Signal Processing

Questions tagged [butterworth]

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Butterworth Filter Transfer Function

Butterworth Filter frequency response is given as: $$H_a(j\Omega)=\frac{1}{\sqrt{{1+\left(\frac{\Omega}{\Omega_c}\right)^{2N}}}}\quad \text{where $N$ is the order of the filter}$$ and for the transfer ...
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1answer
44 views

Paper replication: Validating the proper way to pass .wav audio breathing data through a bandpass filter

I am working on trying to apply a low and high pass filter to an audio file that contains a set of exhalations over a microphone. The inhalations have been cut out of the file, and the exhalations are ...
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2answers
62 views

What is the $Q$ of successive Second-Order Sections of an $N$th-order Butterworth low-pass filter?

What if you had an $N$th-order Butterworth lowpass filter filter with -3 dB frequency of $\Omega_0$? $$ \Big| H(j\Omega) \Big|^2 = \frac{1}{1 + \left(\frac{\Omega}{\Omega_0}\right)^{2N}} $$ The number ...
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1answer
32 views

narrow band filtering of a signal that is sampled at high frequency

I have a signal that is sampled at 2KHz. The frequency band of interest is from 1/60 Hz to 1 Hz, and I want the final signal to be downsampled to 10 Hz. What is the best way to do this? I read that ...
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2answers
53 views

Butterworth filter higher order

I am new (very beginner) to signal processing and I am trying to understand how the Butterworth filter operates. According to my current understanding of filters, there seems to be a tradeoff between ...
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2answers
127 views

Transfer functions for Scipy and Matlab's Butterworth filter don't seem to match theory

The squared transfer function for a Butterworth filter of order $n$ should be $$ |H(f)|^2 = \frac{1}{1+\left(\frac{f}{f_c}\right)^{2n}} $$ where $f_c$ is the cut-off frequency. (Here's one of many ...
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50 views

Filter 3D volumetric image with a Butterworth filter in Python

I have been looking for a way to filter a 3D volumetric image in python with a Butterworth filter, but I haven't found any good solution. I have tried this: ...
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1answer
138 views

why does butterworth IIR filter for a square pulse show ripple on edges in time domain but not the same for sine wave

I am using butterworth filter for both square pulse and sine wave. In case of square pulse, butterworth produces some sharp ripple of edges of square pulse in time domain for varying butterworth order ...
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1answer
58 views

Difference between MATLAB zp2sos and python zpk2sos functions

I am trying to port some code from MATLAB to python. The goal is to use Butterworth filter (4th order, bandpass) API and convert it to second-order sections. I get the same output between MATLAB and ...
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1answer
98 views

LPF in the stage of IQ demodulator is it a analgor filter or digital filter?

I recently designed the LPF of the IQ demodulator using the Butterworth LPF refering to https://dspillustrations.com/pages/posts/misc/baseband-up-and-downconversion-and-iq-modulation.html. But I have ...
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158 views

Pre-Processing Wi-Fi Channel State Information (CSI) Data

I was successfully able to collect some CSI data using the existing tool(s) on GitHub (https://github.com/StevenMHernandez/ESP32-CSI-Tool). The CSI data is a pair of imaginary and real number which ...
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1answer
112 views

Creating a 4th order Butterworth filter R

I have sampled my data at 2000 Hz and want to generate a fourth order low-pass zero-lag filter with a cut-off frequency of 150 Hz. I have put the code below that I have created but I have the ...
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1answer
31 views

I am looking for an analytic description of a continuous-time Butteworth High-pass filter in the time domain (=impulse response)

having derived the Butterworth Lowpass Time domain response, I am now struggling to find a similar function for a Butterworth Highpass filter. I understand you need to replace s by 1/s. But this leads ...
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1answer
87 views

Butterworth filter's gain formula does not agree with R's `signal` package

I'm trying to calculate the Butterworth filter gain. If I use the formula mentioned on Wikipedia: $$ G^2(\omega) = \frac{G_0^2} {1+\left(\frac{j\omega}{j\omega_c}\right)^{2n}} $$ I don't get a ...
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1answer
55 views

Why use both a high pass and a low pass filter in a Butterworth implementation for noise reduction?

I am a new to audio processing . I want to develop an application that reduces audio noise using a Butterworth filter. I found some existing code doing this, but I still do not understand the use of ...
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1answer
71 views

Offset after Butterworth bandpass filtering

guess I'm stuck with this filtering problem and I'm thinking it has something to do with my raw data but I'm not so sure. So the problem is the following, please refer to the figures below, basically, ...
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1answer
46 views

Third octave band zero-phase forwards-backwards Butterworth filter adds amplitude to complex signals?

Overall aim: to take a short signal (likely to be noisy with some tonal components) and filter it into third-octave bands (TOBs), apply frequency-dependent spectral adjustments, then recombine the ...
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1answer
76 views

How to determine the type of a digital filter given its expression?

I'm trying to understand a variant of the filter presented in http://www.stockspotter.com/files/PredictiveIndicators.pdf in the "Code Listing 1.". Its expression is given as follow: $$y_n = ...
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3answers
442 views

How to practically correct for group delay imposed by a digital filter (Python)

I'm using Python to filter a signal using a Butterworth filter (scipy.signal.butter) and subsequently passing this through a forward-backward filter with cascaded second order sections (scipy.signal....
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1answer
108 views

Ripple in a SciPy Butterworth SOS Filter

I have a script using SciPy for checking the RMS of various Butterworth Bandpass Filters of varying orders. I would expect the RMS values to increase and decrease linearly and consistently as you get ...
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1answer
222 views

Butterworth filter of the acceleration and drifting displacement problem

I am only mechanic engineering and I need to filter my acceleration from MEMS mobile phone which has a noise and drifts. Here is my data. Acceleration vs time from an app mobile phone ...
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2answers
210 views

Pre-Warping is not working on bilinear transform

New here and I just wanna ask the question of what happens when your pre warping doesnt work on your bilinear transform? I am assuming my isnt working as part of my research I have read that the ...
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1answer
182 views

number of multiplications per second required by the system

Consider a system implementing a rational sampling rate change by 5/7: for this, we cascade upsampler by 5, a lowpass filter with cutoff frequency π/7 and a downsampler by 7. The lowpass filter is a ...
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0answers
195 views

Number of multiplication operations needed in rational sampling rate change with IIR Butterworth filters

I am trying to get a general sense of how many multiplication operations are needed for a 4th-order Butterworth filter (IIR filter) with a rational sampling rate change. I am excluding any ...
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43 views

Butterworth filter

Can someone please explain how would the image of a biosignal say PPG be affected when a higher-order Butterworth filter is used. Please don't tell about bode curve, I need practical aspects of it. ...
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1answer
131 views

How to figure out number of multiplications in rational sampling

I am trying to understand the following: Consider a system implementing a rational sampling rate change by $\frac{5}{7}$: for this, we cascade upsampler by 5, a lowpass filter with cutoff frequency $\...
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2answers
743 views

Are IIR filters (and specifically Butterworth filter) causal?

I am new to signal processing. I am learning now about filtering and I am trying to implement high pass filter (HPF),and later band-pass filter (BPF). I implement the filters in ...
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1answer
201 views

Roll off rate vs filter order?

The concept of "increasing roll off rate with increasing filter order" applies only to butter worth or also chebyshev and other filter types?
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1answer
72 views

Filtering artefacts and filtering short signals

I have a signal from EEG sensors and I try to denoise it from AC frequencies. For that reason, I estimated PSD of my signal and found that 50 Hz and 100 Hz are likely to represent noise. I constructed ...
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1answer
55 views

How to derive 2nd order Butterworth condition for the damping coefficient mathematically?

The magnitude of 2nd order low pass filter is given as $$|H(\omega)|^2= \frac{1}{(1-(\frac{\omega}{\omega_o})^2)^2+(\frac{2\zeta\omega}{\omega_o})^2}$$ Now in order to achieve maximally flat within ...
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1answer
100 views

Pole locations of Butterworth filter

I am reading Proakis book "DSP using Matlab", 3rd edition. I am reading chapter 8, section 8.3, p. 402, and I am confused regarding the equation of poles (roots of denominator of system ...
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2answers
55 views

Design and a notch filter using two Butterworth filters in parallel (MATLAB)

I am doing a project to filter out a 1kHz noise inserted to a 30sec .wav audio file. To filter out the 1kHz noise, I am required to design using two Butterworth filters connected in parallel where ...
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2answers
98 views

Relationship between order of filter and amplitude/phase response

I am learning about digital filters, for example a lowpass butterworth filter. In many languages, the implmentation requires specification of the order of the filter, which I believe is the number ...
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1answer
74 views

What is absolute ripple specification and how does it arrive in low pass prototype for Butterworth?

Digital Signal Processing by John G. Proakis, Dimitris G. Manolakis(4th Edition) gives the prototype function for Butterworth low pass filter in an analog system which is fine till the point where the ...
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65 views

Lowpass Butterworth filter equation

I am using a 5th order lowpass Butterworth filter with a varying cutoff frequency, $f_c$, to smoothen some data coming from a spectrometer. An example of a spectrum, plotted with the filtered data, ...
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0answers
145 views

removing noise using Scipy.signal.butter:

I am going to remove the noise from a brain recorded signal. It was a continuous recording and with sample rate=30kHz, it was digitized. So now it is a digital signal. I have written the code here ...
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4answers
2k views

Butterworth filter transfer function in time domain

Preliminaries I need to know the response of Butterworth filter in time domain of the following input (at least numerically): $$ x(t) = \theta(t)(1-\exp\{-at\})\exp\{-bt\}, \quad a,b>0,\quad a\gg b ...
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1answer
643 views

How is the formula of the cutoff frequency of a 2nd order Butterworth low-pass filter derived?

According to articles and notes, the cutoff frequency of a 2nd order Butterworth lowpass filter: is expressed by the formula: $\omega _c = {1\over\sqrt{R_1R_2C_1C_2}}$ and since $\omega _c = 2 \pi ...
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1answer
62 views

Converting a simple analog Butterworth filter into a digital filter

I was just studying an old circuit analysis textbook that was describing how to design a Butterworth filter, and that seemed easy enough.. then, I started to wonder if I can take this analog filter ...
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2answers
150 views

Why is my signal attenuated after applying a HighPass-filter?

I am new to DSP, but I've been attempting apply a butterworth high-pass filter on a 1D array (Values peeking at 300~) to eliminate any noise, yet when applying a high pass filter, I'm ending up with ...
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1answer
101 views

Cut-off frequency in Fourier-Spectrum of a noise message

I have a problem involving cut-off frequency. I have a voice message in an audio file .mat which have an eletromagnetic noise. I am trying to recover the original message by applying digital ...
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1answer
522 views

Large spike at beginning of signal after applying Bandpass filter

Foreword: I am a PhD student and fairly unexperienced with many signal processing and engineering concepts, please be gentle. I am attempting to filter out a frequency range of 1Hz to 2Hz from a 2....
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1answer
1k views

Applying a 2D band pass filter (Butterworth ?) to an array with NaNs

I am trying to filter out the low frequencies of an array looking like this : For now, I am taking transects of this array and applying a 1D - butterworth band pass filter : ...
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1answer
129 views

Plotting curved peaks on PSD graph

I am a PhD student with little engineering experience, currently attempting to recreate the signal processing techniques used in this paper: Monitoring Vital Signs and Postures During Sleep Using WiFi ...
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1answer
76 views

Frequency response plot and actual behavior of a digital Butterworth LPF

I have been struggling with a not-too-high (2nd) order digital Butterworth low-pass filter both in SciPy and MatLab (latest of both). The intention is to apply this filter on signals with different ...
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1answer
343 views

Using a Butterworth high-pass filter together with Fast Fourier transform

I have a signal and I'm interested in identifying the dominant frequencies greater than 1/3600 Hz. To do this, I use Fast Fourier Transforms and examine the locations of the peaks in the frequency ...
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2answers
517 views

How Butterworth low-pass filter can be applied on a digital signal (i.e. discrete representation of a signal)?

I would like to know how to apply a low pass filter (Butterworth) to a digital signal. So, I have some values of the signal, let's say $S(t)$. Those values are equally spaced in time. I have read the ...
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1answer
123 views

what is the theory behind Butter function?

I want to understand why this code used tan and cos ? ...
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0answers
20 views

What is the meaning of these Fixed Point Properties e.g.CustomSectionInputDataType?

I was trying tom implement a Butterworth filter and i came across a example on Mathworks site which emphasizes to customize various terms related to the filter. Following are some of the terms i could ...
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1answer
2k views

How to choose order and cut-off frequency for low-pass Butterworth filter?

When using IMU data (accelerations and angular velocities), many papers use a 4th order low-pass butterworth filter with a cutoff frequency of 5 Hz. However, none of them really justify why those ...

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