firgr (Digital Filter Design Toolkit, MathScript Function)
Owning Class: singlerate
Syntax
b = firgr(m, f, mag, ripple)
b = firgr(m, f, mag, ripple, tm)
b = firgr(n, f, mag)
b = firgr(n, f, mag, w)
b = firgr(n, f, mag, w, ftype)
b = firgr(n, f, mag, w, ftype, t)
Description
Designs a finite impulse response (FIR) filter using the minimax principle. The FIR filter minimizes the maximum error between the target frequency response and the designed filter frequency response. You can use this function to design the following FIR filters: types IIV linear phase, minimum and maximum phase, ripple constraint, singlepoint band, exact gain control, arbitrary shape, Hilbert transformers, and differentiators. You can specify the filter order to use. This function also can calculate the minimum filter order, including the minimum odd and minimum even filter orders.
Inputs
Name  Description  
m  Specifies the order of the filter. m is a string that accepts the following values:


f  Specifies the frequency points. f is a vector whose values increase monotonically between 0 and 1.  
mag  Specifies the magnitude response of the filter at f. mag is a vector of the same length as f.  
ripple  Specifies the ripple of each frequency band. ripple is a vector whose length must equal length(f)/2. Every two consecutive elements in f make up one frequency band.  
tm  Specifies the type of filter you want to design. If you specify a value for tm, you must set m to 'minorder'. If you do not specify a value for tm, you must set m to either 'mineven' or 'minodd'. tm is a string that accepts the following values:


n  Specifies the order of the filter. n is a nonnegative integer.  
w  Specifies the weight of each frequency point. w is a vector of the same length as f.  
ftype  Specifies the type of each frequency point in f. ftype is a string of the same length as f that accepts a combination of the following values:


t  Specifies the type of filter you want to design. t is a string that accepts the following values:

Outputs
Name  Description 
b  Returns the coefficients of the designed FIR filter. b is a real vector with a length of n+1 or m+1. 
Examples
b = firgr('mineven', [0, 0.4, 0.5, 1], [1, 1, 0, 0], [0.1, 0.02]);
fft_mag = abs(fft(b, 16384));
figure;
plot(0:1/8192:1, fft_mag(1:8193));
b = firgr(24, [0, 0.26, 0.3, 0.6, 0.64, 1], [0, 0, 1, 1, 0, 0], [1, 1, 1, 1, 2, 2], 'nnnnnn', 'minphase');
fft_mag = abs(fft(b, 16384));
figure;
plot(0:1/8192:1, fft_mag(1:8193));
b = firgr(20, [0.2, 0.8], [0.2, 0.8], [1, 1], 'nn', 'differentiator');
fft_mag = abs(fft(b, 16384));
figure;
plot(0:1/8192:1, fft_mag(1:8193));
b = firgr('minorder', [0.04, 0.9], [1, 1], [0.1], 'type III');
fft_mag = abs(fft(b, 16384));
figure;
plot(0:1/8192:1, fft_mag(1:8193));