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Library - lti_filter
lti_filter is a library which provides functions for the design of analog (continuous-time) and digital (discrete-time) linear filters given as LTI (linear time-invariant) zpk (zero/pole/gain) objects. It relies on library filter filter for the filter design and lti for LTI objects.
The following statement makes available functions defined in lti_filter:
use lti_filter
In order to manipulate or display the result, library lti must also be imported.
Functions
zpkbesself
Bessel filter as zpk object.
Syntax
use lti_filter f = zpkbesself(n, w0) f = zpkbesself(n, [wl, wh]) f = zpkbesself(n, w0, 'high') f = zpkbesself(n, [wl, wh], 'stop') f = zpkbesself(..., Ts=ts, var=v)
Description
zpkbesself calculates a Bessel filter. The result is given as a zpk object (zeros, poles and gain).
zpkbesself(n,w0), where w0 is a scalar, gives an analog (continuous-time) lowpass filter of order n with a cutoff frequency of w0.
zpkbesself(n,[wl,wh]), where the second input argument is a vector of two numbers, gives an analog bandpass filter of order 2*n with passband between wl and wh.
zpkbesself(n,w0,'high') gives an analog highpass filter of order n with a cutoff frequency of w0.
besself(n,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives an analog bandstop filter of order 2*n with stopband between wl and wh.
Two named arguments can be specified: sampling period Ts, to get a digital (discrete-time) filter, and variable var, string 's' or 'p' for analog filters (Laplace variable), 'z' or 'q' for digital filter with forward-shift operator, or 'z^-1' or 'q^-1' for digital filter with backward-shift operator.
Cutoff frequencies are specified in rad/s for analog filters and in fraction of the Nyquist frequency (between 0 and 1) for digital filters.
See also
zpkbutter, zpkcheby1, zpkcheby2, zpkellip, besself
zpkbutter
Butterworth filter as zpk object.
Syntax
use lti_filter f = zpkbutter(n, w0) f = zpkbutter(n, [wl, wh]) f = zpkbutter(n, w0, 'high') f = zpkbutter(n, [wl, wh], 'stop') f = zpk(..., Ts=ts, var=v)
Description
zpkbutter calculates a Butterworth filter. The result is given as a zpk object (zeros, poles and gain).
zpkbutter(n,w0), where w0 is a scalar, gives an analog (continuous-time) lowpass filter of order n with a cutoff frequency of w0.
zpkbutter(n,[wl,wh]), where the second input argument is a vector of two numbers, gives an analog bandpass filter of order 2*n with passband between wl and wh.
butter(n,w0,'high') gives an analog highpass filter of order n with a cutoff frequency of w0.
zpkbutter(n,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives an analog bandstop filter of order 2*n with stopband between wl and wh.
Two named arguments can be specified: sampling period Ts, to get a digital (discrete-time) filter, and variable var, string 's' or 'p' for analog filters (Laplace variable), 'z' or 'q' for digital filter with forward-shift operator, or 'z^-1' or 'q^-1' for digital filter with backward-shift operator.
Cutoff frequencies are specified in rad/s for analog filters and in fraction of the Nyquist frequency (between 0 and 1) for digital filters.
See also
zpkbesself, zpkcheby1, zpkcheby2, zpkellip, butter
zpkcheby1
Chebyshev type 1 filter as zpk object.
Syntax
use lti_filter f = zpkcheby1(n, rp, w0) f = zpkcheby1(n, rp, [wl, wh]) f = zpkcheby1(n, rp, w0, 'high') f = zpkcheby1(n, rp, [wl, wh], 'stop') f = zpkcheby1(..., Ts=ts, var=v)
Description
zpkcheby1 calculates a Chebyshev type 1 filter. The result is given as a zpk object (zeros, poles and gain).
zpkcheby1(n,rp,w0), where w0 is a scalar, gives an analog (continuous-time) lowpass filter of order n with a cutoff frequency of w0. Ripples in the passband have a peak-to-peak magnitude of rp dB, i.e. the peak-to-peak ratio is 10^(rp/20).
zpkcheby1(n,rp,[wl,wh]), where the second input argument is a vector of two numbers, gives an analog bandpass filter of order 2*n with passband between wl and wh.
zpkcheby1(n,rp,w0,'high') gives an analog highpass filter of order n with a cutoff frequency of w0.
zpkcheby1(n,rp,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives an analog bandstop filter of order 2*n with stopband between wl and wh.
Two named arguments can be specified: sampling period Ts, to get a digital (discrete-time) filter, and variable var, string 's' or 'p' for analog filters (Laplace variable), 'z' or 'q' for digital filter with forward-shift operator, or 'z^-1' or 'q^-1' for digital filter with backward-shift operator.
Cutoff frequencies are specified in rad/s for analog filters and in fraction of the Nyquist frequency (between 0 and 1) for digital filters.
See also
zpkbesself, zpkbutter, zpkcheby2, zpkellip, cheby1
zpkcheby2
Chebyshev type 2 filter as zpk object.
Syntax
use lti_filter f = zpkcheby2(n, rs, w0) f = zpkcheby2(n, rs, [wl, wh]) f = zpkcheby2(n, rs, w0, 'high') f = zpkcheby2(n, rs, [wl, wh], 'stop') f = zpkcheby2(..., Ts=ts, var=v)
Description
zpkcheby2 calculates a Chebyshev type 2 filter. The result is given as a zpk object (zeros, poles and gain).
zpkcheby2(n,rs,w0), where w0 is a scalar, gives an analog (continuous-time) lowpass filter of order n with a cutoff frequency of w0. Ripples in the stopband have a peak-to-peak magnitude of rs dB, i.e. the peak-to-peak ratio is 10^(rs/20).
zpkcheby2(n,rs,[wl,wh]), where the second input argument is a vector of two numbers, gives an analog bandpass filter of order 2*n with passband between wl and wh.
zpkcheby2(n,rs,w0,'high') gives an analog highpass filter of order n with a cutoff frequency of w0.
zpkcheby2(n,rs,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives an analog bandstop filter of order 2*n with stopband between wl and wh.
Two named arguments can be specified: sampling period Ts, to get a digital (discrete-time) filter, and variable var, string 's' or 'p' for analog filters (Laplace variable), 'z' or 'q' for digital filter with forward-shift operator, or 'z^-1' or 'q^-1' for digital filter with backward-shift operator.
Cutoff frequencies are specified in rad/s for analog filters and in fraction of the Nyquist frequency (between 0 and 1) for digital filters.
See also
zpkbesself, zpkbutter, zpkcheby1, zpkellip, cheby2
zpkellip
Elliptic filter as zpk object.
Syntax
use lti_filter f = zpkellip(n, rp, rs, w0) f = zpkellip(n, rp, rs, [wl, wh]) f = zpkellip(n, rp, rs, w0, 'high') f = zpkellip(n, rp, rs, [wl, wh], 'stop') f = zpkellip(..., Ts=ts, var=v)
Description
zpkellip calculates a elliptic filter, or Cauer filter. The result is given as a zpk object (zeros, poles and gain).
zpkellip(n,rp,rs,w0), where w0 is a scalar, gives an analog (continuous-time) lowpass filter of order n with a cutoff frequency of w0. 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)).
zpkellip(n,rp,rs,[wl,wh]), where the second input argument is a vector of two numbers, gives an analog bandpass filter of order 2*n with passband between wl and wh.
zpkellip(n,rp,rs,w0,'high') gives an analog highpass filter of order n with a cutoff frequency of w0.
zpkellip(n,rp,rs,[wl,wh],'stop'), where the second input argument is a vector of two numbers, gives an analog bandstop filter of order 2*n with stopband between wl and wh.
Two named arguments can be specified: sampling period Ts, to get a digital (discrete-time) filter, and variable var, string 's' or 'p' for analog filters (Laplace variable), 'z' or 'q' for digital filter with forward-shift operator, or 'z^-1' or 'q^-1' for digital filter with backward-shift operator.
Cutoff frequencies are specified in rad/s for analog filters and in fraction of the Nyquist frequency (between 0 and 1) for digital filters.