(15 points) Using the convolution property of the Fourier transform and the derivative property o...
4. Use the convolution property to derive the Fourier Transform of the signal else 4. Use the convolution property to derive the Fourier Transform of the signal else
Using the convolution property of Fourier Transform to find the following convolution: sinc (t) * sinc (4t): [Hint: sinc (t) ön rect(w/2)] sinc(t)sinc(2t) 8 TT 2 sinc(t) п sinc (2t) п sinc (4t) 4
Using the convolution property of Fourier Transform to find the following convolution: sinc (t) * sinc(41) [Hint: sinc(t) TE rect(w/2)) 77 4 sinc (41) 71 sinc(2) TT sinc(t) RICO sinc(t)sinc(20)
need help with these two. thank you! Using the convolution property of Fourier Transform to find the following convolution: sinc(t) * sinc(40) [Hint: sinc(t) rect(w/2)] F TT sinc (4t) TE z sinc (26) TE 2 sinc(t) TT sinc (t) sinc(2t) Question 6 (10 points) Determine poles and zeros of transfer function H(s) 2(3-3) +58 +6 Zero: -3; Poles: -2 and -3 Zero: 3; Poles: -2 and -3 Zero: 2; Poles: -2 and 3 Zero: 0; Poles: 2 and -3
The Fourier transform of a convolution of two functions is equivalent to ( ) the Fourier transform of each individual function a. the cross product b. convoluting c. adding d. multiplying
[b] State and prove frequency shifting property of Fourier transform Also find the fourier transform of gate function. [c] It is given that x[0] =1, x[1]=2, x[2]=1, h[0]=1. Let y[n] be linear convolution of x[n) and h[n]. Given that y[1]=3 and y[2]-4. Find the value of the expression 10y[3]+y[4].
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...
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)...
2. (14 points) This problem shows an example of using the Fourier transform to analyze communication systems. The system in Figure 4, where (t)-f(t)+sin(wt) and has been proposed for amplitude modulation. f(t) + sin(o) Figure 4: System proposed for amplitude modulation. (a) (7 points) The spectrum of the input f(t) is shown in Figure 1, where 2mB o/100. Sketch and label the spectrum Y(w) of the signal y(t). Hint: You will need to use the frequency convolution property of the...
4. (a) Use the convolution theorem to show that otherwise (b) Let a > 0. Use the Fourier transforms of sincx and sin(), together with the basic tools of Fourier transform theory to show the following sin as /sin as 4. (a) Use the convolution theorem to show that otherwise (b) Let a > 0. Use the Fourier transforms of sincx and sin(), together with the basic tools of Fourier transform theory to show the following sin as /sin as