WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

Chebyshev2FilterModel

✖

creates a lowpass Chebyshev type 2 filter of order n.

✖

uses the cutoff frequency ωc.

✖
Chebyshev2FilterModel[{"type",spec}]

uses the full filter specification {"type",spec}.

✖
Chebyshev2FilterModel[{"type",spec},var]

expresses the model in terms of the variable var.

Details

  • Chebyshev2FilterModel returns the filter as a TransferFunctionModel.
  • Chebyshev2FilterModel[{n,ω}] returns a lowpass filter with attenuation of (approximately 3 dB) at frequency ω.
  • Chebyshev2FilterModel[n] uses the cutoff frequency of 1.
  • Filter specification {"type",spec} can be any of the following:
  • {"Lowpass",{ωp,ωs},{ap,as}}lowpass filter using passband and stopband frequencies and attenuations
    {"Highpass",{ωs,ωp},{as,ap}}highpass filter
    {"Bandpass",{ωs1,ωp1,ωp2,ωs2},{as,ap}}bandpass filter
    {"Bandstop",{ωp1,ωs1,ωs2,ωp2},{ap,as}}bandstop filter
  • 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 .

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

A Chebyshev type 2 filter model:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-yxebjp
Out[1]=1

Bode plot of the modeled filter:

In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-z59prv
Out[2]=2

Scope  (7)Survey of the scope of standard use cases

A symbolic representation of an order 2 lowpass filter:

In[4]:=4
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-b6f36i
Out[4]=4

Exact computation of the model:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-m1h6eu
Out[1]=1

Computation of the model with precision 24:

In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-6sdcvs
Out[2]=2

Create a filter model using the variable s:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-kvokb4
Out[1]=1

Create a lowpass Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-5vax1w
Out[1]=1

Create a highpass Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-ptjo49
Out[1]=1

Create a bandpass Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-p6d6sm
In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-s8yf1q
Out[2]=2

Create a bandstop Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-vq55om
In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-2wjc7x
Out[2]=2

Applications  (6)Sample problems that can be solved with this function

Create a lowpass Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-3wi1v

Filter out high-frequency noise from a sinusoidal signal:

In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-ifgc2o

Chebyshev type 2 filter phase shifts the response by Arg[tf[ω ]], where ω is the frequency of the input sinusoid:

In[4]:=4
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-2jrez2
Out[4]=4

Correct for the phase shift:

In[5]:=5
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-0cddd
Out[6]=6

Create a highpass Chebyshev type 2 filter from the lowpass prototype:

In[7]:=7
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-n0gy7m

Filter out low-frequency sinusoid from the input:

In[8]:=8
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-ztenhq
Out[8]=8

Design a digital FIR lowpass filter using the Chebyshev 2 approximation that satisfies the following passband and stopband frequencies and attenuations:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-b807jm

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

In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-e72bzc
Out[2]=2

Compute the analog Chebyshev 1 transfer function:

In[3]:=3
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-h6kooi
Out[3]=3

Convert to discrete-time model:

In[4]:=4
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-hbv1kc
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-49i4n
Out[5]=5

Create an FIR approximation of a discrete-time Chebyshev type 2 IIR filter.

Implement a lowpass digital Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-buj3xd
Out[1]=1

Obtain the impulse response of the IIR filter and evaluate for the desired number of samples:

In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-carst7
Out[2]=2

Plot the FIR filter:

In[3]:=3
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-obd08
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-detozt
Out[1]=1

Filter an image using a lowpass Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-yc21cz
Out[1]=1

Filter an image using a highpass Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-nmld7q
Out[1]=1

Properties & Relations  (5)Properties of the function, and connections to other functions

Compare Chebyshev type 1 and type 2 lowpass filters:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-7vwi3k
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-uz37cn
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-4o59cn
Out[3]=3

Extract the order of the Chebyshev type 2 polynomial:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-xr2bzi
Out[1]=1

Find the poles and zeros of a Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-8mo9vy

Plot poles and zeros of the Chebyshev filter:

In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-cbtnsh
Out[2]=2

Implement a lowpass digital Chebyshev type 2 filter:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-ipgw7i
Out[1]=1

Plot poles and zeros of the digital Chebyshev type 2 filter:

In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-bu0m6
Out[2]=2

Convert a lowpass filter to high pass:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-jsttxk
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-qzc40d
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

A symbolic filter cannot be returned with full specification since the order is not computable:

In[1]:=1
✖
https://wolfram.com/xid/0k2n7di5tjmfbf3ds5p-st8ul8
Out[1]=1
Wolfram Research (2012), Chebyshev2FilterModel, Wolfram Language function, https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html.
✖
Wolfram Research (2012), Chebyshev2FilterModel, Wolfram Language function, https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html.

Text

Wolfram Research (2012), Chebyshev2FilterModel, Wolfram Language function, https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html.

✖
Wolfram Research (2012), Chebyshev2FilterModel, Wolfram Language function, https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html.

CMS

Wolfram Language. 2012. "Chebyshev2FilterModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html.

✖
Wolfram Language. 2012. "Chebyshev2FilterModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html.

APA

Wolfram Language. (2012). Chebyshev2FilterModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html

✖
Wolfram Language. (2012). Chebyshev2FilterModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html

BibTeX

@misc{reference.wolfram_2025_chebyshev2filtermodel, author="Wolfram Research", title="{Chebyshev2FilterModel}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html}", note=[Accessed: 03-June-2025 ]}

✖
@misc{reference.wolfram_2025_chebyshev2filtermodel, author="Wolfram Research", title="{Chebyshev2FilterModel}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html}", note=[Accessed: 03-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_chebyshev2filtermodel, organization={Wolfram Research}, title={Chebyshev2FilterModel}, year={2012}, url={https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html}, note=[Accessed: 03-June-2025 ]}

✖
@online{reference.wolfram_2025_chebyshev2filtermodel, organization={Wolfram Research}, title={Chebyshev2FilterModel}, year={2012}, url={https://reference.wolfram.com/language/ref/Chebyshev2FilterModel.html}, note=[Accessed: 03-June-2025 ]}