Periodic Windows

Be careful to define your own windows for exact overlap-add, or else at least check the definitions in use to make sure they work. E.g., in Matlab:

• hamming(M) $\isdef$
  .54 - .46*cos(2*pi*(0:M-1)'/(M-1));
  gives constant overlap-add for $R=(M-1)/2$ , $(M-1)/4$ , etc., when endpoints are divided by 2 or one endpoint is zeroed
• hanning(M) $\isdef$
  .5*(1 - cos(2*pi*(1:M)'/(M+1)));
  does not give constant overlap-add for $R=(M-1)/2$ , but does for $R=(M+1)/2$

• blackman(M) $\isdef$
  (.42 - .5*cos(2*pi*(0:M-1)/(M-1)) + .08*cos(4*pi*(0:M-1)/(M-1)))';
  gives constant overlap-add for $R=(M-1)/3$ when $M$ is odd and $R$ is an integer, and $R=M/3$ when $M$ is even and $R$ is integer