8 Convolution arid Iiiiaulse ResBunse 186 Figure 8.29: Convolution by iiispection (Example 8.9) t =3 t 1 rectangle ~ is cornplctely superirnpt the higher part of f (z), the rectangle stops being coinplctt~lysuperimposed o.ver the liigher part of f ( r ) and starts being part idly superiniposed over the lower part of f( z), f =4 a t =5 t =G the lower part of f (z) is completely covered by the rectangle, t all overlapping with f (z) stops the rectangle no longer covers aiiy part of thc higher part, aiid oiily partially overlaps the lower part, =7 By m d t iplyiiig the signal with constant sections at the characteristic points, constant products are obtained Deterinirriirg tlir areas gives thr: following va Iucs fol the convolution ii-itcgral: ix t=l j f(-z)g(z)dt- = -m f =3 s” f ( s” j ( )g(ir)dz - 12 -% t= I - ).CI(ir)d? = 12 N 00 t T J’ f ( - )g(z)dr = - 3= -& cv t=6 J’,f(5-z)g(z)dt=3 -T