COLA Examples

The constant-overlap-add examples we've seen so far are the

• Rectangular window at 0% overlap (hop size $R$ = window size $M$).
• Bartlett window at 50% overlap ( $R\approx M/2$) (Since normally $M$ is odd, `` $R\approx M/2$'' means ``R=(M-1)/2,'' etc.)
• Hamming window at 50% overlap ( $R\approx M/2$)

In addition, we can mention the following cases (referring to window types discussed in Chapter 3):

• Rectangular window at 50% overlap ( $R\approx M/2$)
• Hamming window at 75% overlap ($R=M/4=25$% hop size)
• Any member of the Generalized Hamming family at 50% overlap
• Any member of the Blackman family at 2/3 overlap (1/3 hop size); e.g., blackman(33,'periodic'), $R=11$
• Any member of the $L$-term Blackman-Harris family with $R\approx M/L$.
• Any window with R=1 (``sliding FFT'')

Recall from §3.2.6 that many audio coders use the MLT sine window. The window is applied twice: once before the FFT (the ``analysis window'') and secondly after the inverse FFT prior to reconstruction by overlap-add (the so-called ``synthesis window''). Since the window is effectively squared, it functions as a Hann window for overlap-add purposes (a member of the Generalized Hamming family). As such, it can be used with 50% overlap. More generally, any positive COLA window can be split into an analysis and synthesis window pair by taking its square root.