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A4. Show that the Fourier transform of the function f(x) in Figure 1 is given by...
The Fourier Transform of a certain time function, x(t), is shown below F{x(t) x(f) 2.5 7...
The Fourier Transform of a certain time function, x(t), is shown below F{x(t) x(f) 2.5 7 1.5 1 0.5 -30 -20 -10 10 20 30 f(Hz) equation for X(f A. Write an B. Write an equation for x(t). C. Write and equation for the Fourier Transform of x(2t) and draw a sketch D. Write and equation for the Fourier Transform of x(t) and draw a sketch equation for the Fourier Transform of x()cos(2 E. Write an 15 t and draw...
The Fourier transform of the following signal 2(t) = cos (F.) () is X(s) 47 cos(278)...
The Fourier transform of the following signal 2(t) = cos (F.) () is X(s) 47 cos(278) 772 – 167232 where II is the rectangle function defined in A2 (a)(iii). Determine the Fourier transform of the function 47 Cos (2) y(t) 72 – 16722
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...
1. Consider the function f(x)-e- (a) Find its Fourier transform. (b) Use the result of part (a) t...
1. Consider the function f(x)-e- (a) Find its Fourier transform. (b) Use the result of part (a) to find the value of the integral o0 cos kx dk 0 1 +k2 (c) Show explicitly that Parseval's theorem is satisfied for eand its Fourier transform
1. Consider the function f(x)-e- (a) Find its Fourier transform. (b) Use the result of part (a) to find the value of the integral o0 cos kx dk 0 1 +k2 (c) Show explicitly that Parseval's...
Check the existence of the Laplace transform for the given function and hence show that -...
Check the existence of the Laplace transform for the given function and hence show that - cos 20 1s² + 4 L = In t s2 where L{f(t)} is represent the Laplace transform of f(t). [Hint: 2 cos A cos B = COSIA+B) + cos(A - B) sin(A + B) + sin(A - B) = sinA cosB, sin(A + B) – sin(A - ?) = os AsmB] [2+ Find the Fourier Sine series of [8 f(x) = e-*,0<x<. Using the...
- Given the function f(x) = { 2, -1<x<i 10, otherwise find its Fourier sine transform...
- Given the function f(x) = { 2, -1<x<i 10, otherwise find its Fourier sine transform g(a), such that f(x) g(a) sin oz da
Please finish these questions. Thank you 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 giv...
Please finish these questions. Thank you
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...
1. A certain function of time x (t) has the Fourier transform X(f) shown below Sketch...
1. A certain function of time x (t) has the Fourier transform X(f) shown below Sketch the spectrum of [x(t)]2 and find its bandwidth. Sketch the spectrum of [x(t)cos(2r15t)] and find its bandwidth. a. b. 11 -10 9 9 10 11
Find the Fourier transform of f(x) = 1–x?, for -1 < x < 1 and f(x)...
Find the Fourier transform of f(x) = 1–x?, for -1 < x < 1 and f(x) = 0 otherwise. Hence evaluate the integral 6 * * cos sin cos des.
3. If x(t) has the Fourier transform j2π f + 10 Find the Fourier transform of...
3. If x(t) has the Fourier transform j2π f + 10 Find the Fourier transform of the following signals Hint: use the properties of Fourier transform) a. v(t)-x(1):cos(10π t) d. v(t)X(t) e. v()-e"x(t-1)
The Fourier Transform of a certain time function, x(t), is shown below F{x(t) x(f) 2.5 7 1.5 1 0.5 -30 -20 -10 10 20 30 f(Hz) equation for X(f A. Write an B. Write an equation for x(t). C. Write and equation for the Fourier Transform of x(2t) and draw a sketch D. Write and equation for the Fourier Transform of x(t) and draw a sketch equation for the Fourier Transform of x()cos(2 E. Write an 15 t and draw...
The Fourier transform of the following signal 2(t) = cos (F.) () is X(s) 47 cos(278) 772 – 167232 where II is the rectangle function defined in A2 (a)(iii). Determine the Fourier transform of the function 47 Cos (2) y(t) 72 – 16722
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...
1. Consider the function f(x)-e- (a) Find its Fourier transform. (b) Use the result of part (a) to find the value of the integral o0 cos kx dk 0 1 +k2 (c) Show explicitly that Parseval's theorem is satisfied for eand its Fourier transform
1. Consider the function f(x)-e- (a) Find its Fourier transform. (b) Use the result of part (a) to find the value of the integral o0 cos kx dk 0 1 +k2 (c) Show explicitly that Parseval's...
Check the existence of the Laplace transform for the given function and hence show that - cos 20 1s² + 4 L = In t s2 where L{f(t)} is represent the Laplace transform of f(t). [Hint: 2 cos A cos B = COSIA+B) + cos(A - B) sin(A + B) + sin(A - B) = sinA cosB, sin(A + B) – sin(A - ?) = os AsmB] [2+ Find the Fourier Sine series of [8 f(x) = e-*,0<x<. Using the...
- Given the function f(x) = { 2, -1<x<i 10, otherwise find its Fourier sine transform g(a), such that f(x) g(a) sin oz da
Please finish these questions. Thank you
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...
1. A certain function of time x (t) has the Fourier transform X(f) shown below Sketch the spectrum of [x(t)]2 and find its bandwidth. Sketch the spectrum of [x(t)cos(2r15t)] and find its bandwidth. a. b. 11 -10 9 9 10 11
Find the Fourier transform of f(x) = 1–x?, for -1 < x < 1 and f(x) = 0 otherwise. Hence evaluate the integral 6 * * cos sin cos des.
3. If x(t) has the Fourier transform j2π f + 10 Find the Fourier transform of the following signals Hint: use the properties of Fourier transform) a. v(t)-x(1):cos(10π t) d. v(t)X(t) e. v()-e"x(t-1)
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