Question

In: Advanced Math

fourier transform of the following with steps: x(t) = z(t) + z(t - 30) x(t) =...

fourier transform of the following with steps:

x(t) = z(t) + z(t - 30)

x(t) = z(2*t) + z(t + 30)

x(t) = z^(2)(t)

Solutions

Expert Solution

1)

we have to find the Fourier transform of,

we can write,

we know that according to linearity property of fourier transform,

Hence,

we know that,

Hence,

2)

we have to find the Fourier transform of,

we can write,

we know that according to linearity property of fourier transform,

Hence,

we know that,

Hence,

3)

we have to find the Fourier transform of,

we can write,

we know that,

Hence,

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Starting with the Fourier transform pair x ( t ) = u ( t + 1...
Starting with the Fourier transform pair x ( t ) = u ( t + 1 )   -   u ( t - 1 )     ⇔   X ( Ω ) = 2 sin ( Ω ) / Ω and using no integration indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals x 1 ( t )   =   - u ( t + 2 ) + 2 u ( t ) - u ( t - 2...
Determine the Fourier transform of a Gaussian pulse defined as x(t) = e?t2. Plot both x(t) and X(?).
Determine the Fourier transform of a Gaussian pulse defined as x(t) = e?t2. Plot both x(t) and X(?).
Given a sinusoidal signal: x(t) = Asin(2πft) Find Fourier Transform (FT) of the sinusoidal x(t) given...
Given a sinusoidal signal: x(t) = Asin(2πft) Find Fourier Transform (FT) of the sinusoidal x(t) given above and plot the spectrum with: a. A = 2, f = 1000Hz b. A = 2, f = 9000Hz c. A = 5, f = 1000Hz d. A = 10, f = 10000Hz
Consider the following periodic signal : x(t)=∑∞n=−∞Π(t−4n2). 1. Determine and plot the spectrum Fourier Transform of...
Consider the following periodic signal : x(t)=∑∞n=−∞Π(t−4n2). 1. Determine and plot the spectrum Fourier Transform of signal x(t) ( For plot : Use only interval n=-2 to n=2). 2. Based on the result obtained in part one. Determine Complex Exponential Fourier Series, and trigonometric Fourier Series. 3. Evaluate the energy spectral density of the periodic signal x(t) in rang (n=-2 to n=2)
What's the Fourier transform of the following equations: 1) f(t)=1/(t^2+a^2) a is a constant 2) e^[-absolute...
What's the Fourier transform of the following equations: 1) f(t)=1/(t^2+a^2) a is a constant 2) e^[-absolute value(t)/a]*cos(b*t) a and b are constants
(TCO 7) What is the difference between discrete Fourier transform (DFT) and fast Fourier transform (FFT)?...
(TCO 7) What is the difference between discrete Fourier transform (DFT) and fast Fourier transform (FFT)? can you please type it cant see images.
Given the following functions, can you have the corresponding a) Fourier series, b) Fourier transform and...
Given the following functions, can you have the corresponding a) Fourier series, b) Fourier transform and c) Laplace transform? If yes, find them, if not, explain why you can not. A, x(t) = -1+cos(2t) + sin（pai*t+1)                                               (4-1) B, x(t) = 2d(t) cos(2t) +d(t-1.5p) sin(2t)                                          (4-2) C, x(t) = 1+cos(1.5t) + cos(4t)                                           (4-3)
Given the following functions, can you have the corresponding a) Fourier series, b) Fourier transform and...
Given the following functions, can you have the corresponding a) Fourier series, b) Fourier transform and c) Laplace transform? If yes, find them, if not, explain why you can not. A, x(t) = -1+cos(2t) + sin(pt+1)                                                                                 (4-1) B, x(t) =2d(t) cos(2t) +d(t-1.5p) sin(2t)                                                                    (4-2) C, x(t) = 1+cos(1.5t) + cos(4t)                                                                                    (4-3)
Define phase term (fourier transform)
Define phase term (fourier transform)
Find the Fourier coefficients of the following signal. x(t) = 5 + 2sin(w0.t) + cos(2.w0.t) -...
Find the Fourier coefficients of the following signal. x(t) = 5 + 2sin(w0.t) + cos(2.w0.t) - 3sin(2.w0.t)
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT