Problem 2. Fourier Transform Find the Fourier transform of the following signal fo) 3- 0 2....
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...
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
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...
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)...
Find the Fourier Transform of this signal. 1. (45 p) Find the signal corresponding to the following Fourier transforms: X. (W) 0 1 3 W
Problem 5. (Properties of Fourier transform) Consider a continuous time signal x(1) with the following Fourier transform: X(jw) = J 1 - if we l-207, 207] if|wl > 207 (3) Let y(t) = x(26) cos? (507). Sketch Y (w), i.e., the Fourier transform of y(t). (Note that 2 1 + cos(20) cos? (0) = 2
8. (a) Find the Fourier transform of the signal by direct integration. f(t) = ((t-5)+e-Y(-5))u(t-5) (5 points) (b) Use the convolution theorem of Fourier transform, find the convolution of the following signals: (5 points) x(t) = 5e-4tu(t) and h(t) = 7e-3tu(t)
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. (25p) Find the Fourier transform of the following signal. Sketch the amplitude phase spectrum of the signal. x(1) 1 -2 2
Problem 3. The Fourier transform pairs of cosine and sine functions can be written as y(t) = A cos 2nfot = Y(f) = 4 [86f - fo) +8(f + fo)], and y(t) = B sin 2nfot = Y(f) =-j} [8(f - fo) – 8(f + fo]. The FFT code is revised such that the resulting amplitudes in frequency domain should coincide with those in time domain after discarding the negative frequency portion of Fourier transform or the frequency domain after...