Question

2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this system? (b) Find and sketch the frequency response magnitude, Hfwl. (c) Find and sketch the frequency response phase, ZHw). (d) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.7 When the continuous-time signal x(t) x(t) = sin(107 t) + cos(51 t) is applied as the input to an unknown continuous-time system, the observed output signal y(t) is y(t) = 3 sin(107 t) + 2 cos(77 t). Which of the following statements is true? Given an explanation for your choice. (a) The system is LTI. (b) The system is not LTI. (c) There is not enough information to decide.

Answer 1

5 h = &A) - t Pourier Hin) = 1 ētuG) Transform - 1 - [foto] = jwti- jot MW) = jw - Hfcw) jwt) ® 14W) = क wzo = w oo wz1 4 (W))=0 D 14 (W)) = D 1Hw TIHOW 1 O 6 from Abort graph we can say that it is righ Pass filter of Ist order o 24 = 8(A-2) l Fit. H(W) = e 122 =HfCw) & IMCwl = 1 - 4

LH(W) – – 2W <H(0) / Radicin 6 ง from com Abor magnitude Response we say that it is All pass filter According to you none of these Note - SEчер еть de) jota

if X ) Fetið XW). x t-to) akta ē Thoto XA) = A cos (Wotto) o system 7 ( = B hoo (wot+o). B = A. IHCwlwzwol p= 0 + LH (w/wzwo Any 2Tf system never charage frequency of anget signal.

х4) = sin (tort) + los (60) Lowozloh to Wozz 50 soul (gee. x 4 = 3sih (lott) + 2 cop tent) د 1۲۲ =وما نام ها loec. Since output hang chinged frequency re. Wor =711 sad/per. Hence system changed the frequency of Input signal. Honce it is not LTE system ®

Note XA) = A coolen fot to) - A los (wot to Input I LITI. system H(W) Dyq Loutput) or HE output Yo = = B coolenfot + o) coo (wot to) B = A TH(wo) Ins-100 FT = 0 + LHCW/o-wozotkralfato fato * LTI system Mever change frequency of input fignal Hence only magnitude And Angle will be changed of suputo