fircls1 (Signal Processing Toolbox)

Design a constrained least square filter for lowpass and highpass linear phase FIR filters

Syntax

b = fircls1(n,wo,dp,ds)
b = fircls1(n,wo,dp,ds,'high')
b = fircls1(n,wo,dp,ds,wt)
b = fircls1(n,wo,dp,ds,wt,'high')
b = fircls1(n,wo,dp,ds,wp,ws,k)
b = fircls1(n,wo,dp,ds,wp,ws,k,'high')
b = fircls1(n,wo,dp,ds,...,'design_flag')

Description

b = fircls1(n,wo,dp,ds) generates a lowpass FIR filter b, where n+1 is the filter length, wo is the normalized cutoff frequency in the range between 0 and 1 (where 1 corresponds to the Nyquist frequency), dp is the maximum passband deviation from 1 (passband ripple), and ds is the maximum stopband deviation from 0 (stopband ripple).

b = fircls1(n,wo,dp,ds,'high') generates a highpass FIR filter b. fircls1 always uses an even filter order for the highpass configuration. This is because for odd orders, the frequency response at the Nyquist frequency is necessarily 0. If you specify an odd-valued n, fircls1 increments it by 1.

b = fircls1(n,wo,dp,ds,wt) and

b = fircls1(n,wo,dp,ds,wt,'high') specifies a frequency wt above which (for wt > wo) or below which (for wt < wo) the filter is guaranteed to meet the given band criterion. This will help you design a filter that meets a passband or stopband edge requirement. There are four cases:

Lowpass:

0 < wt < wo < 1: the amplitude of the filter is within dp of 1 over the frequency range 0 < < wt.
0 < wo < wt < 1: the amplitude of the filter is within ds of 0 over the frequency range wt < < 1.

Highpass:

0 < wt < wo < 1: the amplitude of the filter is within ds of 0 over the frequency range 0 < < wt.
0 < wo < wt < 1: the amplitude of the filter is within dp of 1 over the frequency range wt < < 1.

b = fircls1(n,wo,dp,ds,wp,ws,k) generates a lowpass FIR filter b with a weighted function, where n+1 is the filter length, wo is the normalized cutoff frequency, dp is the maximum passband deviation from 1 (passband ripple), and ds is the maximum stopband deviation from 0 (stopband ripple). wp is the passband edge of the L2 weight function and ws is the stopband edge of the L2 weight function, where wp < wo < ws. k is the ratio (passband L2 error)/(stopband L2 error)

b = fircls1(n,wo,dp,ds,wp,ws,k,'high') generates a highpass FIR filter b with a weighted function, where ws < wo < wp.

b = fircls1(n,wo,dp,ds,...,'design_flag') enables you to monitor the filter design, where 'design_flag' can be

'trace', for a textual display of the design table used in the design
'plots', for plots of the filter's magnitude, group delay, and zeros and poles
'both', for both the textual display and plots

Note In the design of very narrow band filters with small dp and ds, there may not exist a filter of the given length that meets the specifications.

Examples

Design an order 55 lowpass filter with a cutoff frequency at 0.3:

n = 55; wo = 0.3;
dp = 0.02; ds = 0.008;
b = fircls1(n,wo,dp,ds,'plots'); % Plot magnitude response

Algorithm

The algorithm is a multiple exchange algorithm that uses Lagrange multipliers and Kuhn-Tucker conditions on each iteration.

See Also

fircls, firls, remez

References

[1] Selesnick, I.W., M. Lang, and C.S. Burrus, "Constrained Least Square Design of FIR Filters without Specified Transition Bands," Proceedings of the IEEE Int. Conf. Acoust., Speech, Signal Processing, Vol. 2 (May 1995), pp. 1260-1263.

[2] Selesnick, I.W., M. Lang, and C.S. Burrus, "Constrained Least Square Design of FIR Filters without Specified Transition Bands," IEEE Transactions on Signal Processing, Vol. 44, No. 8 (August 1996).

fircls firgauss