Raised-cosine window for OFDM intersymbol transitions

Calculates a raised-cosine window pair for OFDM windowing. Results in a smooth transition between symbols that causes less interference to adjacent frequency bands.

% *************************************************************
% Raised cosine window for OFDM intersymbol transitions
% *************************************************************
% Use the window for the guard period between adjacent symbols
% to smoothen the waveform transition, limit sidelobes and prevent 
% unwanted emissions into adjacent frequency ranges
%
% reference:
% Data transmission by Frequency Division Multiplexing 
% using the Discrete Fourier Transform
% S.B. Weinstein and Paul M. Ebert
% IEEE transactions on Communications technology, No. 5,
% October 1971
% *************************************************************

% Length of the guard period in samples
n=64; 

index=linspace(0, 1, n+2);
index=index(2:end-1);

windowNextSymbol=(1-cos(pi*index))/2;
windowPreviousSymbol=fliplr(windowNextSymbol);
  
% plot

figure(); title('raised cosine window for OFDM symbol transitions');
xlabel('sample index into the guard period between symbols');
ylabel('window weight');
hold on; 
plot(windowPreviousSymbol, 'r+');
plot(windowNextSymbol, 'b+');
legend({'cyclic extension of symbol i-1', 'cyclic extension of symbol i'});