# Questions tagged [butterworth]

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### Butterworth Filter at high Frequencies

So I have this signal sampled at 300 Hz to begin with and this is the frequency domain: I apply a second order butterworth filter using scipy with a cutoff frequency of 12.6 Hz and this is the ...
831 views

### Signal processing in Python vs C++ (band-pass filter)

I have implemented Python signal processing code using a butter bandpass filter and order 3. It is working pretty well. I am required to implement the same signal ...
• 131
624 views

### Why don't unit circle poles lead to infinite amplitude response for Butterworth lowpass?

This is probably a very stupid question. In many places (e.g. here), the Butterworth filters, e.g. lowpass, are described as being "allpole" filters, that have all of these poles on the unit ...
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36 views

### Lowpass Filter for Lock-In-Amplifier

I am implementing a Lock-In-Amplifier in Python with scipy for measurements with light with a decimation afterwards. Right now, this is implemented with an average. This works fine, but I am trying to ...
43 views

### Butterworth filter cutoff attenuation is not exactly 0.707(-3dB)

The documentation of scipy Butterworth filter says its cutoff attenuation is 0.707(-3dB). To validate this, I created a square wave signal, performed FFT and implemented a bandpass filter with a band ...
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### Formula to compute FIR and IIR Filter coefficients

I am trying to understand filter design. I am trying to implement butterworth filter which would have high,low and bandpass using the difference equation representation for FIR and IIR. Given the low ...
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### Accounting for phase shift in time-dependent signals

Background: I am using a vibration sensor and arduino to record signals and log them with timestamps, where the signals need to be time accurate so that I can glean information about which frequencies ...
71 views

### Performing STFT after Butterworth Filter Seems Lower in Resolution

I have a signal recorded at 2MHz sampling rate. Before any decimation might be required, I first looked for peaks in my periodic recorded signal using STFT/spectrogram. From here, I can clearly see ...
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### Questionable results of on-line butterworth bandpass filtering using scipy.signal.lfilter

I have a data_stream that I'm attempting to filter using two on-line butterworth bandpass filters to extract two frequency bands of interest. The original ...
53 views

### Sampling frequency vs Signal frequency

I've started recently working with the ADXL345 accelerometer with the goal of finding the velocity. And so far, I'm getting "okay" results after applying a second-order Butterworth filter to ...
1 vote
48 views

### I do not understand the frequency calculation used in the construction of this IIR digital Butterworth Low pass filter using MATLAB

The question is to design a Low Pass Butterworth IIR Digital filter. The following code below has the specifications with $A_p$ being the passband attenuation, $A_s$ the stop band attenuation, $f_{pb}$...
1 vote
71 views

### How can I reverse engineer the parameters of this butterworth filter?

I am trying to develop an application which will need a bandpass filter. The sampling rate is 30Hz, and the frequency range I'd like the filter to preserve is: 0.5Hz-4Hz. I've used mkfilter to ...
• 13
184 views

### How to apply Butterworth high pass filter in the frequency domain?

I have a time series of measurements which I want to high pass with Butterworth filter. Python scipy package has a built in function for Butterworth filter (signal.butter) and I know how to apply it ...
1 vote
82 views

### I can't hear my sound after filtering

I am studying on a project which my supervisor gave me this semester. It has multiple steps. Basically, I have my own audio. I added AWGN to this sound using awgn() ...
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### SOS-matrices' order does not correspond to given parameter when designing bandpass with scipy.signal.butter

I do not understand why this scipy operation: ...
21 views

### How to deal with [h] coefficients which are 0 from sos-matrix

Calling scipy.signal.sosfreqz with a sos-matrix describing an ordinary butterworth bandpass returns an array of h coefficients, ...
63 views

### Theory behind the matlab butter function with the parameters n and [Wl, Wh]

I am writing the theoretical background in my thesis but my thesis is more centered on deep learning and the signals that I am using for classification were filtered through the ...
93 views

### BPF Filtering with DSP IIR Realtime C++ filter library

I am working with complex samples, I have a main signal at 630KHz, my Fs is 1.26MHz and BW is 12.6KHz. If I plot a frequency-magntitude spectrum it looks like this: As you can see along with my main ...
• 159
840 views

### Implementing a Butterworth Filter Manually in C/C++ via Second Order Sections

Short background: I want to implement a lowpass butterworth filter in C/C++. The end goal is to use this in a low-latency Python program, for which of course ...
• 143
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### What is the warm-up period of a Butterworth filter?

I am not sure if I use the correct term which may be the reason why I was not able to find the answer, but what I mean by the warm-up period is the number of samples required for the filter to produce ...
• 217
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### Butterworth filter poles

Hi, I'm looking at this textbook question and trying to get a better idea of exactly what its asking. For the processing to be real valued each pole would have to have a complex conjugate right? So ...
453 views

### Mapping of Classic Filters for Digital Filter Design

Of the four classic analog filter types: Butterworth, Chebyshev, Elliptic and Bessel- are any of these relegated to obsolescence for purposes of digital filter design in comparison to optimized ...
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104 views

### Signal values explode when filtering with bandpass and wiener in Python

I have a five second audio (speech with background noise), which I want to process first with bandpass filter and then with wiener filter to reduce noise. Audio is normalized between [-1, 1] and I ...
150 views

### 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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### 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 ...
1 vote
90 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 ...
78 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 ...
103 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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1 vote
406 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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170 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: ...
1 vote
194 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 ...
170 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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1 vote
233 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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376 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 ...
213 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 ...
44 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 ...
1 vote
139 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 ...
104 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 ...
1 vote
136 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, ...
1 vote
129 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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1 vote
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### 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 = ...
1 vote
833 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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1 vote
246 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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### 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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### 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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1 vote
213 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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1 vote
255 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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### 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. ...
179 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 \$\...
• 109