Overlap–add method: Difference between revisions

Revision as of 15:32, 22 April 2016

Revision as of 20:09, 4 June 2016

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where &nbsp;<math>y_k[n] \ \stackrel{\mathrm{def}}{=} \ x_k[n]*h[n]\,</math>&nbsp; is zero outside the region [1,&nbsp;''L''&nbsp;+&nbsp;''M''&nbsp;&minus;&nbsp;1]. &nbsp;And for any parameter &nbsp;<math>N\ge L+M-1,\,</math>&nbsp; it is equivalent to the <math>N\,</math>-point [[circular convolution]] of <math>x_k[n]\,</math> with <math>h[n]\,</math>&nbsp; in the region&nbsp;[1,&nbsp;''N''].

The advantage is that the [[circular convolution]] can be computed very efficiently as follows, according to the [[Discrete_Fourier_transformDiscrete Fourier transform#Circular_convolution_theorem_and_crossCircular convolution theorem and cross-correlation_theoremcorrelation theorem|circular convolution theorem]]''':'''

{{NumBlk|:|<math>y_k[n] = \textrm{IFFT}\left(\textrm{FFT}\left(x_k[n]\right)\cdot\textrm{FFT}\left(h[n]\right)\right)</math>|{{EquationRef|Eq.1}}}}

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*{{Cite book

| authorauthor1=Rabiner, Lawrence R.; |author2=Gold, Bernard | title=Theory and application of digital signal processing

| authorlink=

| coauthors=

| title=Theory and application of digital signal processing

| year=1975

| publisher=Prentice-Hall

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}}

*{{Cite book

| authorauthor1=Oppenheim, Alan V.; |author2=Schafer, Ronald W. | title=Digital signal processing

| authorlink=

| coauthors=

| title=Digital signal processing

| year=1975

| publisher=Prentice-Hall

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*{{Cite book

| author=Hayes, M. Horace

| authorlink=

| coauthors=

| title = Digital Signal Processing

| series = Schaum's Outline Series