{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ece431notesForLec_2007_09_24

ece431notesForLec_2007_09_24 - LinearConvolution The...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: LinearConvolution The linearconvolution oftwosequences x n and y n isdefinedby ( x * y ) n : = ∞ ∑ m =- ∞ x m y n- m . Ifoneofthesequences,say x m ,hasfiniteduration,say x m = 0for m < M 1 and m > M 2 , then ( x * y ) n : = M 2 ∑ m = M 1 x m y n- m . Letusfurthersupposethatweinterestedintheconvolutiononlyfor N 1 ≤ n ≤ N 2 ,sayfor plottingpurposes.Thenincomputingtheconvolution,thevaluesofthesubscriptof y ,that is, n- m ,rangefrom N 1- M 2 to N 2- M 1 .Thepointhereisthattocompute ( x * y ) n for n = N 1 ,..., N 2 requiresonlythevalues x M 1 ,..., x M 2 and y N 1- M 2 ,..., y N 2- M 1 .Forexample, if N 1 = M 1 = 0,thenweneed y- M 2 ,..., y N 2 . [Drawpictures] Letusnowdefineˆ y n : = y n for n = N 1- M 2 ,..., N 2- M 1 andˆ y n : = 0otherwise.A graphicalargumentwith y n- m ,ˆ y n- m ,and x m showsthat ( x * y ) n and ( x * ˆ y ) n areequalfor n = N 1 ,..., N 2 .Fortunately,theconvolutionoftwofinite-lengthsequencesiseasilydone withtheM ATLAB command z=conv(x,yhat) .However,sinceM....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online