4. Graphically determine the discrete convolution of h(t) and x(t) for the case shown below. NOTE:...
Please Write clearly Thank you x(t) ht) 2 2 2.12 Functions x(t) and h(t) have the waveforms shown in Fig. P2.12. Determine and plot y(t) = x(t) *h(t) using the following methods. (a) Integrating the convolution analytically. (b) Integrating the convolution graphically. h 0 0 t(s) t(s) 0 + 1 0 2 Figure P2.12: Waveforms for Problem 2.12.
From homework section of CD: Continuous-time convolution Consider the linear time-invariant system shown below. 7ylt) (t) The input alt) and the impulse response h(t) are shown in the figures below. ht) Time, sec Time, sec Calculate (using convolution) the output of this system, yo).
2. Using direct convolution (i.e., the integral), determine the convolution between r(t) and h(t), where h(t) and r(t) are defined as (note: please do NOT just plug in the formulas we derived in the class): h(t) exp(-2t) u (t) and x(t) = exp(-t)u(t), u(t) is the unit step function. h(t) exp(-t)u (t) and r(t)= exp(-t)u(t)
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...
1. Assume y(t)x(th(t), where x(0) and h(t) are shown below (a) By foldi ng and sliding h(t), use time convolution to determine the numerical value of y(t) to four decimal places at t O seconds. (llustrate the graphical convolution by including sketches.) (b) Repeat part (a) for t = 3 seconds. (c) Repeat part (a) for 8 seconds. (o 3 t (sec) 7 -l t sec) 5 -&t χ(t)
4. Convolution EX4. The input X(t) and impulse response h(t) for a system are given. Using convolution evaluating the system output y(t). X(t)=1 O<t1 h(t)=sin pi*t 0<<2 =0 else where =0 elsewhere Xit) ↑ hlt) E mer
(1) For the impulse response (h(t)) and input signal (x(t)) of an LTI system shown below, find and plot the output response (y(t)) by integrating the convolution analytically h(t) x(t) t (s)
2(a). Compute and plot the convolution of ytryh)x where h(t) t)-u(t-4), x(t)u(t)-u(t-1) and zero else b). Compute and plot the convolution y(n) h(n)*x (n) where h(n)-1, for 0Sns4, x(n) 1, n 0, 1 and zero else.
A digital communication system uses the signals si(t) and s2(t) shown in Fig. 1 to t equally likely bits '0' and '1', respectively. The signaling duration is 4 seconds. The receiver uses a filter h(t) shown in Fig. 2 s1 (t) s2(t) 0 Figure 1: Set of signals in Problem 1 h(t) 0 Figure 2: h(t) in Problem 1 (a) Determine the parameter ri for this system. HINT: Remember that ri is equal to this convolution 81(t) * h(t) evaluated...
8) Convolution Integral (7 points). Given the following signals x(t) and h(t), compute and plot the convolution y(t) = x(t) *h(t). x(t) = u(t+2) - u(t – 4) h(t) = 5u(t)e-2t