 votes

Why is the median filter called 'edge-preserving'?

Non-linearity A linear filter is mathematically described by the convolution sum (for discrete signals) and the convolution integral for continuous signals. The median cannot be found using a linear ...
user avatar
  • 235
7 votes
Accepted

How to Classify a Kernel as Low Pass Filter (LPF) or High Pass Filter (HPF)? How to Transform an LPF Kernel into HPF Kernel?

General We assume 2 modes of filters: LPF or HPF. Classifying Filter Type Usually, if it is a well planned LPF and well Planned HPF a simple test will do. Calculate the sum of all coefficients. The ...
user avatar
  • 39.6k
7 votes
Accepted

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

Kalman filters really aren't that special, and you seem to be missing the point of a Kalman filter. A Kalman filter is really just a generally time-varying, generally IIR, generally multi-input ...
user avatar
  • 8,151
6 votes

Difference Between Equiripple & Least Squares Design for FIR Digital Filters

While I completely agree with Jason R's answer, I would like to add a few things that I consider important. First of all, it is a misunderstanding to believe that for least squares designs the ...
user avatar
  • 79.3k
6 votes

Digital Anti Aliasing Filter For Waveform Band Limiting

Let us say your sample rate is 48kHz. You are generating a sawtooth wave at a fundamental frequency of 10kHz, using your code. First harmonic is at 10kHz. Second harmonic at 20kHz. Third harmonic at ...
user avatar
6 votes
Accepted

Digital Anti Aliasing Filter For Waveform Band Limiting

I am generating my waves in a "Raw" mathematical way, meaning that i am creating a ramp for a saw wave and my square wave consists of pure 1's and 0's. The issue is that this technique is inherently ...
user avatar
  • 14.9k
6 votes

How to produce a high-pass filter from a low-pass one?

For an LTI system another method to generate a highpass filter impulse response $h_{hp}[n]$, from an existing lowpass filter impulse reponse $h_{lp}[n]$ is the following: $$h_{high}[n]=(-1)^n h_{low}[...
user avatar
  • 26.6k
6 votes
Accepted

How to test the FIR filter in C++?

The first basic test could be to use a unit impulse as an input signal and see if the output signal equals the impulse response (i.e. the filter coefficients). Another simple test signal is a unit ...
user avatar
  • 79.3k
6 votes
Accepted

Why Butterworth filter always starts my signal from from zero mark (amplitude)?

Filters do have a delay (a lag) since they do not act immediately on your signal. Also all samples before the time 0 are zeros, thus in general you will start from the "zero mark", as you said (just ...
user avatar
  • 10.4k
6 votes

Can you turn a square wave into a sine wave using a low pass filter?

In principle you can, in practice you almost can. The square wave consits of sinusoids with frequencies that are at multiples of the fundamental one (the inverse of the length of one high and one low)....
user avatar
  • 945

Only top scored, non community-wiki answers of a minimum length are eligible