function frameT = iFilterbank(frameF, frameType, winType)
%Implementation of the Inverse Filter Bank step
%   Usage frameT = iFilterbank(frameF, frameType, winType), where:
%       Inputs
%       - frameF is the frame in the frequency domain, in MDCT coefficients
%       representation containing both channels of the audio stored in an
%       array of dimensions 1024X2
%       - frameType is the type of the current frame in string
%       representation, can be one of "OLS" (ONLY_LONG_SEQUENCE), "LSS"
%       (LONG_START_SEQUENCE), "ESH" (EIGHT_SHORT_SEQUENCE), "LPS"
%       (LONG_STOP_SEQUENCE)
%       - winType is the type of the window selected, can be one of "KBD",
%       "SIN"
%
%       Output
%        - frameT is a frame in the time domain, containing both channels of
%       the audio stored in an array of dimensions 2048X2

    % Declares persistent windows variables and initializes if empty
    persistent kaiserWindowLong kaiserWindowShort sinWindowLong sinWindowShort;
    if isempty(kaiserWindowLong) || isempty(kaiserWindowShort) || ...
            isempty(sinWindowLong) || isempty(sinWindowShort)
        kaiserLong = kaiser(1025, 6*pi);
        kaiserSumLong = sum(kaiserLong);
        kaiserShort = kaiser(129, 4*pi);
        kaiserSumShort = sum(kaiserShort);

        kaiserWindowLong(1:1024) = movsum(kaiserLong(1:1024), [1024 0]);
        kaiserWindowLong(1025:2048) = movsum(flipud(kaiserLong(1:1024)), [0 1024]);
        kaiserWindowLong = sqrt(kaiserWindowLong ./ kaiserSumLong);
        
        sinWindowLong = sin(pi * ((0:2047) + 0.5) / 2048);
        
        kaiserWindowShort(1:128) = movsum(kaiserShort(1:128), [128 0]);
        kaiserWindowShort(129:256) = movsum(flipud(kaiserShort(1:128)), [0 128]);
        kaiserWindowShort = sqrt(kaiserWindowShort ./ kaiserSumShort);
        
        sinWindowShort = sin(pi * ((0:255) + 0.5) / 256);
    end

    frameT(2048, 2) = 0;

    % Applies appropriate window to the frame
    for channel=1:2
        if strcmp(frameType, 'OLS')
            frameT(:, channel) = imdct4(frameF(:, channel));

            if strcmp(winType, 'KBD')
                frameT(:, channel) = frameT(:, channel) .* kaiserWindowLong(:);
            elseif strcmp(winType, 'SIN')
                frameT(:, channel) = frameT(:, channel) .* sinWindowLong(:);
            else
                error('filterbank, l[20]: Unsupported window type input!')
            end
        elseif strcmp(frameType, 'LSS')
            frameT(:, channel) = imdct4(frameF(:, channel));

            if strcmp(winType, 'KBD')
                frameT(1:1024, channel) = frameT(1:1024, channel) .* kaiserWindowLong(1:1024)';
                frameT(1473:1600, channel) = frameT(1473:1600, channel) .* kaiserWindowShort(129:end)';
                frameT(1601:end, channel) = 0;
            elseif strcmp(winType, 'SIN')
                frameT(1:1024, channel) = frameT(1:1024, channel) .* sinWindowLong(1:1024)';
                frameT(1473:1600, channel) = frameT(1473:1600, channel) .* sinWindowShort(129:end)';
                frameT(1601:end, channel) = 0;
            else
                error('filterbank, l[20]: Unsupported window type input!')
            end
        elseif strcmp(frameType, 'LPS')
            frameT(:, channel) = imdct4(frameF(:, channel));

            if strcmp(winType, 'KBD')
                frameT(1:448, channel) = 0;
                frameT(449:576, channel) = frameT(449:576, channel) .* kaiserWindowShort(1:128)';
                frameT(1025:end, channel) = frameT(1025:end, channel) .* kaiserWindowLong(1025:end)';
            elseif strcmp(winType, 'SIN')
                frameT(1:448, channel) = 0;
                frameT(449:576, channel) = frameT(449:576, channel) .* sinWindowShort(1:128)';
                frameT(1025:end, channel) = frameT(1025:end, channel) .* sinWindowLong(1025:end)';
            else
                error('filterbank, l[20]: Unsupported window type input!')
            end
        elseif strcmp(frameType, 'ESH')
            for subFrameIndex = 1:8
                subFrame = imdct4(frameF((subFrameIndex - 1) * 128 + 1:subFrameIndex * 128, channel));

                if strcmp(winType, 'KBD')
                    subFrame = subFrame .* kaiserWindowShort';
                elseif strcmp(winType, 'SIN')
                    subFrame = subFrame .* sinWindowShort';
                end
                
                frameT(448 + (subFrameIndex - 1) * 128 + 1:448 + (subFrameIndex + 1) * 128, channel) = ...
                    frameT(448 + (subFrameIndex - 1) * 128 + 1:448 + (subFrameIndex + 1) * 128, channel) + subFrame;
            end
        end
    end
end