English: Depiction of the implementation and operation of a Weighted Overlap Add (WOLA) channelizer (DTFT sampler). Wrap-around of a circular input buffer is used to offset phase discontinuities, caused by lack of a true time reference for the Fourier transform (DFT).[1][2]
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With no frequency or time decimation, the channelizer's DFT stage (fixed time-reference) calculation would be:
With frequency decimation by 4 and time-decimation by 2, it becomes:
The phase-correcting sequence is equivalent to which repeats periodically.
The diagram shows that these corrections are produced automatically, by using the buffer's natural wrap-around characteristic as a time-reference. No buffer unwrapping logic or phase-correcting logic is required. Or, in other words (Multirate Digital Signal Processing, p. 321 ),
The modulation to convert the short-time spectrum from the sliding to the fixed-time references can be achieved without multiplication by recognizing that a modulo K shift of the (time-domain) sequence at the input of the DFT introduces a linear phase-shift of the DFT (frequency-domain).
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Depiction of the implementation and operation of a Weighted Overlap-Add (WOLA) channelizer