HW2_soln_set

# HW2_soln_set - Now lr= r_s which is the desired integral We...

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Now, ryl : ft ur(r -,) cos(2trr)dr dt lr=, r _s which is the desired integral. We now evaluate the value of the integral as ffi*, : sin(2ert)lt=t : o' 2.2t, (a) The desired convolution is (b) Ftom (a), rlnl + hlnl @ I x[klhln- k] k=-oo n O"[email protected]/p)k for n) o /c=0 - Iff*l- o"*' lr[r] for a # o. ' 0-q vlnl : ulnl: q" (n * I)a"ulnl. 31) rr-;)-i n-l 't ) P,(-;)-i ', n S 6 n)6 fE'] utn): {['-*)- {['-]r-- (8/e)(-rlq{4 (8/e)(-L12), (c) For n16, Forn)6, a[nl:4 u[nl - 4 Therefore, ,trl : { (d) The desired convolution is sl"j : f ctrlnl"-kl tb=-oo _ r[O]h[n] + r[tlhln - lJ + u[zlhln -2]+ r[3]h[n - 3] + ulalhln - al _ hlnl+hln- 1l + h[n, -2]+hln- 3l +h[rz - 4].

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,.22. (a) The desired convolution is This may be written as Figure 52.21 ,(r) : t (b) The desired convolution is f€ : l_*"(r)o(t - r)dr _ [' "-or"-P(t-r)dr,f > o Jo &effiu(t) a*p te-atu(t) u: 0 v(t) u\$) : ll"vlo(t - r)dr : Io'on - r)d,r - Iru on - r)d,r. ['"r{r-,)d,r
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HW2_soln_set - Now lr= r_s which is the desired integral We...

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