In (9.19) of the previous section, we derived that the FBS reconstruction sum gives

(10.20) |

where . From this we see that if (where is the window length and is the DFT size), as is normally the case, then for . This is the Fourier dual of the ``strong COLA constraint'' for OLA (see §8.3.2). When it holds, we have

(10.21) |

This is simply a gain term, and so we are able to recover the original signal exactly. (Zero-phase windows are appropriate here.)

If the window length is larger than the number of analysis frequencies ( ), we can still obtain perfect reconstruction provided

(10.22) |

When this holds, we say the window is . (This is the dual of the weak COLA constraint introduced in §8.3.1.)

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University