Problem 2 Consider a continuous-time LTI system whose frequency response is given by 2 sin(40 (a)...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t) 5. (12 points) Consider a continuous-time LTI system whose frequency response is...
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...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
2.7.5 The impulse response of a continuous-time LTI system is given by (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) = δ(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...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
Consider a discrete-time LTI system with impulse response Sketch the magnitude of the frequency response of the system. Provide enough details in your sketch to convey the pattern. sin((2n/3)n hln h[n] =
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
Consider a continuous-time LTI system S with impulse response h(t) = 2(u(t + 1)-u(t 1)). Determine the values of the amplitude scaling and the tme shifting that takes place when each of the following input signals is provided to the system S. Don't use the convolution integral, instead use the result about how LTI systems respond to complex exponential signals. (a) x(t) 2 (b) x(t) ej0.5Tt (c) x(t) = e-j0.5πt (d) x(t) = e-jmt (e) x(t) = cos (0.5t) (f)...
This is a fourier series/ transform question Consider an LTI system whose response to the input x)lee3ut) is y)12e-2e4Ju) (a) Find the frequency response of this system. (b) Determine the system's impulse response (c) Find the differential equation relating the input and the output of this system.
1. (20 p) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t) = el-tuſt - 1)for an input signal x(t) = u(t) - ut - 3). 2. (20p) Consider an input x[n] and an unit impulse response h[n] given by n-2 x[n] = (4)”- u[n – 2] h[n] = u(n + 2] Determine and plot the output y[n] = x[n] *h[n].