Question

Exercise 3 (a). Use the method of truncation to obtain a length L = 2 FIR full-band differentiator filter. The impulse response is: ha[n] = 30mm (b) Obtain the filter's output y given the following input x: x = Table[Triangleklave [n/32], in, e, 63)]; Solution

Answer 1

@ given in Bd (A) = cos Con) - sin(n T) 0 given filter Length L=2 we need to obtain a length L=2 FIR full band differentiater runcation is achieved by multiplying bd [n] by some window function w [n]: which yieeds finite lenge5 Impulse response band of lenges and b -= C3. MU (0) @ h [n] - truncated Impulse response hd (n] - desired Impulse resp : w (n) - window junction let us consider rectangular window win) = si:-(4) ans otherwise na N = L=2 -(22)=n= (+) - (1) En = |-oogena ooh

n=-005 helm) = cos (-0.51) (-0.15) - sin (-001656) a 60.B)? T Ihd 1-00%) = 4 na Ooh hein) = cos(0.57) sin (005) (005) 0.5 ndin) = hd 10.5) - - neo. Moden = os (6) – simbo) % form apply L Hospital nele ! hdco) = - -sin (MT) T - cos(07) X It I 770 1 20 LT) asin (MA) T 4 Sin (na). I hdeo so bloo desired filter efficients are for hen) heo) = o. blo.) = Hlí hl005)=-415 Here 1=2 R=01112

$12= s him in 41%) = 660) C+ 6 20-5) 10m 5 + 6.0.6) 7:5 to.5 * 1. Tres = * (****) 0 *= Table [Tanglemose Colos. ], 40,07632]; 06 X ane - = Table жжя ЧР find output y=? t Input filter him xlm) yon) yen) = 20 * has to apply z transform on boll sides M(7) = x(z) 4(2) Ym) = Table {mangle ware [r32], {n, o, 63y] * I hen hoſ onco 1 -4 = 0,5 n=-0.5.