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Find the even and odd parts of each of these CT functions 48. cos(Tt) 8 g(t)...
2. Problem 3.16 in the text. Find and graph the even and odd parts of these functions. g[r] = u[n]=u[n=4] (a) g[n] = e"* u[n] -n/4 (b) g[n] = cos(2m /4) (c) g[r] = sin(2m/4)u[1] (d)
A. By hand, find the Fourier transform of g(t)-cos(4t)+ cos(5t) Page 2 of3 B. Now assume that g(t) can be observed for only a finite time, say T seconds. Then, t-T/2 what we observe is actually y(t) g (t)rect . Find (analytically) the Fourier transtorm of y(t). Write your answer in terms of sinc functions. A. By hand, find the Fourier transform of g(t)-cos(4t)+ cos(5t) Page 2 of3 B. Now assume that g(t) can be observed for only a finite...
1. If fand g are both even functions, is the product fg even? If f and g both odd functions, is fg odd? What if f is even and g is odd? Justify your answers. (10 points) Find the domain g(x) =-. (10 points) 2. of the composited function fog, where f(x)=x+ and x +1 x+2 3. Let ifx <1 g(x) = x-3 ifx >2 Evaluate each of the following, if it exists. (10 points) lim g(x) lim gx)(i) lim...
Odd and Even Functions An even function has the property f(x) =f(-x). Consider the function f(x) Now, f (-a)-(-a)"-d f(a) An odd function has the property f(-x)-f(x). Consider the function f(x) Now, f (-a) = (-a)' =-a3 =-f(a) Declarative & Procedural Knowledge Comment on the meaning of the definitions of even and odd functions in term of transformations. (i) (ii) Show that functions of the formx) are even. bx2 +c Show, that f(x) = asin xis odd and g(x) =...
Use the even-odd and periodic properties of the trigonometric functions to simplify. a) csc(t) - 4 csc(-t) b) -2 sin(3t + 2) - 3 sin(-3t)
Q1) For the continuous time signal below, x(t)=1+t (a) Determine the even and odd parts of the signal. (b) Sketch the signal from t = -3 to t = 3. (c) Explain why the signal does not possess BIBO stability.
For the signal x(t)= 3 cos(2+)- 41t+1) 4 205! t €600,00) a) Find the even xect) and odd part Xolt) of this signal. bl Plot the part Xolt).
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 f(t) = 14 + cos 3t + 3e-2t 2. 2 h(t) = (1 - 3t)? (Hint: expand...) 3. 2 g(t) = t sin’t (Hint: use half angle formula first...) 4. 2 h(t) = e-2 cos(v3t) - tet
8. Find the Laplace transform e{f(t)} ( 3 points each) . a. f(t) = 7e4t – 2 cosh(5t) b. f(t) = 8 cos(2t) + 7 sinh(4t) – 5t4
2- In cach of the following, we specify the Fourier series coefficients of a CT signal that i periodic with period To 4. Determine the signal x(t) in each case k 0 a) a sin ,k 0 km -j= ei= (j* = e#. Hint: using Euler's formula: Jkl3 jk b) a fo.0therwise -4 (1,k even c) a 2.k odd Hint: Suppose x(t) 8(t-kT) ke- is an impulse train with impulses spaced every T seconds apart (Figure 2). This is a...