187 8.5 Applicatioiis x e t-7 f f(S-z)y(z)cJr = x l\iIxking thc\ points (I,())% (3.12) (4,12), (5,9), (6,3), (7,0) and linking them with straight limbs forms the result depicted iii Figure 8.29 Comparing Figures 8.27, 8.28 and 8.29 it becomes clear that the length of the convolution product is equal to the s l i m of thc lcnglits of the two signals The points at the start and end of the corivolutiori product iire also the siiiiis of the iridividual start and e i d points It can casily be shown that this is generally true for the corivdiition of all t h e bounded fiirictions (not just those with ronsOarit sections), by usiiig point of our procedure on the start arid end points of overlap for general signals, as in Figure 8.31 Figure 8.30: Length of the convolution product of' two finite functions T h e prescribed procedim for signals with constant sections can be used on all signals that can be described i on!, by polynomials The convolritioii of these signals willi ckgrccs 1%-arid d s to a convolution product with order K L That ~iieanslhat corivctlution of a t r i a n g i h signal (I{ = 1) with a ngular sigrtal ( L '= 0) would have a corivolnt ion product for rnetl from secondorder parabolic sections ( K +L+ = ) The coiir-oliition ot two triangular signals ( K = L = 1) give5 n third-order convolution product (I< L = 3) + + + + Many irrt,ercsting uses o f signal 1)roccssing are hasrd on convolution relationships Here we will cxaniine two exariiples, rnatched filters arid de-c.onvolutiorr