BandpassFilter [data,{ω1,ω2}]
applies a bandpass filter with cutoff frequencies ω1 and ω2 to an array of data.
BandpassFilter [data,{{ω,q}}]
uses center frequency ω and quality factor q.
BandpassFilter [data,spec,n]
uses a filter kernel of length n.
BandpassFilter [data,spec,n,wfun]
applies a smoothing window wfun to the filter kernel.
BandpassFilter
BandpassFilter [data,{ω1,ω2}]
applies a bandpass filter with cutoff frequencies ω1 and ω2 to an array of data.
BandpassFilter [data,{{ω,q}}]
uses center frequency ω and quality factor q.
BandpassFilter [data,spec,n]
uses a filter kernel of length n.
BandpassFilter [data,spec,n,wfun]
applies a smoothing window wfun to the filter kernel.
Details and Options
- Bandpass filtering is commonly used in audio equalizers and audio receivers to attenuate low and high frequencies in a signal while leaving the mid-range frequencies unchanged.
- BandpassFilter convolves a digital signal with a finite impulse response (FIR) kernel created using the window method.
- Longer kernels result in a better frequency discrimination.
- The data can be any of the following:
-
list arbitrary-rank numerical arraytseries temporal data such as TimeSeries and TemporalDatavideo a Video object
- The range of frequencies that are attenuated is dependent on the values of the cutoff frequencies ω1 and ω2, with ω2>ω1.
- When applied to images and multidimensional arrays, filtering is applied successively to each dimension starting at level 1. BandpassFilter [data,{{ω11,ω21},…}] uses the frequencies {ω1i,ω2i} for the i^(th) dimension.
- BandpassFilter [data,{ω1,ω2}] uses a filter kernel length and smoothing window suitable for the cutoff frequencies {ω1,ω2} and the input data.
- Typical smoothing windows wfun include:
-
BlackmanWindow smoothing with a Blackman windowDirichletWindow no smoothingHammingWindow smoothing with a Hamming window{v1,v2,…} use a window with values vif create a window by sampling f between and
- The following options can be given:
-
- By default, SampleRate->1 is assumed for images as well as data. For audio signals and time series, the sample rate is either extracted or computed from the input data.
- With SampleRate sr, the cutoff frequency ωc should be between 0 and sr.
Examples
open all close allBasic Examples (3)
Bandpass filtering of a sum of cosines:
Bandpass filtering of audio:
Bandpass filtering of an image:
Scope (14)
Data (8)
Filter a 1D pulse sequence:
Filter a 2D pulse sequence:
Filter a TimeSeries :
Bandpass filtering of a Sound object of a tri-tone signal:
Eliminate the outer tones using a bandpass filter with a Blackman window of length 101:
Bandpass filtering of a halftone image:
Filter video frames:
Bandpass filtering of a 3D image:
Filter using exact precision:
Parameters (6)
With an audio signal of sample rate s, a numeric frequency will be interpreted as a rad/s quantity:
Filter a white noise signal using a bandpass filter with cutoff frequencies of 8000 Hz and 12000 Hz:
Use center frequency of 9798 Hz and a quality factor q of 2:
Make the passband narrower by increasing the quality factor:
Use a filter of length 33:
Increase frequency discrimination by using a longer kernel:
Vary the amount of attenuation by using different window functions:
Vary the amount of attenuation by using the adjustable Kaiser window:
Specify the window function as a numeric list:
Bandpass filtering using different center frequencies:
Use the same center frequency and different quality factors:
Use different center frequencies in each dimension:
Options (3)
Padding (1)
Different padding methods result in different edge effects:
SampleRate (2)
Use a filter centered on the frequency π/2 assuming a sample rate of sr=1:
Assume a sample rate of sr=3:
Apply a bandpass filter centered on the half-band frequency to audio sampled at a rate of 44100 Hz:
Applications (1)
On a modern 88-key piano, key 55 (note C5) has a fundamental frequency of approximately 523 Hz. Use BandpassFilter to effectively remove all the harmonics of this key while retaining the fundamental in the following audio clip:
Use a narrow filter (Q=3) of length 63 centered on the fundamental frequency (523 Hz):
Compare the frequency spectra of the two audio clips:
Properties & Relations (6)
Using cutoff frequencies of 0 and π returns the original sequence:
Create a bandpass filter using LeastSquaresFilterKernel and a Hamming window:
Compare with the result of BandpassFilter :
Impulse response of a bandpass filter of length 21:
Magnitude spectrum of the filter:
Impulse response of a bandpass filter of length 21 without a smoothing window:
Magnitude spectrum of the filter:
The frequency discrimination of the bandpass filter improves as the length of the filter is increased:
The length of the impulse response increases as the filter's quality factor is increased:
Possible Issues (1)
With PaddingNone, the returned output will be shorter than the input:
Interactive Examples (1)
Bandpass filtering an image using different center frequencies and quality factors:
History
Introduced in 2012 (9.0) | Updated in 2015 (10.2) ▪ 2015 (10.3) ▪ 2016 (11.0) ▪ 2017 (11.1) ▪ 2025 (14.3)
Text
Wolfram Research (2012), BandpassFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/BandpassFilter.html (updated 2025).
CMS
Wolfram Language. 2012. "BandpassFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/BandpassFilter.html.
APA
Wolfram Language. (2012). BandpassFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BandpassFilter.html
BibTeX
@misc{reference.wolfram_2025_bandpassfilter, author="Wolfram Research", title="{BandpassFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/BandpassFilter.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_bandpassfilter, organization={Wolfram Research}, title={BandpassFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/BandpassFilter.html}, note=[Accessed: 17-November-2025]}