ellipord
Minimum order for elliptic filters
Syntax
[n,Wp] = ellipord(Wp,Ws,Rp,Rs)
[n,Wp] = ellipord(Wp,Ws,Rp,Rs,'s')
Description
ellipord calculates the minimum order of
a digital or analog elliptic filter required to meet a set of filter
design specifications.
Digital Domain
[n,Wp] = ellipord(Wp,Ws,Rp,Rs) returns the lowest order, n, of the
elliptic filter that loses no more than Rp dB
in the passband and has at least Rs dB
of attenuation in the stopband. The scalar (or vector) of corresponding
cutoff frequencies Wp, is also returned. Use the
output arguments n and Wp in ellip.
Choose the input arguments to specify the stopband and passband
according to the following table.
Description of Stopband and Passband Filter
Parameters
Parameter | Description |
Wp | Passband corner frequency Wp, the
cutoff frequency, is a scalar or a two-element vector with values between 0 and 1, with 1 corresponding to the
normalized Nyquist frequency, π radians per sample. |
Ws | Stopband corner frequency Ws, is a
scalar or a two-element vector with values between 0 and 1, with 1
corresponding to the normalized Nyquist frequency. |
Rp | Passband ripple, in decibels. This value is the maximum
permissible passband loss in decibels. |
Rs | Stopband attenuation, in decibels. This value is the
number of decibels the stopband is attenuated with respect to the
passband response. |
Use the following guide to specify filters of different types.
Filter Type Stopband and Passband Specifications
Filter Type | Stopband
and Passband Conditions | Stopband | Passband |
Lowpass | Wp < Ws, both
scalars | (Ws,1) | (0,Wp) |
Highpass | Wp > Ws, both
scalars | (0,Ws) | (Wp,1) |
Bandpass | The interval specified by Ws contains
the one specified by Wp (Ws(1) < Wp(1)
< Wp(2) < Ws(2)). | (0,Ws(1)) and (Ws(2),1) | (Wp(1),Wp(2)) |
Bandstop | The interval specified by Wp contains
the one specified by Ws (Wp(1) < Ws(1)
< Ws(2) < Wp(2)). | (0,Wp(1)) and (Wp(2),1) | (Ws(1),Ws(2)) |
If your filter specifications call for a bandpass or bandstop
filter with unequal ripple in each of the passbands or stopbands,
design separate lowpass and highpass filters according to the specifications
in this table, and cascade the two filters together.
Analog Domain
[n,Wp] = ellipord(Wp,Ws,Rp,Rs,'s') finds the minimum order n and cutoff
frequencies Wp for an analog filter. You specify
the frequencies Wp and Ws similar
to those described in the Description of Stopband and Passband Filter
Parameters table
above, only in this case you specify the frequency in radians per
second, and the passband or the stopband can be infinite.
Use ellipord for lowpass, highpass, bandpass,
and bandstop filters as described in the Filter Type Stopband and Passband Specifications table above.
Examples
expand all
For 1000 Hz data, design a lowpass filter with less than 3 dB of ripple in the passband, defined from 0 to 40 Hz, and at least 60 dB of ripple in the stopband, defined from 150 Hz to the Nyquist frequency, 500 Hz. Find the filter order and cutoff frequency.
Wp = 40/500; Ws = 150/500;
Rp = 3; Rs = 60;
[n,Wp] = ellipord(Wp,Ws,Rp,Rs)
n =
4
Wp =
0.0800
Specify the filter in terms of second-order sections and plot the frequency response.
[z,p,k] = ellip(n,Rp,Rs,Wp);
sos = zp2sos(z,p,k);
freqz(sos,512,1000)
title(sprintf('n = %d Elliptic Lowpass Filter',n))
Design a bandpass filter with a passband from 60 Hz to 200 Hz with at most 3 dB of ripple and at least 40 dB attenuation in the stopbands. Specify a sampling rate of 1 kHz. Have the stopbands be 50 Hz wide on both sides of the passband. Find the filter order and cutoff frequencies.
Wp = [60 200]/500; Ws = [50 250]/500;
Rp = 3; Rs = 40;
[n,Wp] = ellipord(Wp,Ws,Rp,Rs)
n =
5
Wp =
0.1200 0.4000
Specify the filter in terms of second-order sections and plot the frequency response.
[z,p,k] = ellip(n,Rp,Rs,Wp);
sos = zp2sos(z,p,k);
freqz(sos,512,1000)
title(sprintf('n = %d Elliptic Bandpass Filter',n))
More About
expand all
ellipord uses the elliptic lowpass filter
order prediction formula described in [1]. The function performs its calculations
in the analog domain for both the analog and digital cases. For the
digital case, it converts the frequency parameters to the s-domain
before estimating the order and natural frequencies, and then converts
them back to the z-domain.
ellipord initially develops a lowpass filter
prototype by transforming the passband frequencies of the desired
filter to 1 rad/s (for low- and highpass filters) and to -1 and 1
rad/s (for bandpass and bandstop filters). It then computes the minimum
order required for a lowpass filter to meet the stopband specification.
References
[1] Rabiner, Lawrence R., and B. Gold. Theory
and Application of Digital Signal Processing. Englewood
Cliffs, NJ: Prentice-Hall, 1975.
See Also
buttord | cheb1ord | cheb2ord | ellip