rest_IdealFilter.m

function [Data_Filtered] = rest_IdealFilter(Data, SamplePeriod, Band)
% FORMAT    [Data_Filtered] = y_IdealFilter(Data, SamplePeriod, Band)
% Input:
% 	Data		    -	2D data matrix (nDimTimePoints * nTimeSeries)
% 	SamplePeriod	-   Sample period, i.e., 1/sample frequency. E.g., TR
%   Band            -   The frequency for filtering, 1*2 Array. Could be:
%                   [LowCutoff_HighPass HighCutoff_LowPass]: band pass filtering
%                   [0 HighCutoff_LowPass]: low pass filtering
%                   [LowCutoff_HighPass 0]: high pass filtering
% Output:
%	Data_Filtered       -   The data after filtering
%-----------------------------------------------------------
% Written by YAN Chao-Gan 120504 based on REST.
% The Nathan Kline Institute for Psychiatric Research, 140 Old Orangeburg Road, Orangeburg, NY 10962, USA
% Child Mind Institute, 445 Park Avenue, New York, NY 10022, USA
% The Phyllis Green and Randolph Cowen Institute for Pediatric Neuroscience, New York University Child Study Center, New York, NY 10016, USA
% ycg.yan@gmail.com


sampleFreq 	 = 1/SamplePeriod;
sampleLength = size(Data,1);
paddedLength = rest_nextpow2_one35(sampleLength); %2^nextpow2(sampleLength);
LowCutoff_HighPass = Band(1);
HighCutoff_LowPass = Band(2);

% Get the frequency index
if (LowCutoff_HighPass >= sampleFreq/2) % All high stop
    idxLowCutoff_HighPass = paddedLength/2 + 1;
else % high pass, such as freq > 0.01 Hz
    idxLowCutoff_HighPass = ceil(LowCutoff_HighPass * paddedLength * SamplePeriod + 1);
end

if (HighCutoff_LowPass>=sampleFreq/2)||(HighCutoff_LowPass==0) % All low pass
    idxHighCutoff_LowPass = paddedLength/2 + 1;
else % Low pass, such as freq < 0.08 Hz
    idxHighCutoff_LowPass = fix(HighCutoff_LowPass * paddedLength * SamplePeriod + 1);
end

FrequencyMask = zeros(paddedLength,1);
FrequencyMask(idxLowCutoff_HighPass:idxHighCutoff_LowPass,1) = 1;
FrequencyMask(paddedLength-idxLowCutoff_HighPass+2:-1:paddedLength-idxHighCutoff_LowPass+2,1) = 1;

FrequencySetZero_Index = find(FrequencyMask==0);

%Remove the mean before zero padding
Data = Data - repmat(mean(Data),size(Data,1),1);

Data = [Data;zeros(paddedLength -sampleLength,size(Data,2))]; %padded with zero

Data = fft(Data);

Data(FrequencySetZero_Index,:) = 0;

Data = ifft(Data);

Data_Filtered = Data(1:sampleLength,:);