Use tables of Fourier transform pairs and properties to find the Fourier transform of each of the signals
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Use tables of Fourier transform pairs and properties to find the
Fourier transform of each of...
only number 8 Figure 3.2 Figure 3.1 Find the Fourier transform of the following signals a....
only number 8
Figure 3.2 Figure 3.1 Find the Fourier transform of the following signals a. x(t) - e-at cos(wt) u(t) ,a>0 8. 1+j2)t 9. Compute the discrete Fourier transform of the following signals.
4-6. Using the Fourier transform integral, find Fourier transforms of the following signals: (a) xa(1)-1 exp(-α)...
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) 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) =
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 sign...
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. Consider the signal co(t) = et, 0<t<1 , elsewhere Determine the Fourier transform of each...
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
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...
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...
IF Let x(t) Show that e 20" σ>0, and let (o) be the Fourier transform of...
IF Let x(t) Show that e 20" σ>0, and let (o) be the Fourier transform of x(t) .
Find the Laplace Transform (d) f(t) = te, 0<t<1, et, t > 1. l
Find the Laplace Transform
(d) f(t) = te, 0<t<1, et, t > 1. l
Using Fourier transform, prove that a solution of the Laplace equation in the half plane: Urn+...
Using Fourier transform, prove that a solution of the Laplace equation in the half plane: Urn+ Uyy=0,- << ,y>0, with the boundary conditions u(1,0) = f(t), - <I< u(x,y) +0,31 +0,+0, is given by r(2, y) == Love you > 0. Hint: 1. Take Fourier transform on the variable r, 2. Observe U(k, y) +0 as y → 00, 3. Use pt {e-Mliv = Vice in
(c). Determine the Fourier transform of s(t)={! -1<i<1 14 > 1
(c). Determine the Fourier transform of s(t)={! -1<i<1 14 > 1
only number 8
Figure 3.2 Figure 3.1 Find the Fourier transform of the following signals a. x(t) - e-at cos(wt) u(t) ,a>0 8. 1+j2)t 9. Compute the discrete Fourier transform of the following signals.
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) =
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. 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
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...
IF Let x(t) Show that e 20" σ>0, and let (o) be the Fourier transform of x(t) .
Find the Laplace Transform
(d) f(t) = te, 0<t<1, et, t > 1. l
Using Fourier transform, prove that a solution of the Laplace equation in the half plane: Urn+ Uyy=0,- << ,y>0, with the boundary conditions u(1,0) = f(t), - <I< u(x,y) +0,31 +0,+0, is given by r(2, y) == Love you > 0. Hint: 1. Take Fourier transform on the variable r, 2. Observe U(k, y) +0 as y → 00, 3. Use pt {e-Mliv = Vice in
(c). Determine the Fourier transform of s(t)={! -1<i<1 14 > 1
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