Chebyshev1FilterModel

Chebyshev1FilterModel[n]

creates a lowpass Chebyshev type 1 filter of order n.

Chebyshev1FilterModel[{n,ωc}]

uses the cutoff frequency ωc.

Chebyshev1FilterModel[{"type",spec}]

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

Chebyshev1FilterModel[{"type",spec},var]

expresses the model in terms of the variable var.

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

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Basic Examples  (2)

A third-order Chebyshev type 1 filter model:

Bode magnitude plot of the modeled filter:

A lowpass Chebyshev type 1 filter using the full specification:

Magnitude response of the filter showing the ideal filter characteristics:

Scope  (8)

Create a symbolic Chebyshev type 1 filter model:

Exact computation of the model:

Computation of the model with precision 24:

Create a filter model using the variable s:

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

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

Create a highpass Chebyshev type 1 filter:

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

Use center frequency 1 and quality factor 1/3:

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

Create a bandstop Chebyshev type 1 filter:

Applications  (6)

Create a lowpass Chebyshev type 1 filter:

Filter out high-frequency noise from a sinusoidal signal:

Chebyshev type 1 filter phase shifts the response by Arg[tf[ω ]], where ω is the frequency of the input sinusoid:

Correct for the phase shift:

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

Filter out low-frequency sinusoid from the input:

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

Obtain the equivalent analog frequencies assuming a sampling period of 1:

Compute the analog Chebyshev 1 transfer function:

Convert to discrete-time model:

Create an FIR approximation of a discrete-time Chebyshev 1 IIR filter.

Implement a lowpass digital Chebyshev type 1 filter:

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

Plot the FIR filter:

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

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

Filter an image using a highpass Chebyshev type 1 filter:

Properties & Relations  (8)

Stopband attenuation increases as order n increases:

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

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

Compare phase responses for different filter orders:

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

Compare Chebyshev type 1 and type 2 lowpass filters:

Extract the order of the Chebyshev type 1 polynomial:

Find the poles of a Chebyshev type 1 filter:

Plot poles of the Butterworth filter:

Implement a lowpass digital Chebyshev type 1 filter:

Plot poles of the digital Chebyshev type 1 filter:

Convert a lowpass filter to highpass:

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).

CMS

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

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: 18-April-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: 18-April-2025 ]}