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My question is on the aliasing cancellation of the OLA method when spectral modification is involved. The book related to this question is given by this link.

As stated by the webpage, for weak COLA condition, the aliasing cancellation is disturbed by spectral modifications. I am not quite clear about this statement.

In my opinion, spectral modification can NOT disturb aliasing cancellation if reconstruction method is OLA. If sufficient zero is padded on the analysis window and the frame data, time domain aliasing due to circular convolution with the impulse response of the spectral modification is cancelled. When the weak COLA condition is satisfied, we can recover the filtered signal in time domain using the overlap-add method. Such operation is independent of whatever spectral modifications are made as long as sufficient zero-padding is used.

For example, when a M-point periodic Hamming window is used and the hop size between adjacent frames of data is M/2. In this case, the weak COLA condition is met but the strong COLA is not. Whatever spectral modifications are made to the DFT of the frame data, such modifications can be interpretated as a circular convolution with the frame data. Though the frequency responses of the channel filters are heavily aliased from the perspective of downsampled filter bank, the original signal can be perfected reconstructed using the OLA method, which is a time domain method.

What am I missing? Hope you can clarify.

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