Chebyshev1FilterModel
✖
Chebyshev1FilterModel
creates a filter of a given "type" using the specified parameters spec.
Details



- Chebyshev1FilterModel returns the filter as a TransferFunctionModel.
- Chebyshev1FilterModel[{n,ω}] returns a lowpass filter with attenuation of
(approximately 3 dB) at frequency ω.
- Chebyshev1FilterModel[n] uses the cutoff frequency of 1.
- Lowpass filter specification {"type",spec} can be any of the following:
-
{"Lowpass",n} lowpass filter of order n and cutoff frequency 1 {"Lowpass",n,ωp} use cutoff frequency ωp {"Lowpass",{ωp,ωs},{ap,as}} use full filter specification giving passband and stopband frequencies and attenuations - Highpass filter specifications:
-
{"Highpass",n} highpass filter with cutoff frequency 1 {"Highpass",n,ωp} use cutoff frequency ωp {"Highpass",{ωs,ωp},{as,ap}} full filter specification - Bandpass filter specifications:
-
{"Bandpass",n,{ωp1,ωp2}} bandpass filter with passband frequencies ωp1 and ωp2 {"Bandpass",n,{{ω,q}}} use center frequency ω and quality factor q {"Bandpass",{ωs1,ωp1,ωp2,ωs2},{as,ap}} full filter specification - Bandstop filter specifications:
-
{"Bandstop",n,{ωp1,ωp2}} bandstop filter with passband frequencies ωp1 and ωp2 {"Bandstop",n,{{ω,q}}} use center frequency ω and quality factor q {"Bandstop",{ωp1,ωs1,ωs2,ωp2},{ap,as}} full filter specification - Frequency values should be given in an ascending order.
- Values ap and as are respectively absolute values of passband and stopband attenuations.
- Given a gain fraction
, the attenuation is
.
- The quality factor q is defined as
, with ω being the center frequency of a bandpass or bandstop filter. Higher values of q give narrower filters.
Examples
open allclose allBasic Examples (2)Summary of the most common use cases
A third-order Chebyshev type 1 filter model:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-7pxsg8

Bode magnitude plot of the modeled filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-iwz0u8

A lowpass Chebyshev type 1 filter using the full specification:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-irwass

Magnitude response of the filter showing the ideal filter characteristics:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-rb0mpv

Scope (8)Survey of the scope of standard use cases
Create a symbolic Chebyshev type 1 filter model:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-zg2ty0

Exact computation of the model:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-m1h6eu

Computation of the model with precision 24:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-6sdcvs

Create a filter model using the variable s:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-kvokb4

Create a lowpass Chebyshev type 1 filter model with a cutoff frequency of 10:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-bbncb9

Create a lowpass Chebyshev type 1 filter using the full specification:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-bri75x

Create a highpass Chebyshev type 1 filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-ddbdez

Create a bandpass filter with passband frequencies 1 and 10 and attenuation of order 3:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-i2mdrk

Use center frequency 1 and quality factor 1/3:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-bmcf4k

Create a bandpass Chebyshev type 1 filter using the full specification:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-fuw4l3

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-pzw9dh

Create a bandstop Chebyshev type 1 filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-hwapls

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-bg42k

Applications (6)Sample problems that can be solved with this function
Create a lowpass Chebyshev type 1 filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-3wi1v
Filter out high-frequency noise from a sinusoidal signal:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-ifgc2o
Chebyshev type 1 filter phase shifts the response by Arg[tf[ω ]], where ω is the frequency of the input sinusoid:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-2jrez2


https://wolfram.com/xid/0k2n7di4ufs79wb5by1-0cddd

Create a highpass Chebyshev type 1 filter from the lowpass prototype:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-n0gy7m
Filter out low-frequency sinusoid from the input:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-ztenhq

Design a digital FIR lowpass filter using the Chebyshev 1 approximation that satisfies the following passband and stopband frequencies and attenuations:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-b807jm
Obtain the equivalent analog frequencies assuming a sampling period of 1:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-l3l58

Compute the analog Chebyshev 1 transfer function:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-dg7zm

Convert to discrete-time model:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-ecvjhx


https://wolfram.com/xid/0k2n7di4ufs79wb5by1-fld0kc

Create an FIR approximation of a discrete-time Chebyshev 1 IIR filter.
Implement a lowpass digital Chebyshev type 1 filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-buj3xd

Obtain the desired number of FIR samples from the impulse response of the discrete-time Chebyshev filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-carst7


https://wolfram.com/xid/0k2n7di4ufs79wb5by1-obd08

Smooth financial data using an FIR approximation of a Chebyshev filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-detozt

Filter an image using a discrete-time lowpass Chebyshev type 1 filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-yc21cz

Filter an image using a highpass Chebyshev type 1 filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-1hnfn

Properties & Relations (8)Properties of the function, and connections to other functions
Stopband attenuation increases as order n increases:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-khcsbq

Passband width of "Bandpass" filter decreases with increasing quality factor q:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-ejl0fl

Phase response of a third-order "Lowpass" type 1 Chebyshev filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-fqxb00

Compare phase responses for different filter orders:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-b58ugj

Phase response of a "Bandpass" filter for several quality factors:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-g3rv0t

Compare Chebyshev type 1 and type 2 lowpass filters:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-7vwi3k


https://wolfram.com/xid/0k2n7di4ufs79wb5by1-uz37cn


https://wolfram.com/xid/0k2n7di4ufs79wb5by1-4o59cn

Extract the order of the Chebyshev type 1 polynomial:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-xr2bzi

Find the poles of a Chebyshev type 1 filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-8mo9vy

Plot poles of the Butterworth filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-cbtnsh

Implement a lowpass digital Chebyshev type 1 filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-ipgw7i

Plot poles of the digital Chebyshev type 1 filter:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-bu0m6

Convert a lowpass filter to highpass:

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-jsttxk

https://wolfram.com/xid/0k2n7di4ufs79wb5by1-xuxdi

Wolfram Research (2012), Chebyshev1FilterModel, Wolfram Language function, https://reference.wolfram.com/language/ref/Chebyshev1FilterModel.html (updated 2016).
Text
Wolfram Research (2012), Chebyshev1FilterModel, Wolfram Language function, https://reference.wolfram.com/language/ref/Chebyshev1FilterModel.html (updated 2016).
Wolfram Research (2012), Chebyshev1FilterModel, Wolfram Language function, https://reference.wolfram.com/language/ref/Chebyshev1FilterModel.html (updated 2016).
CMS
Wolfram Language. 2012. "Chebyshev1FilterModel." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/Chebyshev1FilterModel.html.
Wolfram Language. 2012. "Chebyshev1FilterModel." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/Chebyshev1FilterModel.html.
APA
Wolfram Language. (2012). Chebyshev1FilterModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Chebyshev1FilterModel.html
Wolfram Language. (2012). Chebyshev1FilterModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Chebyshev1FilterModel.html
BibTeX
@misc{reference.wolfram_2025_chebyshev1filtermodel, author="Wolfram Research", title="{Chebyshev1FilterModel}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/Chebyshev1FilterModel.html}", note=[Accessed: 29-March-2025
]}
BibLaTeX
@online{reference.wolfram_2025_chebyshev1filtermodel, organization={Wolfram Research}, title={Chebyshev1FilterModel}, year={2016}, url={https://reference.wolfram.com/language/ref/Chebyshev1FilterModel.html}, note=[Accessed: 29-March-2025
]}