RESAMPLE Change the sampling rate of a signal. !!!!! lower LP corner than Matlab's resample, which gives inadequate antialias filtering !!!!! Y = RESAMPLE(X,P,Q) resamples the sequence in vector X at P/Q times the original sample rate using a polyphase implementation. Y is P/Q times the length of X (or the ceiling of this if P/Q is not an integer). P and Q must be positive integers. RESAMPLE applies an anti-aliasing (lowpass) FIR filter to X during the resampling process, and compensates for the filter's delay. The filter is designed using FIRLS. RESAMPLE provides an easy-to-use alternative to UPFIRDN, relieving the user of the need to supply a filter or compensate for the signal delay introduced by filtering. In its filtering process, RESAMPLE assumes the samples at times before and after the given samples in X are equal to zero. Thus large deviations from zero at the end points of the sequence X can cause inaccuracies in Y at its end points. Y = RESAMPLE(X,P,Q,N) uses a weighted sum of 2*N*max(1,Q/P) samples of X to compute each sample of Y. The length of the FIR filter RESAMPLE applies is proportional to N; by increasing N you will get better accuracy at the expense of a longer computation time. If you don't specify N, RESAMPLE uses N = 10 by default. If you let N = 0, RESAMPLE performs a nearest neighbor interpolation; that is, the output Y(n) is X(round((n-1)*Q/P)+1) ( Y(n) = 0 if round((n-1)*Q/P)+1 > length(X) ). Y = RESAMPLE(X,P,Q,N,BTA) uses BTA as the BETA design parameter for the Kaiser window used to design the filter. RESAMPLE uses BTA = 5 if you don't specify a value. Y = RESAMPLE(X,P,Q,B) uses B to filter X (after upsampling) if B is a vector of filter coefficients. RESAMPLE assumes B has odd length and linear phase when compensating for the filter's delay; for even length filters, the delay is overcompensated by 1/2 sample. For non-linear phase filters consider using UPFIRDN. [Y,B] = RESAMPLE(X,P,Q,...) returns in B the coefficients of the filter applied to X during the resampling process (after upsampling). If X is a matrix, RESAMPLE resamples the columns of X. % Example: % Resample a sinusoid at 3/2 the original rate. tx = 3:3:300; % Time vector for original signal x = sin(2*pi*tx/300); % Define a sinusoid ty = 2:2:300; % Time vector for resampled signal y = resample(x,3,2); % Change sampling rate plot(tx,x,'+-',ty,y,'o:') legend('original','resampled'); xlabel('Time') See also UPFIRDN, INTERP, DECIMATE, FIRLS, KAISER, INTFILT.
0001 function [y, h] = resample( x, p, q, N, bta ) 0002 %RESAMPLE Change the sampling rate of a signal. 0003 %!!!!! lower LP corner than Matlab's resample, which gives inadequate 0004 %antialias filtering !!!!! 0005 % Y = RESAMPLE(X,P,Q) resamples the sequence in vector X at P/Q times 0006 % the original sample rate using a polyphase implementation. Y is P/Q 0007 % times the length of X (or the ceiling of this if P/Q is not an integer). 0008 % P and Q must be positive integers. 0009 % 0010 % RESAMPLE applies an anti-aliasing (lowpass) FIR filter to X during the 0011 % resampling process, and compensates for the filter's delay. The filter 0012 % is designed using FIRLS. RESAMPLE provides an easy-to-use alternative 0013 % to UPFIRDN, relieving the user of the need to supply a filter or 0014 % compensate for the signal delay introduced by filtering. 0015 % 0016 % In its filtering process, RESAMPLE assumes the samples at times before 0017 % and after the given samples in X are equal to zero. Thus large 0018 % deviations from zero at the end points of the sequence X can cause 0019 % inaccuracies in Y at its end points. 0020 % 0021 % Y = RESAMPLE(X,P,Q,N) uses a weighted sum of 2*N*max(1,Q/P) samples of X 0022 % to compute each sample of Y. The length of the FIR filter RESAMPLE applies 0023 % is proportional to N; by increasing N you will get better accuracy at the 0024 % expense of a longer computation time. If you don't specify N, RESAMPLE uses 0025 % N = 10 by default. If you let N = 0, RESAMPLE performs a nearest 0026 % neighbor interpolation; that is, the output Y(n) is X(round((n-1)*Q/P)+1) 0027 % ( Y(n) = 0 if round((n-1)*Q/P)+1 > length(X) ). 0028 % 0029 % Y = RESAMPLE(X,P,Q,N,BTA) uses BTA as the BETA design parameter for the 0030 % Kaiser window used to design the filter. RESAMPLE uses BTA = 5 if 0031 % you don't specify a value. 0032 % 0033 % Y = RESAMPLE(X,P,Q,B) uses B to filter X (after upsampling) if B is a 0034 % vector of filter coefficients. RESAMPLE assumes B has odd length and 0035 % linear phase when compensating for the filter's delay; for even length 0036 % filters, the delay is overcompensated by 1/2 sample. For non-linear 0037 % phase filters consider using UPFIRDN. 0038 % 0039 % [Y,B] = RESAMPLE(X,P,Q,...) returns in B the coefficients of the filter 0040 % applied to X during the resampling process (after upsampling). 0041 % 0042 % If X is a matrix, RESAMPLE resamples the columns of X. 0043 % 0044 % % Example: 0045 % % Resample a sinusoid at 3/2 the original rate. 0046 % 0047 % tx = 3:3:300; % Time vector for original signal 0048 % x = sin(2*pi*tx/300); % Define a sinusoid 0049 % ty = 2:2:300; % Time vector for resampled signal 0050 % y = resample(x,3,2); % Change sampling rate 0051 % plot(tx,x,'+-',ty,y,'o:') 0052 % legend('original','resampled'); xlabel('Time') 0053 % 0054 % See also UPFIRDN, INTERP, DECIMATE, FIRLS, KAISER, INTFILT. 0055 0056 % NOTE-1: digital anti-alias filter is desiged via windowing 0057 0058 % Author(s): James McClellan, 6-11-93 0059 % Modified to use upfirdn, T. Krauss, 2-27-96 0060 % Copyright 1988-2011 The MathWorks, Inc. 0061 % 0062 0063 if nargin < 5, bta = 5; end %--- design parameter for Kaiser window LPF 0064 if nargin < 4, N = 10; end 0065 if abs(round(p))~=p || p==0 0066 error(message('signal:resample:MustBePosInteger', 'P')); 0067 end 0068 if abs(round(q))~=q || q==0 0069 error(message('signal:resample:MustBePosInteger', 'Q')); 0070 end 0071 0072 [p,q] = rat( p/q, 1e-12 ); %--- reduce to lowest terms 0073 % (usually exact, sometimes not; loses at most 1 second every 10^12 seconds) 0074 if (p==1) && (q==1) 0075 y = x; 0076 h = 1; 0077 return 0078 end 0079 pqmax = max(p,q); 0080 if length(N)>1 % use input filter 0081 L = length(N); 0082 h = N; 0083 else % design filter 0084 if( N>0 ) 0085 fc = 1/2/pqmax; 0086 FCFACTOR=0.8; % put corner at Nyquist * 0.8 0087 fc=fc*FCFACTOR; 0088 L = 2*N*pqmax + 1; 0089 h = p*firls( L-1, [0 2*fc 2*fc 1], [1 1 0 0]).*kaiser(L,bta)' ; 0090 % h = p*fir1( L-1, 2*fc, kaiser(L,bta)) ; 0091 else 0092 L = p; 0093 h = ones(1,p); 0094 end 0095 end 0096 0097 Lhalf = (L-1)/2; 0098 isvect = any(size(x)==1); 0099 if isvect 0100 Lx = length(x); 0101 else 0102 Lx = size(x, 1); 0103 end 0104 0105 % Need to delay output so that downsampling by q hits center tap of filter. 0106 nz = floor(q-mod(Lhalf,q)); 0107 z = zeros(1,nz); 0108 h = [z h(:).']; % ensure that h is a row vector. 0109 Lhalf = Lhalf + nz; 0110 0111 % Number of samples removed from beginning of output sequence 0112 % to compensate for delay of linear phase filter: 0113 delay = floor(ceil(Lhalf)/q); 0114 0115 % Need to zero-pad so output length is exactly ceil(Lx*p/q). 0116 nz1 = 0; 0117 while ceil( ((Lx-1)*p+length(h)+nz1 )/q ) - delay < ceil(Lx*p/q) 0118 nz1 = nz1+1; 0119 end 0120 h = [h zeros(1,nz1)]; 0121 0122 % ---- HERE'S THE CALL TO UPFIRDN ---------------------------- 0123 y = upfirdn(x,h,p,q); 0124 0125 % Get rid of trailing and leading data so input and output signals line up 0126 % temporally: 0127 Ly = ceil(Lx*p/q); % output length 0128 % Ly = floor((Lx-1)*p/q+1); <-- alternately, to prevent "running-off" the 0129 % data (extrapolation) 0130 if isvect 0131 y(1:delay) = []; 0132 y(Ly+1:end) = []; 0133 else 0134 y(1:delay,:) = []; 0135 y(Ly+1:end,:) = []; 0136 end 0137 0138 h([1:nz (end-nz1+1):end]) = []; % get rid of leading and trailing zeros 0139 % in case filter is output 0140