designs a lowpass elliptic filter of order n.


uses the cutoff frequency ωc.


designs an elliptic filter of the specified type "type", using the spec.


expresses the model in terms of the variable var.


  • EllipticFilterModel returns the designed filter as a TransferFunctionModel.
  • EllipticFilterModel[{n,ω}] returns a lowpass filter with attenuation of (approximately 3 dB) at frequency ω.
  • EllipticFilterModel[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 absolute values of passband and stopband attenuations, respectively.
  • Given a gain fraction , the attenuation is .


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Basic Examples  (2)

A third-order elliptic filter model with cutoff frequency at :

Bode plot of the filter:

A lowpass elliptic filter using the full specification:

Magnitude response of the filter showing the ideal filter characteristics:

Scope  (8)

A symbolic representation of an order 2 lowpass filter:

Exact computation of the model:

Computation of the model with precision 24:

Create a filter model using the variable s:

Create a lowpass filter model with a cutoff frequency of 10:

Create a lowpass elliptic filter:

Create a highpass elliptic filter:

Create a bandpass elliptic filter:

Create a bandstop elliptic filter:

Applications  (6)

Create a lowpass elliptic filter:

Filter out high-frequency noise from a sinusoidal signal:

Elliptic 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 elliptic filter from the lowpass prototype:

Filter out low-frequency sinusoid from the input:

Design a digital lowpass filter using the elliptic 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 elliptic filter transfer function:

Convert to discrete-time model:

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

Implement a lowpass digital elliptic filter:

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

Plot the FIR filter:

Smooth financial data using an FIR approximation of an elliptic filter:

Filter an image using a lowpass elliptic filter:

Filter an image using a highpass elliptic filter:

Properties & Relations  (3)

Extract the order of the elliptic filter:

Extract the poles and zeros of an elliptic filter:

Convert a lowpass filter to highpass:

Introduced in 2012