4. Use the convolution property to derive the Fourier Transform of the signal else
(15 points) Using the convolution property of the Fourier transform and the derivative property of the Fourier transform, show that ) g(0) ) 90) 0& g'(0) (15 points) Using the convolution property of the Fourier transform and the derivative property of the Fourier transform, show that ) g(0) ) 90) 0& g'(0)
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)
Derive and sketch the fourier transform: g(x) = sinc(x/10)*cos(2πx) (where * denotes convolution)
Problem 2. Fourier Transform Find the Fourier transform of the following signal fo) 3- 0 2. -r1/2 This is an alternating polarity sequence of impulses, weighted by e2. You can leave your answer as a convolution.
Use the Amplitude Modulation property of the Fourier Transform to modulate x(t) to the carrier signal m(t). x(t) = t*exp(-100t)u(t), m(t) = cos(2*π*500t). Then show demodulation of the result.
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
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].
how to derive the underlying signal x(t) using the definition of the Inverse Fourier transform Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T) Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)