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Library - filter
filter is a library which adds to LME functions for designing analog (continuous-time) and digital (discrete-time) linear filters.
The following statement makes available functions defined in filter:
use filter
This library provides three kinds of functions:
- besselap, buttap, cheb1ap, cheb2ap, and ellipap, which compute the zeros, poles and gain of the prototype of analog low-pass filter with a cutoff frequency of 1 rad/s. They correspond respectively to Bessel, Butterworth, Chebyshev type 1, Chebyshev type 2, and elliptic filters.
- besself, butter, cheby1, cheby2, and ellip, which provide a higher-level interface to design filters of these different types. In addition to the filter parameters (degree, bandpass and bandstop ripples), one can specify the kind of filter (lowpass, highpass, bandpass or bandstop) and the cutoff frequency or frequencies. The result can be an analog or a digital filter, given as a rational transfer function or as zeros, poles and gain.
- lp2lp, lp2hp, lp2bp, and lp2bs, which convert analog lowpass filters respectively to lowpass, highpass, bandpass, and bandstop with specified cutoff frequency or frequencies.
Transfer functions are expressed as the coefficient vectors of their numerator num and denominator den in decreasing powers of s (Laplace transform for analog filters) or z (z transform for digital filters); or as the zeros z, poles p, and gain k.
Functions
besselap
Bessel analog filter prototype.
Syntax
use filter (z, p, k) = besselap(n)
Description
besselap(n) calculates the zeros, the poles, and the gain of a Bessel analog filter of degree n with a cutoff angular frequency of 1 rad/s.
See also
besself, buttap, cheb1ap, cheb2ap, ellipap
besself
Bessel filter.
Syntax
use filter (z, p, k) = besself(n, w0) (num, den) = besself(n, w0) (...) = besself(n, [wl, wh]) (...) = besself(n, w0, 'high') (...) = besself(n, [wl, wh], 'stop') (...) = besself(..., 's')
Description
besself calculates a Bessel filter. The result is given as zeros, poles and gain if there are three output arguments, or as numerator and denominator coefficient vectors if there are two output arguments.
besself(n,w0), where w0 is a scalar, gives a digital lowpass filter of order n with a cutoff frequency of w0 relatively to half the sampling frequency.
besself(n,[wl,wh]), where the second input argument is a vector of two numbers, gives a digital bandpass filter of order 2*n with passband between wl and wh relatively to half the sampling frequency.
besself(n,w0,'high') gives a digital highpass filter of order n with a cutoff frequency of w0 relatively to half the sampling frequency.
besself(n,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives a digital bandstop filter of order 2*n with stopband between wl and wh relatively to half the sampling frequency.
With an additional input argument which is the string 's', besself gives an analog Bessel filter. Frequencies are given in rad/s.
See also
besselap, butter, cheby1, cheby2, ellip
bilinear
Analog-to-digital conversion with bilinear transformation.
Syntax
use filter (zd, pd, kd) = bilinear(zc, pc, kc, fs) (numd, dend) = bilinear(numc, denc, fs)
Description
bilinear(zc,pc,kc,fs) converts the analog (continuous-time)
transfer function given by its zeros zc, poles pc,
and gain kc to a digital (discrete-time) transfer function
given by its zeros, poles, and gain in the domain of the forward-shift
operator
With three input arguments, bilinear(numc,denc,fs) uses the coefficients of the numerators and denominators instead of their zeros, poles and gain.
buttap
Butterworth analog filter prototype.
Syntax
use filter (z, p, k) = buttap(n)
Description
buttap(n) calculates the zeros, the poles, and the gain of a Butterworth analog filter of degree n with a cutoff angular frequency of 1 rad/s.
See also
butter, besselap, cheb1ap, cheb2ap, ellipap
butter
Butterworth filter.
Syntax
use filter (z, p, k) = butter(n, w0) (num, den) = butter(n, w0) (...) = butter(n, [wl, wh]) (...) = butter(n, w0, 'high') (...) = butter(n, [wl, wh], 'stop') (...) = butter(..., 's')
Description
butter calculates a Butterworth filter. The result is given as zeros, poles and gain if there are three output arguments, or as numerator and denominator coefficient vectors if there are two output arguments.
butter(n,w0), where w0 is a scalar, gives a nth-order digital lowpass filter with a cutoff frequency of w0 relatively to half the sampling frequency.
butter(n,[wl,wh]), where the second input argument is a vector of two numbers, gives a 2nth-order digital bandpass filter with passband between wl and wh relatively to half the sampling frequency.
butter(n,w0,'high') gives a nth-order digital highpass filter with a cutoff frequency of w0 relatively to half the sampling frequency.
butter(n,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives a 2nth-order digital bandstop filter with stopband between wl and wh relatively to half the sampling frequency.
With an additional input argument which is the string 's', butter gives an analog Butterworth filter. Frequencies are given in rad/s.
See also
buttap, besself, cheby1, cheby2, ellip
cheb1ap
Chebyshev type 1 analog filter prototype.
Syntax
use filter (z, p, k) = cheb1ap(n, rp)
Description
cheb1ap(n,rp) calculates the zeros, the poles, and the gain of a Chebyshev type 1 analog filter of degree n with a cutoff angular frequency of 1 rad/s. Ripples in the passband have a peak-to-peak magnitude of rp dB, i.e. the peak-to-peak ratio is 10^(rp/20).
See also
cheby1, cheb2ap, ellipap, besselap, buttap
cheb2ap
Chebyshev type 2 analog filter prototype.
Syntax
use filter (z, p, k) = cheb2ap(n, rs)
Description
cheb2ap(n,rs) calculates the zeros, the poles, and the gain of a Chebyshev type 2 analog filter of degree n with a cutoff angular frequency of 1 rad/s. Ripples in the stopband have a peak-to-peak magnitude of rs dB, i.e. the peak-to-peak ratio is 10^(rs/20).
See also
cheby1, cheb1ap, ellipap, besselap, buttap
cheby1
Chebyshev type 1 filter.
Syntax
use filter (z, p, k) = cheby1(n, rp, w0) (num, den) = cheby1(n, rp, w0) (...) = cheby1(n, rp, [wl, wh]) (...) = cheby1(n, rp, w0, 'high') (...) = cheby1(n, rp, [wl, wh], 'stop') (...) = cheby1(..., 's')
Description
cheby1 calculates a Chebyshev type 1 filter. The result is given as zeros, poles and gain if there are three output arguments, or as numerator and denominator coefficient vectors if there are two output arguments.
cheby1(n,rp,w0), where w0 is a scalar, gives a nth-order digital lowpass filter with a cutoff frequency of w0 relatively to half the sampling frequency. Ripples in the passband have a peak-to-peak magnitude of rp dB, i.e. the peak-to-peak ratio is 10^(rp/20).
cheby1(n,rp,[wl,wh]), where the second input argument is a vector of two numbers, gives a 2nth-order digital bandpass filter with passband between wl and wh relatively to half the sampling frequency.
cheby1(n,rp,w0,'high') gives a nth-order digital highpass filter with a cutoff frequency of w0 relatively to half the sampling frequency.
cheby1(n,rp,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives a 2nth-order digital bandstop filter with stopband between wl and wh relatively to half the sampling frequency.
With an additional input argument which is the string 's', cheby1 gives an analog Chebyshev type 1 filter. Frequencies are given in rad/s.
See also
cheb1ap, besself, butter, cheby2, ellip
cheby2
Chebyshev type 2 filter.
Syntax
use filter (z, p, k) = cheby2(n, rs, w0) (num, den) = cheby2(n, rs, w0) (...) = cheby2(n, rs, [wl, wh]) (...) = cheby2(n, rs, w0, 'high') (...) = cheby2(n, rs, [wl, wh], 'stop') (...) = cheby2(..., 's')
Description
cheby2 calculates a Chebyshev type 2 filter. The result is given as zeros, poles and gain if there are three output arguments, or as numerator and denominator coefficient vectors if there are two output arguments.
cheby2(n,rs,w0), where w0 is a scalar, gives a nth-order digital lowpass filter with a cutoff frequency of w0 relatively to half the sampling frequency. Ripples in the stopband have a peak-to-peak magnitude of rs dB, i.e. the peak-to-peak ratio is 10^(rs/20).
cheby2(n,rs,[wl,wh]), where the second input argument is a vector of two numbers, gives a 2nth-order digital bandpass filter with passband between wl and wh relatively to half the sampling frequency.
cheby2(n,rs,w0,'high') gives a nth-order digital highpass filter with a cutoff frequency of w0 relatively to half the sampling frequency.
cheby2(n,rs,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives a 2nth-order digital bandstop filter with stopband between wl and wh relatively to half the sampling frequency.
With an additional input argument which is the string 's', cheby2 gives an analog Chebyshev type 2 filter. Frequencies are given in rad/s.
See also
cheb2ap, besself, butter, cheby1, ellip
ellip
Elliptic filter.
Syntax
use filter (z, p, k) = ellip(n, rp, rs, w0) (num, den) = ellip(n, rp, rs, w0) (...) = ellip(n, rp, rs, [wl, wh]) (...) = ellip(n, rp, rs, w0, 'high') (...) = ellip(n, rp, rs, [wl, wh], 'stop') (...) = ellip(..., 's')
Description
ellip calculates a elliptic filter, or Cauer filter. The result is given as zeros, poles and gain if there are three output arguments, or as numerator and denominator coefficient vectors if there are two output arguments.
ellip(n,rp,rs,w0), where w0 is a scalar, gives a nth-order digital lowpass filter with a cutoff frequency of w0 relatively to half the sampling frequency. Ripples have a peak-to-peak magnitude of rp dB in the passband and of rs dB in the stopband (peak-to-peak ratios are respectively 10^(rp/20) and 10^(rs/20)).
ellip(n,rp,rs,[wl,wh]), where the second input argument is a vector of two numbers, gives a 2nth-order digital bandpass filter with passband between wl and wh relatively to half the sampling frequency.
ellip(n,rp,rs,w0,'high') gives a nth-order digital highpass filter with a cutoff frequency of w0 relatively to half the sampling frequency.
ellip(n,rp,rs,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives a 2nth-order digital bandstop filter with stopband between wl and wh relatively to half the sampling frequency.
With an additional input argument which is the string 's', ellip gives an analog elliptic filter. Frequencies are given in rad/s.
See also
ellipap, besself, butter, cheby1, cheby2
ellipap
Elliptic analog filter prototype.
Syntax
use filter (z, p, k) = ellipap(n, rp, rs)
Description
ellipap(n,rp,rs) calculates the zeros, the poles, and the gain of an elliptic analog filter of degree n with a cutoff angular frequency of 1 rad/s. Ripples have a peak-to-peak magnitude of rp dB in the passband and of rs dB in the stopband (peak-to-peak ratios are respectively 10^(rp/20) and 10^(rs/20)).
See also
ellip, cheb1ap, cheb1ap, besselap, buttap
lp2bp
Lowpass prototype to bandpass filter conversion.
Syntax
use filter (z, p, k) = lp2bp(z0, p0, k0, wc, ww) (num, den) = lp2bp(num0, den0, wc, ww)
Description
lp2bp convert a lowpass analog filter prototype (with unit angular frequency) to a bandpass analog filter with the specified center angular frequency w0 and bandwidth ww. lp2bp(z0,p0,k0,wc,ww) converts a filter given by its zeros, poles, and gain; lp2bp(num0,den0,wc,ww) converts a filter given by its numerator and denominator coefficients in decreasing powers of s.
The new filter
where
See also
lp2bs
Lowpass prototype to bandstop filter conversion.
Syntax
use filter (z, p, k) = lp2bs(z0, p0, k0, wc, ww) (num, den) = lp2bs(num0, den0, wc, ww)
Description
lp2bs convert a lowpass analog filter prototype (with unit angular frequency) to a bandstop analog filter with the specified center angular frequency w0 and bandwidth ww. lp2bs(z0,p0,k0,wc,ww) converts a filter given by its zeros, poles, and gain; lp2bs(num0,den0,wc,ww) converts a filter given by its numerator and denominator coefficients in decreasing powers of s.
The new filter
where
See also
lp2hp
Lowpass prototype to highpass filter conversion.
Syntax
use filter (z, p, k) = lp2hp(z0, p0, k0, w0) (num, den) = lp2hp(num0, den0, w0)
Description
lp2hp convert a lowpass analog filter prototype (with unit angular frequency) to a highpass analog filter with the specified cutoff angular frequency w0. lp2hp(z0,p0,k0,w0) converts a filter given by its zeros, poles, and gain; lp2hp(num0,den0,w0) converts a filter given by its numerator and denominator coefficients in decreasing powers of s.
The new filter
where
See also
lp2lp
Lowpass prototype to lowpass filter conversion.
Syntax
use filter (z, p, k) = lp2lp(z0, p0, k0, w0) (num, den) = lp2lp(num0, den0, w0)
Description
lp2lp convert a lowpass analog filter prototype (with unit angular frequency) to a lowpass analog filter with the specified cutoff angular frequency w0. lp2lp(z0,p0,k0,w0) converts a filter given by its zeros, poles, and gain; lp2lp(num0,den0,w0) converts a filter given by its numerator and denominator coefficients in decreasing powers of s.
The new filter
where