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Commit d2280a3e authored by Achilles Kappis's avatar Achilles Kappis
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Update winSincFracDel.m to fix errors and bugs and provide four window functions

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Signal Processing/Generic/MATLAB/Functions/winSincFracDel.m
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− 75
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...@@ -12,8 +12,8 @@ ...@@ -12,8 +12,8 @@
% -------------------------------------------------- % --------------------------------------------------
% Input % Input
% %
% delay [numeric]: The delay in samples. This must be a non-negative real % del [numeric]: The delay in samples. This must be a non-negative real
% scalar. % scalar.
% %
% len [numeric] (Optional): This is the length of the filter. This must be % len [numeric] (Optional): This is the length of the filter. This must be
% a positive real integer. If this values is less % a positive real integer. If this values is less
...@@ -21,18 +21,16 @@ ...@@ -21,18 +21,16 @@
% equals the "delay" value rounded up. % equals the "delay" value rounded up.
% [Default: ceil(delay)]. % [Default: ceil(delay)].
% %
% win [numeric] (Optional): A window to apply to the FIR filter. This can % winFun [string/char, numeric] (Optional): Windowing functions to be
% be a vector in which case the same window will % applied to the truncated sinc
% be applied to the filter for all signals, or it % function. The available options
% can be a matrix in which case each column will % are "Rectangular", "Hann" and
% contain the window corresponding to the filter % "Hamming" and are not
% for each signal. The number of rows must be % case-sensitive. Additionally, a
% equal to "len" and the number of columns to the % non-negative scalar can be
% number of columns of "sig". If left empty, no % given to be used as the
% window is applied. It has to be noted that the % parameter for a Kaiser window.
% provided window has to be shifted by "delay" % [Default: "Rectangular"].
% samples.
% [Default: []].
% %
% sig [numeric] (Optional): The signal(s) to be delayed in the time-domain. % sig [numeric] (Optional): The signal(s) to be delayed in the time-domain.
% This can be a matrix with each column being a % This can be a matrix with each column being a
...@@ -52,74 +50,75 @@ ...@@ -52,74 +50,75 @@
% -------------------------------------------------- % --------------------------------------------------
% Output % Output
% %
% delFilt [numeric]: The fractional delay windowed-sinc FIR filter(s). If % sincFilt [numeric]: The fractional delay windowed-sinc FIR filter(s).This
% multiple windows are provided then a matrix is % argument is a vector with the FIR filter. This is the
% returned with each column corresponding to the filter % causal version of the filter. If the non-causal
% for each signal. Otherwise, this argument is a vector % version is required, shift to the left by "causDel".
% with the FIR filter.
% %
% intDel [numeric]: The causal latency of the filter. This value % causDel [numeric]: The delay required to make the filter causal. This
% corresponds to half the length of the filter. % value corresponds to half the length of the filter.
% %
% causalFilt [numeric]: The filter after left shifting "intDel" samples to % dSig [numeric]: The delayed signal(s). The length of each signal is equal
% the left. % to that of the original. If the delay is longer than the
% % original signal vector, a zeroed vector is returned (with
% delSig [numeric]: The delayed signal(s). The length of each signal is % possible artefacts from the filtering process). Only
% equal to that of the original. If the delay is % returned if a signal is provided, otherwise an empty
% longer than the original signal vector, a zeroed vector % array is returned.
% is returned (with possible artefacts from the filtering
% process). Only returned if a signal is provided,
% otherwise an empty array is returned.
%
% causalSig [numeric]: The delayed signal(s) shifted to the left by the
% causal delay of the filter.
% %
% -------------------------------------------------- % --------------------------------------------------
% Notes % Notes
% %
% - The function uses time-domain convolution, which can be quite slow for % - The function uses time-domain convolution, which can be quite slow for
% long signals. If the "delSig" is not asked for this calculation is % long signals. If the "dSig" is not required this calculation is
% omitted so, when the signals are not needed (or want to perform % omitted so, when the signals are not needed (or want to perform
% frequency-domain convolution manually), use only one output argument. % frequency-domain convolution manually), use only one output argument.
%
% -------------------------------------------------- % --------------------------------------------------
function [delFilt, intDel, causalFilt, delSig, causalSig] = winSincFracDel(delay, len, win, sig, sigLen) function [sincFilt, causDel, dSig] = winSincFracDel(del, len, winFun, sig, sigLen)
% ==================================================== % ====================================================
% Check for number of arguments % Check for number of arguments
% ==================================================== % ====================================================
narginchk(1, 5); narginchk(1, 5);
nargoutchk(0, 5); nargoutchk(0, 3);
% ==================================================== % ====================================================
% Validate input arguments % Validate input arguments
% ==================================================== % ====================================================
% Validate mandatory arguments % Validate mandatory arguments
validateattributes(delay, "numeric", {'scalar', 'real', 'nonnegative', 'nonnan', 'nonempty', 'finite'}, mfilename, "Delay in samples", 1); validateattributes(del, "numeric", {'scalar', 'real', 'nonnegative', 'nonnan', 'nonempty', 'finite'}, mfilename, "Delay in samples", 1);
% Validate optional arguments % Validate optional arguments
if nargin > 1 && ~isempty(len) if nargin > 1 && ~isempty(len)
validateattributes(len, "numeric", {'scalar', 'integer', 'real', 'finite', 'nonnan', 'nonnegative'}, mfilename, "Filter length", 2); validateattributes(len, "numeric", {'scalar', 'integer', 'real', 'finite', 'nonnan', 'nonnegative'}, mfilename, "Filter length", 2);
if len < delay if len < del
warning("winSincFracDel(): The length of the filter cannot be less than the delay, setting equal to 'delay',"); warning("winSincFracDel(): The length of the filter cannot be less than the delay, setting equal to 'delay',");
len = ceil(delay); len = ceil(del);
end end
else else
len = ceil(delay); len = ceil(del);
end end
if nargin > 2 && ~isempty(win) if nargin > 2 && ~isempty(winFun)
validateattributes(win, "numeric", {'nonnan', '2d', 'real', 'finite', 'nrows', len}, mfilename, "Window(s) to be applied", 3); validateattributes(winFun, {'char', 'string', 'numeric'}, {'nonempty'}, mfilename, "Window to be applied to the truncated sinc function (or the alpha parameter for a Kaiser window)", 3);
if ischar(winFun) || isStringScalar(winFun)
validatestring(winFun, ["Rectangular", "Hann", "Hamming"], mfilename, "Window to be applied to the truncated sinc function", 3);
winFun = string(winFun);
elseif isscalar(winFun)
validateattributes(winFun, {'numeric'}, {'nonempty', 'nonnan', 'finite', 'nonnegative', 'real', 'scalar'}, mfilename, "Alpha parameter for a Kaiser window to be applied to the truncated sinc function", 3);
end
else else
win = ones(len, 1); winFun = "rectangular";
end end
if nargin > 3 && ~isempty(sig) if nargin > 3 && ~isempty(sig)
validateattributes(sig, "numeric", {'2d', 'nonempty', 'real'}, mfilename, "Signal(s) to be delayed", 4); validateattributes(sig, "numeric", {'2d', 'nonempty', 'real'}, mfilename, "Signal(s) to be delayed", 4);
if size(win, 2) == 1 if size(winFun, 2) == 1
win = repmat(win, 1, size(sig, 2)); winFun = repmat(winFun, 1, size(sig, 2));
else else
if size(win, 2) ~= size(sig, 2) if size(winFun, 2) ~= size(sig, 2)
error("Number of windows must match the number of signals provided"); error("Number of windows must match the number of signals provided");
end end
end end
...@@ -135,46 +134,50 @@ function [delFilt, intDel, causalFilt, delSig, causalSig] = winSincFracDel(delay ...@@ -135,46 +134,50 @@ function [delFilt, intDel, causalFilt, delSig, causalSig] = winSincFracDel(delay
end end
% ==================================================== % ====================================================
% Generate FIR filter % Generate FIR filter for fractional delay
% ==================================================== % ====================================================
delFilt = -len + 1:len; delFilt = delFilt.'; % Filter sample indices idx = (-len + 1:len).'; % Filter sample indices
intDel = -floor(delFilt(1)/2); % The causal delay of the filter causDel = -floor(idx(1)/2); % The causal delay of the filter
delFilt = sinc(delFilt - delay); % Calculate the filter sincFilt = sinc(idx - del); % Calculate the filter
% Keep only the central part of the filter to match length asked for
delFilt = delFilt(intDel + 1:intDel + len);
% Replicate filter and apply window function
delFilt = repmat(delFilt, 1, size(sig, 2)) .* win;
% ==================================================== % ====================================================
% Filter the signals % Apply windowing
% ==================================================== % ====================================================
% Return the shifted filter fracDel = abs(rem(del, 1)); % Total filter delay
if nargout > 2
causalFilt = delFilt(intDel:end);
end
if nargout > 3 % Generate window
for idx = size(sig, 2):-1:1 if isstring(winFun)
delSig(:, idx) = conv(sig, delFilt, "full"); switch lower(winFun)
case "hann"
win = sin(pi * (idx - fracDel)/len).^2;
case "hamming"
alpha = 25/46;
win = alpha - (1 - alpha) * cos(2 * pi * (idx - fracDel)/len);
otherwise % Rectangular
win = ones(length(idx), 1);
end end
else
% Kaiser window
win = besseli(0, pi * winFun * sqrt(1 - (2 * (idx - del)/len).^2))/besseli(0, pi * winFun);
end end
% Shift signal to the left by the amount of the "causal" delay of the filter % Shift window function to centre on sinc's peak
if nargout > 4 if ~isscalar(winFun)
causalSig = delSig(intDel:end, :); win = delayseq(win, floor(del) + causDel);
end end
% Return the length of the signal asked for % Apply window function and keep only the causal part up to the length of the filter
if strcmpi(sigLen, "Same") sincFilt = sincFilt(causDel + 1:causDel + len) .* win(causDel + 1:causDel + len);
if nargout > 3
delSig = delSig(1:size(sig, 1), :);
end % ====================================================
if nargout > 4 % Filter the signals
causalSig = causalSig(1:size(sig, 1), :); % ====================================================
if nargout > 2
for idx = size(sig, 2):-1:1
dSig(:, idx) = conv(sig, sincFilt, lower(sigLen));
end end
end end
end end
\ No newline at end of file
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