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4. Given 2 e lq w2 1 find the Fourier Transform of the following: d (a)...
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Given find the Fourier transform of the following: (a) e dt 2T(2 1) 4 cos (2t) (Using properties of Fourier Transform to find) a) Suppose a signal m(t) is given by m()-1+sin(2 fm) where fm-10 Hz. Sketch the signal m(t) in time domain b) Find the Fourier transform M(jo) of m(t) and sketch the magnitude of M(jo) c) If m(t) is amplitude modulated with a carrier signal by x(t)-m(t)cos(27r f,1) (where fe-1000 Hz), sketch...
Find the Fourier transform of a one-dimensional rectangle function, and sketch the pair. Show how they can both be delta functions Verify that the FT of a Gaussian is a Gaussian, t2 w2 1 202 2/o2 e V2πο2 and so with o2=1, except for the constant 1//2T, ex-2 is its own Fourier transform. Show that they can both be delta functions (but not at the same time!). Sketch the transform cases for large and small variance Note there are several...
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)...
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...
Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier transform of the following signals in terms of X (jw). a. y(t) = e'*x(t – 2) b. y(t) = x(-3) c. y(t) = x(t)dt
(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...
Consider the Fourier transform pair e- 12. (a) Use the appropriate Fourier transform properties to find the Fourier transform of te-tl, (b) Use the result from part (a), along with the duality property, to determine the Fourier transform of 4t (1+t2)2
Question 1 1 Given Y(w) the Fourier transform of y(t -2) is 4+w 1 O Y(w)= 4+(w-22 e 12 4+w2 O e-2w 4+ w2 O -12w 4+ 2
Question 1 1 Given Y(w) the Fourier transform of y(t -2) is 4+w 1 O Y(w)= 4+(w-22 e 12 4+w2 O e-2w 4+ w2 O -12w 4+ 2
please complete all parts
Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think Fourier series.) (cos(nt) - 2sin(5rt)e-Jr dt XCj) (b) (5 points) Find the Fourier transform io of the following signal: 2(t) = sin(4t)sin(30) (c) (5 points) Solve the integral: sin(2t) 4t dt (d) (5 points) Use Parseval's theorem and your Fourier transform table to compute this integral:
Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think...
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = { 0 otherwise See figure(2) above. A) Find the Fourier transform for f( (see figure 2) and sketch its waveform. B) Determine the values of the first three frequency terms (w1, W2, W3) where F(w) = 0. C) Given x(t) = 1.58(-0.8) edt Determine whether or not Fourier transform exists for x(t). If yes, find the Fourier transfe not explain why it does not. Problem...