# EllipticFilterModel

designs a lowpass elliptic filter of order n.

EllipticFilterModel[{n,ωc}]

uses the cutoff frequency ωc.

EllipticFilterModel[{"type",spec}]

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

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

expresses the model in terms of the variable var.

# Details • EllipticFilterModel returns the designed filter as a TransferFunctionModel.
• EllipticFilterModel[{n,ω}] returns a lowpass filter with attenuation of (approximately 3 dB) at frequency ω.
• 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 .

# Examples

open allclose all

## 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: