
2. Find the Fourier transform of 3. Find the Fourier transform of re(r), where e(r) is the Heaviside function. 4. Find the inverse Fourier transform of T h, where fe R3
2. Find the Fourier transform of 3. Find the Fourier transform of re(r), where e(r) is the Heaviside function. 4. Find the inverse Fourier transform of T h, where fe R3
4. a. Using the differentiation theorem and other properties find Fourier transform of X(t)=-2A(-2) b. Find the energy of X(t)=-2A(-2) c. Find the Fourier transform using frequency-translation followed by the time delay theorem. x(t) = n(t-1)exp [j4n(t-1)]
Using the shift or stretch theorem find the Fourier transform of 1 for – 4 <t< -2 b(t) = { 0, otherwise 1 for – 1 <t < 1 given the transform of unit step function a(t) is ā(k) = 2 sin(k) k 0, otherwise b(k) =
Problem 4 (20 points) Given that the Fourier transform of x(t) is find the Fourier transform of the following signals in terms of X(jo) a. y(t)-etx(t 1) b. y(t)-x(-t) x(t-1) c. y(t)tx(t)
Problem 3: a) (2 points) Find the Fourier transform of g(t) = 4u(t)-2u (t-1)-2u (t-2). b) (3 points) Determine the autocorrelation of the signal (t)sin(4rt).
3. If x(t) has the Fourier transform j2π f + 10 Find the Fourier transform of the following signals Hint: use the properties of Fourier transform) a. v(t)-x(1):cos(10π t) d. v(t)X(t) e. v()-e"x(t-1)
M<a a) Find the Fourier transform of b) Graph (x) and its Fourier transform fora c) Hence evaluate f(x) =| 3 d) Deduce r sin u
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier Transform: (a) d(t) -x(t - 2) (d) h(t) = t x( t ) (e) p(t) = x( 2 t ) (f) g(t)-x( t ) cos(2π) (g) s(t) = x2(t ) (h)p()-x(1)* x(t) (convolution)
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal...
Question 4 (2 marks) Attempt 3 f(t)--t Find the Fourier transform of: e-10t 16-+t2)2 Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) =
Question 4 (2 marks) Attempt 3 f(t)--t Find the Fourier transform of: e-10t 16-+t2)2 Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) =
3) [10 pts.] Find the Fourier transform of x(t) = cos(4t)[u(t +4) – ut - 4)] Using only the Fourier the transform table and properties