Overlap–save method: Difference between revisions

Revision as of 20:29, 23 January 2020

Revision as of 20:34, 23 January 2020

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With the substitution  {{math|j ≜ n-kL}},  the task is reduced to computing {{math|y{{sub|k}}(j)}}, for '''''M'''''  ≤  {{mvar|j}}  ≤  '''''L'' +'' M'' − 1'''. These steps are illustrated in the first 3 traces of Figure 1, except that the desired portion of the output (third trace) corresponds to '''''1'''''  ≤  {{mvar|j}}  ≤  '''''L''.{{efn-ua

|Shifting the undesirable edge effects to the last M-1 outputs is a potential run-time convenience, because the IDFT can be computed in the <math>y[n]</math> buffer, instead of being computed and copied. Then the edge effects can be overwritten by the next IDFT. &nbsp; A subsequent footnote explains how the shift is done, by a time-shift of the impulse response.}}

If we periodically extend ''x''_''k''[''n''] with period ''N'' &nbsp;≥&nbsp; ''L''&nbsp;+&nbsp;''M''&nbsp;−&nbsp;1, according to''':'''