Question

Problem 1. (10 points) The unit impulse responses of two linear time-invariant systems are hi(t) = 400me-200t u(t) h (t) = 4007e-200nt cos(20,000nt u(t). a) Find the magnitude responses of these systems. b) Determine the filter type and 3 dB cut-off frequency of the first system hi(t). c) How about the second system hz(t)?

Answer 1

2oont h (t) = 40oT e ult) hylt) = 400t é Lot Col(20x13 Jult) -200, Fourier transform of ha) = H (W) ه ه ھ و و at jw 2ookt 200x tje took & 2002t 4ook 2002 + jou magnitude of hitt) - | Hewl 400k 1(2007ft 1999) sette opp 168 9000 h(t) = JAx lot 24 w² let Met Gate No.2, Saidulajab, New Delhi - 1100

wan 400T (200 + w 1 2 - 4007 - Vereast of (400 m2) - (2002) tw? 400X40X10 w 32 x 103 x2 _ 4x102 to a wh = 28x10272 - w, 3100128 * - 200. 3. dB cutoff frequency wa goroff a 400 a at low frequency H, (W) wzo (2007)² + LP.F. at high frequency ( 4,(W) = 0) 4000 12 o tcool We as passes input @ input at the la filter hit, block the So it is is las high frequency and frequencies. frequencies. Low pass filter for

htt) = High ,65) Coll20000at) - H₂ (W) = 1 (H, (Co-2000 ott) + Hi (cut 400 C hitta 2010tw-zovout) zoop +j(6 +20 007) magnitude of het) = how | Hlwyfs-2004 Vamot (0-20 + 2002)2+(wt2oxia At low frequency (corso HW) - 2000 = A say) 200 R + (20x103 4co (2007)? + +(20x1072 WIO At high frequency, w o 470 woo th AR felter response

فارH ماه2 * و می - 2005 - معلمة ب - ( ۱۰ (20) ها + لاه2