Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier...
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.
Find the Fourier Transform of the following signals: (a) x(t) = Sin (t). Cos (5 t) (b) x(t) = Sin (t + /3). Cos(5t-5) (c) a periodic delta function (comb signal) is given x(t) = (-OS (t-n · T). Express x(t) in Fourier Series. (d) Find X(w) by taking Fourier Transform of the Fourier Series you found in (a). No credit will be given for nlugging into the formula in the formula sheet.
(1 point) Find the Fourier series expansion, i.e., f(x) [an cos(170) + by sin(t, x)] n1 J1 0< for the function f(1) = 30 < <3 <0 on - SIST ao = 1 an = cos npix bn = Thus the Fourier series can be written as f() = 1/2
7. The signal x(t) shown below is modulated (multiplied) by cos(10nt). Find the Fourier transform of x(t)cos(10nt) and neatly sketch the magnitude? Useful transform pairs. rect (9) = t sinc (); «(t)cos (Wgt) }(x(w+wo) + X(w – wo)); «(t – to) ~X(w)e-juto (10 points) x(+) 1 t
2 ANOWI 20 .202019 pd What is the spectrum of the negative half-sine pulse shown in Fig. 1 e) Find the spectrum of the single sinc pulse shown in Fig. (d). Question 5 (20 points) Fourier transform X() of'n signal is shown in Fig. 2. Determine and sketch the Fourier transform of the signal x, (t) = -x(t) + x(t) cos(2000 t) + 2x(t) cos? (3000xt) Question 6 (20 points) Determine the Fourier Series expansion of the following periodic signals....
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)...
4. Given that x(t) has the Fourier transform X(a), p(t) is a periodic signal with frequency of ??. p(t)-??--o nejnaot, where Cn is the Fourier series coefficient of p) (1) Assume y(t)-x(t)p(t), determine Y(?), the Fourier transform of the modulated signal y(t) in terms of X(). (2) Given the spectrum sketch of x(?) shown below, p(t)-cos(2t) cos(t), determine and sketch the Y() X(w) -1
Find a Fourier series expansion of the periodic function 0 -T -asts 2 - f(t) = 6 cost T <<- 2 2 0 I SISE 2 f(t) = f (t +21) Select one: a f(t)= 12 12 5 (-1)** cos nt 1 2n-1 b. f(t) = 12.12 F(-1)** cos 2nt T 4n-1 C 6 12 =+ 125 (-1) C05 211 472-1 6 12 (-1) * cosm d
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...