cheb1ord (Signal Processing Toolbox)

Chebyshev type I filter order selection.

Syntax

[n,Wn] = cheb1ord(Wp,Ws,Rp,Rs)
[n,Wn] = cheb1ord(Wp,Ws,Rp,Rs,'s')

Description

cheb1ord selects the minimum order digital or analog Chebyshev type I filter required to meet a set of filter design specifications:


`Wp`	Passband corner frequency. `Wp`, the cutoff frequency, has a value between 0 and 1, where 1 corresponds to half the sampling frequency (the Nyquist frequency).
`Ws`	Stopband corner frequency. `Ws` is in the same units as `Wp`; it has a value between 0 and 1, where 1 corresponds to half the sampling frequency (the Nyquist frequency).
`Rp`	Passband ripple, in decibels. This value is the maximum permissible passband loss in decibels. The passband is `0` `<` `w` `<` `Wp`.
`Rs`	Stopband attenuation, in decibels. This value is the number of decibels the stopband is down from the passband. The stopband is `Ws` `<` `w <` `1`.

Digital Domain

[n,Wn] = cheb1ord(Wp,Ws,Rp,Rs)

returns the order n of the lowest order Chebyshev filter that loses no more than Rp dB in the passband and has at least Rs dB of attenuation in the stopband. The passband runs from 0 to Wp and the stopband runs from Ws to 1, the Nyquist frequency. cheb1ord also returns Wn, the Chebyshev type I cutoff frequency that allows cheby1 to achieve the given specifications.

Use cheb1ord for lowpass, highpass, bandpass, and bandstop filters. For highpass filters, Wp > Ws. For bandpass and bandstop filters, Wp and Ws are two-element vectors that specify the corner frequencies at both edges of the filter, lower frequency edge first. For the band filters, cheb1ord returns Wn as a two-element row vector for input to cheby1.

If filter specifications call for a bandpass or bandstop filter with unequal ripple in each of the passbands or stopbands, design the filter as separate lowpass and highpass sections and cascade the two filters together.

Analog Domain

[n,Wn] = cheb1ord(Wp,Ws,Rp,Rs,'s')

finds the minimum order n and cutoff frequencies Wn for an analog filter. In this case the frequencies in Wp and Ws are in radians per second and may be greater than 1.

Use cheb1ord for lowpass, highpass, bandpass, and bandstop filters, as described under "Digital Domain."

Examples

For data sampled at 1000 Hz, design a lowpass filter with less than 3 dB of attenuation from 0 to 100 Hz and attenuation at least 15 dB from 150 Hz to the Nyquist frequency:

Wp = 100/500; Ws = 150/500;
Rp = 3; Rs = 15;
[n,Wn] = cheb1ord(Wp,Ws,Rp,Rs)
n =
     3
Wn =
    0.2000
[b,a] = cheby1(n,Rp,Wn);
freqz(b,a,512,1000); title('n=3 Chebyshev Type I Lowpass Filter')

Next design a bandpass filter with a passband of 100 Hz to 200 Hz, less than 3 dB of attenuation throughout the passband, and 30 dB stopbands 50 Hz out on both sides of the passband:

Wp = [100 200]/500; Ws = [50 250]/500;
Rp = 3; Rs = 30;
[n,Wn] = cheb1ord(Wp,Ws,Rp,Rs)
n =
     4
Wn =
    0.2000    0.4000
[b,a] = cheby1(n,Rp,Wn);
freqz(b,a,512,1000);
title('n=4 Chebyshev Type I Bandpass Filter')

Algorithm

cheb1ord uses the Chebyshev lowpass filter order prediction formula described in [1]. The function performs its calculations in the analog domain for both analog and digital cases. For the digital case, it converts the frequency parameters to the s-domain before the order and natural frequency estimation process, then converts them back to the z-domain.

cheb1ord initially develops a lowpass filter prototype by transforming the passband frequencies of the desired filter to 1 rad/sec (for low- or highpass filters) or to -1 and 1 rad/sec (for bandpass or bandstop filters). It then computes the minimum order required for a lowpass filter to meet the stopband specification.

`buttord`	Butterworth filter order selection.
`cheby1`	Chebyshev type I filter design (passband ripple).
`cheb2ord`	Chebyshev type II filter order selection.
`ellipord`	Elliptic filter order selection.
`kaiserord`	Estimate parameters for an FIR filter design with Kaiser window.