Compute the Parks-McClellan optimal FIR filter design Syntaxb = remez(n,f,a)
b = remez(n,f,a,w)
b = remez(n,f,a,'ftype')
b = remez(n,f,a,w,'ftype')
b = remez(...,{lgrid})
b = remez(n,f,'fresp',w)
b = remez(n,f,'fresp',w,'ftype')
b = remez(n,f,{'fresp',p1,p2,...},w)
b = remez(n,f,{'fresp',p1,p2,...},w,'ftype')
stop的用法[b,delta] = remez(...)
[b,delta,opt] = remez(...)人民翻译
Description
remez designs a linear-pha FIR filter using the Parks-McClellan algorithm [1]. The Parks-McClellan algorithm us the Remez exchange algorithm and Chebyshev approximation theory to design filters with an optimal fit between the desired and actual frequency respons. The filters are optimal in the n that the maximum error between the desired frequency respon and the actual frequency respon is minimized. Filters designed this way exhibit an equiripple behavior in their frequency respons and are sometimes called equiripple filters. remez exhibits discontinuities at the head and tail of its impul respon due to this equiripple nature.
b = remez(n,f,a) returns row vector b containing the n+1 coefficients of the order n FIR filter who frequency-amplitude characteristics match tho given by vectors f and a.
The output filter coefficients (taps) in b obey the symmetry relation:
Vectors f and a specify the frequency-magnitude characteristics of the filter:
1.f is a vector of pairs of normalized frequency points, specified in the range between 0 and 1, where 1 corresponds to the Nyquist frequency. The frequencies must be in increasing order.
2.a is a vector containing the desired amplitudes at the points specified in f.
义务教育新课程标准The desired amplitude at frequencies between pairs of points (f(k), f(k+1)) for k odd is the line gment connecting the points (f(k), a(k)) and (f(k+1), a(k+1)).
open houThe desired amplitude at frequencies between pairs of points (f(k), f(k+1)) for k even is unspecified. The areas between such points are transition or "don't care" regions.
3. f and a must be the same length. The length must be an even number.
remez always us an even filter order for configurations with a passband at the Nyquist frequency. This is becau for odd orders, the frequency respon at the Nyquist frequency is necessarily 0. If you specify an odd-valued n, remez increments it by 1.
remez(n,f,a,w) us the weights in vector w to weight the fit in each frequency band. The length of w is half the length of f and a, so there is exactly one weight per band.
b = remez(n,f,a,'ftype') and b = remez(n,f,a,w,'ftype') specify a filter type, where 'ftype' is: 1.'hilbert', for linear-pha filters with odd symmetry (type III and type IV)
The output coefficients in b obey the relation b(k) = -b(n+2-k), k = 1, ..., n + 1. This class of filters includes the Hilbert transformer, which has a desired amplitude of 1 across the entire band.
For example,
h = remez(30,[0.1 0.9],[1 1],'hilbert');
designs an approximate FIR Hilbert transformer of length 31.
2.'differentiator', for type III and type IV filters, using a special weighting technique For nonzero amplitude bands, it weights the error by a factor of 1/f so that the error at low frequencies is much smaller than at high frequencies. For FIR differentiators, which have an amplitude characteristic proportional to frequency, the filters minimize the maximum relative error (the maximum of the ratio of the error to the desired amplitude).
b = remez(...,{lgrid}) us the integer lgrid to control the density of the frequency grid, which has roughly (lgrid*n)/(2*bw) frequency points, where bw is the fraction of the total frequency band interval [0,1] covered by f. Increasing lgrid often results in filters that more exactly match an equiripple filter, but that take longer to compute. The default value of 16 is the minimum value that should be specified for lgrid. Note that the {lgrid} argument must be a 1-by-1 cell array.
b = remez(n,f,'fresp',w) returns row vector b containing the n+1 coefficients of the order n FIR filter who frequency-amplitude characteristics best approximate the respon specified by function fresp. The function is called from within remez with the following syntax.
[dh,dw] = fresp(n,f,gf,w)
The arguments are similar to tho for remez:
1.n is the filter order.
2.f is the vector of normalized frequency band edges that appear monotonically between 0 and 1, where 1 is the Nyquist frequency.
3.gf is a vector of grid points that have been linearly interpolated over each specified frequency band by remez. gf determines the frequency grid at which the respon function must be evaluated, and contains the same data returned by cremez in the fgrid field of the opt structure.
痴情的意思4.w is a vector of real, positive weights, one per band, ud during optimization. w is optional in the call to remez; if not specified, it is t to unity weighting before being pasd to fresp.
5.dh and dw are the desired complex frequency respon and band weight vectors, respectively, evaluated at each frequency in grid gf.
The predefined frequency respon function fresp that remez calls is remezfrf in the signal/private directory.
b = remez(n,f,{'fresp',p1,p2,...},w) allows you to specify additional parameters (p1, p2, etc.) to pass to fresp. Note that b = remez(n,f,a,w) is a synonym for b =
remez(n,f,{'remezfrf',a},w), where a is a vector containing the desired amplitudes at the points specified in f.
b = remez(n,f,'fresp',w,'ftype') and b = remez(n,f,{'fresp',p1,p2,...},w,'ftype') design antisymmetri非主流情侣网名大全
c (odd) rather than symmetric (even) filters, where 'ftype' is either 'd' for a differentiator or 'h' for a Hilbert transformer.
In the abnce of a specification for ftype, a preliminary call is made to fresp to determine the default symmetry property sym. This call is made using the syntax.
sym = fresp('defaults',{n,f,[],w,p1,p2,...})
sdrs
The arguments n, f, w, etc., may be ud as necessary in determining an appropriate value for sym, which remez expects to be either 'even' or 'odd'. If the fresp function does not support this calling syntax, remez defaults to even symmetry.
[b,delta] = remez(...) returns the maximum ripple height in delta.
[b,delta,opt] = remez(...) returns a structure with the following fields.
opt.fgrid: Frequency grid vector ud for the filter design optimization
opt.des: Desired frequency respon for each point in opt.fgrid
opt.wt: Weighting for each point in opt.fgrid
opt.H:Actual frequency respon for each point in opt.fgrid
<：Error at each point in opt.fgrid (opt.des-opt.H)
opt.iextr：Vector of indices into opt.fgrid for extremal frequencies
opt.fextr：Vector of extremal frequencies
Examples
Graph the desired and actual frequency respons of a 17th-order Parks-McClellan bandpass filter:zengzhi
f = [0 0.3 0.4 0.6 0.7 1];
a = [0 0 1 1 0 0];
b = remez(17,f,a);
[h,w] = freqz(b,1,512);
plot(f,a,w/pi,abs(h))
Algorithm
remez is a MEX-file version of the original Fortran code from [1], altered to design arbitrarily long filters with arbitrarily many linear bands. remez designs type I, II, III, and IV linear-pha filters. Type I and type II are the defaults for n even and n odd, respectively, while type III (n even) and type IV (n odd) are obtained with the 'hilbert' and 'differentiator' flags. The different types of filters have different symmetries and certain constraints on their frequency respons (e [5] for more details).
Diagnostics
数学常识
If you get the following warning message, -- Failure to Converge --
Probable cau is machine rounding error.
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it is possible that the filter design may still be correct. Verify the design by checking its frequency respon.
