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Sketch the following function and determine their Inverse Fourier Transforms. (d) X(f)=8(f +10)+8( f - 10)...
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier...
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier transform of the signal x()cn(31-4 marks) 2fX(a), determine the Fourier transform of the signal y(t)dx( F.T. dx(2t) dt (3 marks) 3. Find the Fourier transform of x(t)-cos(2t/4). (3 marks) 4. Let x(t) be the input to a linear time-invariant system. The observed output is y(t) 4x(t 2). Find the transfer function H() of the system. Hence, obtain and sketch the unit-impulse response h(t) of...
Find the fourier transform of the following function
1. Find the Fourier transforms of the following functions:
(1) f(x) = rect * (x) * r * e * c * t * (x - 1)
(2) g(x) = 2sin c * (2x) * sin(x)
(3) p(x) = rect(x - 2)/2x
(4) u(x) = 3sin c * (3x) - sin c * (x)
(5) v(x) = sinc(x) * sinc (x) * sinc (x)
2. Find and sketch the functions and the corresponding Fourier transforms:
(1) f(x) = 1/5 *...
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and prope...
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from Definition)- For (c) r(t) = te-2, 11(1) (b) x(t)-2t rect(t)
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from...
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)...
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the...
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 4 9+w2 9w2 (b) The function f(t) satisfies the integral equation -4u f(t u) H(u) du 6sgn(t)e-3¢|. f(t) 4 Find the Fourier transform of the function f(t) and hence find the solution f(t)
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 4 9+w2 9w2 (b) The function f(t)...
(a) Find the Fourier transform of the following function (b) Using Fourier transforms, solve the wave...
(a) Find the Fourier transform of the following function (b) Using Fourier transforms, solve the wave equation , -∞<x<∞ t>0 and bounded as ∞ f(r)e We were unable to transcribe this imageu(r, 0)e 4(r.0) =0 , t ur. We were unable to transcribe this image f(r)e u(r, 0)e 4(r.0) =0 , t ur.
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...
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the...
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 1 12 8iw w2 _ (b) Hence, determine the inverse Fourier transform of -iw 12 8iw -w2' (c) Use Fourier transforms to solve d2y ,dy + dt2 12y (t 1 8
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 1 12 8iw w2 _ (b) Hence, determine the...
Answers are: 10. (a) Use the Tables of Fourier transforms, along with the operational theorems, to...
Answers are:
10. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 40 w2 - 13iw (b) Use Fourier transforms to solve dy -5t + 8y — 9е эH (). dt 15t H(t) 1 8t (а) (1) Н, 9 Then solve for 5iw (b) Apply the Formula of transform of derivatives to get: (iw+8)Y(w) Y (w) and take the inverse transform to have -8t у(0) — Зе 5 н(t) —...
how to derive the underlying signal x(t) using the definition of the Inverse Fourier transform Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the i...
how to derive the underlying signal x(t) using the
definition of the Inverse Fourier transform
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier transform of the signal x()cn(31-4 marks) 2fX(a), determine the Fourier transform of the signal y(t)dx( F.T. dx(2t) dt (3 marks) 3. Find the Fourier transform of x(t)-cos(2t/4). (3 marks) 4. Let x(t) be the input to a linear time-invariant system. The observed output is y(t) 4x(t 2). Find the transfer function H() of the system. Hence, obtain and sketch the unit-impulse response h(t) of...
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from Definition)- For (c) r(t) = te-2, 11(1) (b) x(t)-2t rect(t)
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from...
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)...
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 4 9+w2 9w2 (b) The function f(t) satisfies the integral equation -4u f(t u) H(u) du 6sgn(t)e-3¢|. f(t) 4 Find the Fourier transform of the function f(t) and hence find the solution f(t)
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 4 9+w2 9w2 (b) The function f(t)...
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...
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 1 12 8iw w2 _ (b) Hence, determine the inverse Fourier transform of -iw 12 8iw -w2' (c) Use Fourier transforms to solve d2y ,dy + dt2 12y (t 1 8
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 1 12 8iw w2 _ (b) Hence, determine the...
Answers are:
10. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 40 w2 - 13iw (b) Use Fourier transforms to solve dy -5t + 8y — 9е эH (). dt 15t H(t) 1 8t (а) (1) Н, 9 Then solve for 5iw (b) Apply the Formula of transform of derivatives to get: (iw+8)Y(w) Y (w) and take the inverse transform to have -8t у(0) — Зе 5 н(t) —...
how to derive the underlying signal x(t) using the
definition of the Inverse Fourier transform
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
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