3.5 Determine the output y(t) for the following pairs of input signals x(t) and impulse responses...
determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): (1) x(t) = u(t), h(t) = u(t) (2) x(t) = exp(2t)u(-t), h(t) = exp(-3t)u(t)
Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): iv) x(t) = exp(2t)u(−t), h(t) = exp(−3t)u(t);
Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t) USING CONVOLUTION THEOREM ONLY: iv) x(t) = exp(2t)u(−t), h(t) = exp(−3t)u(t);
By using convolution theorem, not laplace. !!!!!!! Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): (i) x(t)=u(t), h(t)=u(t): (iii) x(1) 11(1) _ 211(-1) + 11( -2), h(1) 11( 1) _ 11(-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)...
Problem 3. Find by convolution for each pair of waveforms the response to the input r(t) of the LTI system with impulse response h(t). Express your result graphically or analytically as you choose. r(t)u(t) x(t) = eta(-t) a(t) h(t) = e-ta(t) h(t)-eu) h(t) -1 h t) x(t) = sin(nt) (u(t)-u(t-2)) h t) 1, t<0; 1-sin(2Tt), t2 0 x(t) = Problem 3. Find by convolution for each pair of waveforms the response to the input r(t) of the LTI system with...
Problem 2 In each step to follow the signals h(t) r (t) and y(t) denote respectively the impulse response. input, and output of a continuous-time LTI system. Accordingly, H(), X (w) and Y (w) denote their Fourier transforms. Hint. Carefully consider for each step whether to work in the time-domain or frequency domain c) Provide a clearly labeled sketch of y(t) for a given x(t)-: cos(mt) δ(t-n) and H(w)-sine(w/2)e-jw Answer: y(t) Σ (-1)"rect(t-1-n) Problem 2 In each step to follow...
In each step to follow, the signals h(t), a(t), and y(t) denote respectively the impulse response, input, and output of a continuous-time LTI system. Accordingly, H(w), X(w) and Y(w) denote their Fourier transforms. Hint: Carefully consider for each step whether to work in the time domain or frequency domain. (b) (25 points) On the axes below, provide a clearly labeled sketch of y(t) for all t given Σ H(w)-( ) sine? (w/8) j2Tt r(t)-e δ(t-n/2) and with sinc(t) = sin(t)/t...
The following functions have impulse responses from discrete and continuous LTI systems. Determine whether each system is causal and convergent a) h[n] = 2n u[3 - n] b) h(t) = u(1 – t) – 1/2e-t u(t) c) h[n] = [1 – (0.99)n ]u[n] d) h(t) = e15t [u(t – 1) – u(t – 100)]
Find the frqeuncy response and impulse response of the system with the output y(t) for the next input x(t) Please, Solve (a) and (c) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult)