gusucode.com > 信号处理工具箱 - signal源码程序 > signal\signal\signal\interp.m
function [odata,b] = interp(idata,r,l,alpha) %INTERP Resample data at a higher rate using lowpass interpolation. % Y = INTERP(X,R) resamples the sequence in vector X at R times % the original sample rate. The resulting resampled vector Y is % R times longer, LENGTH(Y) = R*LENGTH(X). % % A symmetric filter, B, allows the original data to pass through % unchanged and interpolates between so that the mean square error % between them and their ideal values is minimized. % Y = INTERP(X,R,L,ALPHA) allows specification of arguments % L and ALPHA which otherwise default to 4 and .5 respectively. % 2*L is the number of original sample values used to perform the % interpolation. Ideally L should be less than or equal to 10. % The length of B is 2*L*R+1. The signal is assumed to be band % limited with cutoff frequency 0 < ALPHA <= 1.0. % [Y,B] = INTERP(X,R,L,ALPHA) returns the coefficients of the % interpolation filter B. See also DECIMATE. % Author(s): L. Shure, 5-14-87 % L. Shure, 6-1-88, 12-15-88, revised % Copyright (c) 1988-98 by The MathWorks, Inc. % $Revision: 1.1 $ $Date: 1998/06/03 14:43:00 $ % References: % "Programs for Digital Signal Processing", IEEE Press % John Wiley & Sons, 1979, Chap. 8.1. if nargin < 3 l = 4; end if nargin < 4 alpha = .5; end if l < 1 | r < 1 | alpha <= 0 | alpha > 1 error('Input parameters are out of range.') end if abs(r-fix(r)) > eps error('Resampling rate R must be an integer.') end if 2*l+1 > length(idata) s = int2str(2*l+1); error(['Length of data sequence must be at least ',s, 10,... 'You either need more data or a shorter filter (L).']); end % ALL occurrences of sin()/() are using the sinc function for the % autocorrelation for the input data. They should all be changed consistently % if they are changed at all. % calculate AP and AM matrices for inversion s1 = toeplitz(0:l-1) + eps; s2 = hankel(2*l-1:-1:l); s2p = hankel([1:l-1 0]); s2 = s2 + eps + s2p(l:-1:1,l:-1:1); s1 = sin(alpha*pi*s1)./(alpha*pi*s1); s2 = sin(alpha*pi*s2)./(alpha*pi*s2); ap = s1 + s2; am = s1 - s2; ap = inv(ap); am = inv(am); % now calculate D based on INV(AM) and INV(AP) d = zeros(2*l,l); d(1:2:2*l-1,:) = ap + am; d(2:2:2*l,:) = ap - am; % set up arrays to calculate interpolating filter B x = (0:r-1)/r; y = zeros(2*l,1); y(1:2:2*l-1) = (l:-1:1); y(2:2:2*l) = (l-1:-1:0); X = ones(2*l,1); X(1:2:2*l-1) = -ones(l,1); XX = eps + y*ones(1,r) + X*x; y = X + y + eps; h = .5*d'*(sin(pi*alpha*XX)./(alpha*pi*XX)); b = zeros(2*l*r+1,1); b(1:l*r) = h'; b(l*r+1) = .5*d(:,l)'*(sin(pi*alpha*y)./(pi*alpha*y)); b(l*r+2:2*l*r+1) = b(l*r:-1:1); % use the filter B to perform the interpolation [m,n] = size(idata); nn = max([m n]); if nn == m odata = zeros(r*nn,1); else odata = zeros(1,r*nn); end odata(1:r:nn*r) = idata; % Filter a fabricated section of data first (match initial values and first derivatives by % rotating the first data points by 180 degrees) to get guess of good initial conditions % Filter length is 2*l*r+1 so need that many points; can't duplicate first point or % guarantee a zero slope at beginning of sequence od = zeros(2*l*r,1); od(1:r:(2*l*r)) = 2*idata(1)-idata((2*l+1):-1:2); [od,zi] = filter(b,1,od); [odata,zf] = filter(b,1,odata,zi); odata(1:(nn-l)*r) = odata(l*r+1:nn*r); % make sure right hand points of data have been correctly interpolated and get rid of % transients by again matching end values and derivatives of the original data if nn == m od = zeros(2*l*r,1); else od = zeros(1,2*l*r); end od(1:r:(2*l)*r) = [2*idata(nn)-(idata((nn-1):-1:(nn-2*l)))]; od = filter(b,1,od,zf); odata(nn*r-l*r+1:nn*r) = od(1:l*r);