(a) Find the Fourier transform X() for the following signal: (10 points) at. otherwise (b) Determine...
(a) Find the Fourier transform X(w) for the following signal: (10 points) a(t) = ostsi 0, otherwise (b) Determine the magnitude spectrum and phase spectrum for X(w). (10 points)
2. (25p) Find the Fourier transform of the following signal. Sketch the amplitude phase spectrum of the signal. x(1) 1 -2 2
Find the signal x(t) whose Fourier Transform X(jω) is as follows: 0 otherwise Note that the magnitude signs around w in the definition of X(jo) mean that it is symmetric around the origin (that is, it is even). Also note that you can solve this problem using direct integration, tables, or a combination.
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)] 2) (Fourier Transforms Using Properties)...
Name 2. (10 points) a) Find an expression for the Fourier Transform of the signal use the tables provided. illutrated below- you may 1.5p 0.5 05 2 1.5 1 0.5 0 0.51 1.5 2 b) Using your result from part (a), find an expression for the Fourier Transform of the signal c) Using your result from part (a), find an expression for the Fourier Transform of the signal d) Note that the signal p(o) illustrated below can be expressed as...
1. (25 p) Find the Fourier transform of the following signal. Sketch the amplitude phase spectrum of the signal. Calculate the power of the signa by using Parseval Theorem. X(t) I 1 1 t
Problem 5 (20 points) Find the time-domain signal corresponding to the Fourier transform X(jw) whose magnitude and phase characteristics are shown in Figure P5. ZX(jw) .W o) -22 Figure P5
6) Answer the following questions: a) (5 points) Using the Fourier transform, find the value of the following integral S. sinc(Be)dt b) (5 points) Find the Amplitude and phase spectra of the following signal x(t) Ae=sin(5t), t20, t<0. 10. c) (5 points) Find the Fourier transform of v(t) 1
(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 .3 Find the Fourier transform of the following periodic signal. Sketch the magnitude and phase spectra x(t) -4? -2? 2? 2 The exponential Fourier series of r(t) is n=0 -98 sin n- Odd 2 0, n- Even