Answer :
only number 8 Figure 3.2 Figure 3.1 Find the Fourier transform of the following signals a....
Use tables of Fourier transform pairs and properties to find the Fourier transform of each of the signals a) f(t)=(1-eb )u(t) b) f(t)= Acos(@t+) c) f(t)=e"u(-t), a>0 d) f(t)=C/(t+t)
4-6. Using the Fourier transform integral, find Fourier transforms of the following signals: (a) xa(1)-1 exp(-α) u(t), α > 0; (b) xb(t) = u(t) u(1-t);
29.9) Compute the Fourier transform of the periodic function f(t) to prove the equation shown below: 29.9. Let f(t) = iftl > T. 0 Show that f(w) =
9. Find the Fourier series coefficients and Fourier transform for each of the following signals: a) x(t)= sin(10nt+ b) x(t) = t) 1 + cos(2π cos (2rt S2n
1. Laplace Transform. (10 pts) Find the Laplace Transform of the following signals and sketch the corresponding pole-zero plot for each signal. In the plot, indicate the regions of convergence (ROC). Write X(s) as a single fraction in the forin of (a) (2 pts) z(t) = e-Mu(t) + e-6tu(t). Show that X(s)-AD10 (b) (4 pts)-(t) = e4ta(-t) + e8ta(-t). (c) (4 pts) (t)-(t)-u(-t) . with ROC of Re(s) >-4. (s+4)(8+6)
Need solution pls... 2. Find the Fourier transform of f() = {6 1 – 12 \t <1 1t| > 1 Use the first shift theorem to deduce the Fourier transforms of e3jt (1-12) 11 <1 (a) g(t) 1t| > 1 {" (b)h() = {**"1 –1) "151 It| > 1 Answer: 63 4 cos o 4 sin o + -62 -4 cos(w – 3) (a) (0 – 3)2 -4 cos(w – j) (b) (w – j)2 + 4 sin(0 – 3)...
Find the Fourier Transform of the triangular pulse _(1 + t for -1<t < 0 x(t) = (1 - t for 0 <t<1
3.3-6 The signals in Fig. P3.3-6 are modulated signals with carrier cos 10r. Find the Fourier transforms of these signals using the appropriate properties of the Fourier transform and Table 3.1. Sketch the amplitude and phase spectra for Fig. P3.3-6a and b. Hint: These functions can be expressed in the form g(t) cos 2π for. 0 31t BTI
(1 point) Find the inverse Laplace transform of 2s + 9 $2 + 23 S> 0 y(t) =
4. Consider the signal co(t) = et, 0<t<1 , elsewhere Determine the Fourier transform of each of the signals shown in Figure 2. You should be able to do this by explicitly evaluating only the transform of co(t) and then using properties of the Fourier transform. X(t) X2(t) Xolt) Xp(t) -Xol-t) X3(t) Xolt +1) X4(t) Xolt) txo(t) My Lane 1 0