Determine the Fourier transform of a Gaussian pulse defined as x(t) = e?t2. Plot both x(t) and X(?).

Expert Solution

Manojponduru answered 2 years ago

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)

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...

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)

Determine the Nyquist rate for signal x(t)defined as follows: x(t)= 20,000sinc(20,000pit) Plot the spectrum of the...

Determine the Nyquist rate for signal x(t)defined as follows: x(t)= 20,000sinc(20,000*pi*t) Plot the spectrum of the sampled signal and check whether aliasing error exists for the following values of the sampling rate (ws): 40,000*pi, 20,000*pi,10,000*pi

energy and power of signals. (a) Plot the signal x(t) = e−tu(t) and determine its energy....

energy and power of signals. (a) Plot the signal x(t) = e−tu(t) and determine its energy. What is the power of x(t)? (b) How does the energy of z(t) = e−∣t∣, −∞ < t < ∞, compare to the energy of z1(t) = e−tu(t)? Carefully plot the two signals. (c) Consider the signaly(t) = sign[xi(t)] =  1 xi(t) ≥ 0 −1 xi(t) < 0 for −∞ < t < ∞,i = 1,2. Find the energy and the power of...

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

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

Both the Fourier Series and the Discrete Fourier Transform are calculated using summation. Explain the key...

Both the Fourier Series and the Discrete Fourier Transform are calculated using summation. Explain the key differences in what the inputs each of the Fourier Series and the DFT are AND the requirements the inputs.

Solve this Initial Value Problem using the Laplace transform: x''(t) - x'(t) - 6x(t) = e^(4t),...

Solve this Initial Value Problem using the Laplace transform: x''(t) - x'(t) - 6x(t) = e^(4t), x(0) = 1, x'(0) = 1

Considerthecurvex(t)=t2,y(t)=t3 −3t,for−∞<t<∞. 2 (a) Find all t that give x intercepts and y-intercepts, and plot them....

Considerthecurvex(t)=t2,y(t)=t3 −3t,for−∞<t<∞. 2 (a) Find all t that give x intercepts and y-intercepts, and plot them. (b) Find all t which give horizontal or vertical tangents, and plot the corresponding points, with a short horizontal or vertical segment to indicate the tangent line. (c) Find the values of t for which x(t) is increasing and those for which it is decreasing. Do the same for y. (d) Determine what happens to x(t) and y(t) as t → ∞. (e) Make...

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