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Using the derivation property determine the Fourier Transform of the following signal
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 modulation property)
(a) Determine the Fourier transform of the sequence 0, otherwise. (b) Consider the sequence win-ı弡ーcos(쮜. 2π n 0 otherwise. Sketch win] and express We), the Fourier transform of win], in terms of R (el, the Fourier transform of In]. (Hint First express win] in terms of In] and the complex exponentials el (2M) and el 2n/M)
(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)
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.
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...
(a) Find the Fourier transform X() for the following signal: (10 points) at. otherwise (b) Determine the magnitude spectrum and phase spectrum for X(). (10 points)
Problem 5: Use the duality property of the Fourier transform to find the Fourier transform of x(t) = sinc(Wt).
Problem 5: Use the duality property of the Fourier transform to find the Fourier transform of x(t) = sinc(Wt). Please solve clearly, not copy paste old solutions.
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
(10 pts). Using the transform integral, determine the Fourier transform of each of the following signals: a. x(t) - ecos(200t)u(t) b. x(t) -e ltl 5. Scrambled Answers 4-1400-200)+4+](400 +2o), jo, a 1+?