4. Use the convolution integral to find f, where f = g*h, and g(t) = et...
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...
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
Problem 4. Use the convolution integral to find the response y(t) of the LTI system with impulse response h(t) to input x(t) a) x(I)-2expl_2t)u(t) , h(1)-expl-t)u(t)
Consider f(t) = cos(9t), g(t) = et. Proceed as in this example and find the convolution f ∗ g of the given functions.
Problem 1 Use the convolution integral to find the zero-state response for x(t)-u(t), and h(t)- eu(t)
5, Compute (f *g)(t) where f(t) = t and g(t) = et by using the definition of the convolution
Solve using convolution integral The signals h(t) and f(t) are as shown in Figure 12(a) and (b), respectively. Compute and sketch the graph of h(t) f(t). 1 h(t)--t+1 f(t)-u(t)-u(t-1) Figure 12(a) Figure 12(b)
2.3.5,2.3.8,2.10-2.3.12 23. (a) Convolution: 1 2-5 b) Convolution: 23.6 Find and sketch the coavolution rt)f) gt) where 2.3.7 Find and sketch the convolution z(t) = f(t)-g(t) where 2.3.8 Sketch the continmous-time signals f(e), 9(t) Find and sketch the coavolution y(t)t) git). f(t)e(t) 23.9 Using the convolation integral, ind the convolution of the signal f()-t with itself. 2.3.10 Find and sketch the convolution of and (t) 2.3.11 Sketch the continmous-time signals f(t),g(t) Find and sketch the coavolution y(t)f(t).git) f(t)-u +2)-ut-2) 2.3.12...
Use the convolution integral to calculate g(x) from h(x-x')=a/[a^2+(x-x')^2] and f(x)=cos(kx). Interpret this physically as a spatial frequency filter. Use the convolution integral to calculate g(x) h(x– x') = a/ [a? + (x - x)?) and f(x) = cos(kx). Interpret physically as a spatial frequency filter. Hint: from this cos(ky)dy a po sin(ky)dy = 0. g(t) = f(t)h(t - t') dt'. J-CO