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Problem 1: Determine the convolution of 3(t) and h(t). h(t) time (s) time...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given bel...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(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...
Q2 (a) Given the signal x(t) and system h(t) as presented in Figure Q2(a). Determine the...
Q2 (a) Given the signal x(t) and system h(t) as presented in Figure Q2(a). Determine the output y(t) using the graphical representation of convolution integral. (7 marks) x(1) h(t) 1 e-'u(t) e-2 (1) 0 Figure Q2(a) Q2 (b) Consider a system as shown in Figure Q2(b). t2 - 1 x(t) y(t) Advance by 1 second Х Figure Q2(b) Find the input-output relation between x(t) and y(t). (i) (1 mark) Examine whether the system is time variant or time invariant. (5...
2. Using direct convolution (i.e., the integral), determine the convolution between r(t) and h(t), where h(t)...
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)
3. Find the continuous-time convolution of r(t) = 10e (i 2)u(t - 2) with h(t) =...
3. Find the continuous-time convolution of r(t) = 10e (i 2)u(t - 2) with h(t) = 5e ( 4)u(t – 4)
(1) For the impulse response (h(t)) and input signal (x(t)) of an LTI system shown below,...
(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)
1. Problem 1: (20 pts) Let 3(t) = u(1 – t) and h(t) = tſu(t) -...
1. Problem 1: (20 pts) Let 3(t) = u(1 – t) and h(t) = tſu(t) - t - 2)). (a) Sketch h(t), 3(1), 2(t - T) and carefully label the values on the axes. (6 pts) (b) Determine y(t) = 3(t)h(t) by performing graphical convolution. No need to sketch y(t). (14 pts)
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to...
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to a Linear Time Invariant system of which the impulse response h(t) is shown as h(t) = { .. 12, -osts-2 elsewhere Compute the output y(t) of the system above using convolution in time domain for all values of time t. [8 marks) (b) The impulse response h[n] of an LTI system is given as a[n] = 4(0.6)”u[n] Determine if the system is stable. [3...
Help please! Problem No. P1: Convolution Below is a Matlab code for performing convolution of two...
Help please!
Problem No. P1: Convolution Below is a Matlab code for performing convolution of two sequences. function [y,ny] conv m(x,nx,h,nh) % Modified convolution routine for signal processing [y,ny] convolution result x,nx] first signal Dh,nh] second signal nyb nx(1)+nh(1); nye nx(length(x)) y-conv (x,h); Use the code to perform convolution of r) 1.2,3,4 and h( 3.2,1 nh (length(h));
Problem 1 Use the convolution integral to find the zero-state response for x(t)-u(t), and h(t)- eu(t)
Problem 1 Use the convolution integral to find the zero-state response for x(t)-u(t), and h(t)- eu(t)
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
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...
Q2 (a) Given the signal x(t) and system h(t) as presented in Figure Q2(a). Determine the output y(t) using the graphical representation of convolution integral. (7 marks) x(1) h(t) 1 e-'u(t) e-2 (1) 0 Figure Q2(a) Q2 (b) Consider a system as shown in Figure Q2(b). t2 - 1 x(t) y(t) Advance by 1 second Х Figure Q2(b) Find the input-output relation between x(t) and y(t). (i) (1 mark) Examine whether the system is time variant or time invariant. (5...
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)
3. Find the continuous-time convolution of r(t) = 10e (i 2)u(t - 2) with h(t) = 5e ( 4)u(t – 4)
(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)
1. Problem 1: (20 pts) Let 3(t) = u(1 – t) and h(t) = tſu(t) - t - 2)). (a) Sketch h(t), 3(1), 2(t - T) and carefully label the values on the axes. (6 pts) (b) Determine y(t) = 3(t)h(t) by performing graphical convolution. No need to sketch y(t). (14 pts)
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to a Linear Time Invariant system of which the impulse response h(t) is shown as h(t) = { .. 12, -osts-2 elsewhere Compute the output y(t) of the system above using convolution in time domain for all values of time t. [8 marks) (b) The impulse response h[n] of an LTI system is given as a[n] = 4(0.6)”u[n] Determine if the system is stable. [3...
Help please!
Problem No. P1: Convolution Below is a Matlab code for performing convolution of two sequences. function [y,ny] conv m(x,nx,h,nh) % Modified convolution routine for signal processing [y,ny] convolution result x,nx] first signal Dh,nh] second signal nyb nx(1)+nh(1); nye nx(length(x)) y-conv (x,h); Use the code to perform convolution of r) 1.2,3,4 and h( 3.2,1 nh (length(h));
Problem 1 Use the convolution integral to find the zero-state response for x(t)-u(t), and h(t)- eu(t)
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