Let @ denote the convolution operator. If f (t) = 50 e and g(t) = sin...
4. Find the convolution of the following functions a. f(t)=t g(t) = sin 3t b. f(t)=é g(t)=cos2t
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...
Find the convolution f(t) *g(t) for the following problem. f(t) = g(t) = 9 sint (f*g)(t) =
3.34. Let (X.(t) and (x.(e)) denote two statistically independent zero mean stationary Gaussian random processes with common power spec- tral density given by Ste (f) = S, (f) = 112B(f) Watt/Ha Define X (t) X( t) cos(2 fo t) - Xs (t) sin(2r fot) ) - Xs(t) sin(2T fot where fo》 B (c) Find the pdf of X(0). (d) The process X(t) is passed through an ideal bandpass filter with transfer function given by otherwise. Let Y(t) denote the output...
4. Use the convolution integral to find f, where f = g*h, and g(t) = et ult) h(t) = e-2t u(t) Note that both of these are causal to simplify the integration.
Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00 <t< oo using graphical convolution(s). Determine y(t) = h(t) * x(t) for Prob. 5 (cont.) (b) Let zln] = uln] and h[n]-G)nuln] + (-))' hnnDetermine vinl -h) rin) for -00n< oo using graphical convolution(s) Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00
3. This is an exercise about convolution. Consider the signals f and g below, both periodic with T -2. t sin(2t), -1-t 〈 0; (1+1), It _ 0.51, 一1 〈 t 〈 0; 0
Consider f(t) = cos(9t), g(t) = et. Proceed as in this example and find the convolution f ∗ g of the given functions.
all parts -2t e - (13 points) Let f(t) cos 2t, sin 2t) for t 2 0. F() (a) (4 points) Find the unit tangent vector for the curve d (F(t)-v(t)) using the product rule for dt (b) (5 points) Let v(t) = 7'(t). Calculate the dot product and simplify v(t) (c) (4 points) For an arbitrary vector-valued function 7 (t) with velocity vector = 1, what can be said about the relationship between F(t) and v(t)? if F(t) (t)...
please show all your work (The operator ?? denotes convolution.)? PROBLEM sp-10-F.4: For each of the following time-domain signals, select the correct match from the list of Fourier transforms below. Write your answers in the boxes next to the question.(The operator *denotes convolution.) x()u(t +4)- u(t-4) x(1)=?(1-2) * e-1 + in(1-1)*3(1-1) x(t)-cos(rt) * ?(1-4) -00 Each of the time signals above has a Fourier transform that should be in the list below [0] X(jo) not in the list below 40...