3. A system is excited by a signal x(t) = rect (2t) and its response is...
3. A continuous-time system with impulse response h'n - 5 rect' is excited by x(1) = 4 rect(21). (a) Find the response y(t) at time 1 = 1/2. (b) Change the excitation from part (a) to x. //\= xlt-1and keep the same impulse response. What is the new responsey.(t) at time 1 =1/2?
Fourier transforms using Properties and Table 1·2(t) = tri(t), find X(w) w rect(w/uo), find x(t) 2. X(w) 3, x(w) = cos(w) rect(w/π), find 2(t) X(w)=2n rect(w), find 2(t) 4. 5, x(w)=u(w), find x(t) Reference Tables Constraints rect(t) δ(t) sinc(u/(2m)) elunt cos(wot) sin(wot) u(t) e-ofu(t) e-afu(t) e-at sin(wot)u(t) e-at cos(wot)u(t) Re(a) >0 Re(a) >0 and n EN n+1 n!/(a + ju) sinc(t/(2m) IIITo (t) -t2/2 2π rect(w) with 40 2r/T) 2Te x(u) = F {r) (u) aXi(u) +X2() with a E...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
1. Signal f(t) : (5 + rect( )) cos(60πt) is mixed with signal cos(60πt) to produce the signal y(t). Subsequently, COS y(t) is low-pass filtered with a system having frequency response H(w) = 4recG ) to produce q(t). Sketch F(w),Y(w), Q(u), and determine q(t) 2. If signal f(t) is not band-limited, would it be possible to reconstruct f(t) exactly from its samples f(nT) taken with some finite sampling interval T> 0? Explain your reasoning
1. Signal f(t) : (5 +...
A CT window signal is given as x(t) = u(t+4) – uſt-4) The frequency response of a CT LTI system is a given as H(jw) = {2e-jw 1w 5 31/16 HV) 0 otherwise if xz(t) = x(t)* 8(t - 16k) is applied to this CT LTI system, k=-00 a) Sketch the magnitude spectrum of the output. b) Sketch the phase spectrum of the output. c) Give the mathematical expression for the output y(t)
Problem 1. (10 points) The signal x()u(-2) is applied to the input of an LTI system whose impulse response IS h(1)=-rect |- 4 (a) Sketch x(t), h(t) and x(r)h(t - 7) (b) Determine y)-x(i)* h() for all possible values of (interval by interval).
4. A linear time invariant system has the following impulse response: h(t) =2e-at u(t) Use convolution to find the response y(t) to the following input: x(t) = u(t)-u(t-4) Sketch y(t) for the case when a = 1
3. Solve the following integral equations using Laplace transforms. (a) (t)= te! - 2e x(u)e"du (b) y(t) 1 - sinht +(1+T)y(t - T)dT. netions
3. Solve the following integral equations using Laplace transforms. (a) (t)= te! - 2e x(u)e"du (b) y(t) 1 - sinht +(1+T)y(t - T)dT. netions
Please finish these questions. Thank you
Given find the Fourier transform of the following: (a) e dt 2T(2 1) 4 cos (2t) (Using properties of Fourier Transform to find) a) Suppose a signal m(t) is given by m()-1+sin(2 fm) where fm-10 Hz. Sketch the signal m(t) in time domain b) Find the Fourier transform M(jo) of m(t) and sketch the magnitude of M(jo) c) If m(t) is amplitude modulated with a carrier signal by x(t)-m(t)cos(27r f,1) (where fe-1000 Hz), sketch...