Given that F() = F[f(t)], prove the following results, using the definition of Fourier transform: (a) F[f(t

Question:

Given that F(ω) = F[f(t)], prove the following results, using the definition of Fourier transform:
(a) F[f(t - t0)] = e-jωt, F(ω)
(b) F[df(t)/dt] = jω F(ω)
(c) F[f(-t) = F(-ω)
(d) F[tf(t)] = j d/dω F(ω)

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Fundamentals Of Electric Circuits

ISBN: 9780073301150

3rd Edition

Authors: Matthew Sadiku, Charles Alexander

See More Books

Question Posted: Apr 29, 2016 03:18 PM

See More Questions

Prove the following results used in the proof of the local flatness theorem in 6.2: (a) The number of independent values of 2x/x'x'|0 is 40. (b) The corresponding number for 3x/x' x' xv'|0 is 80....
Find the Fourier transform of the function f (t0 = 12e-2|t| cos 4t.
The Hilbert transform of a Fourier transformable signal m (t), denoted by m (t), is defined by below, in the frequency domain, we have M (?) = -j sgn (?) M (?), where m (t) ? M (?), m (t) ? M (?),...
Two experienced managers at Wilson Boat, Inc. are resisting the introduction of a computerized exponential smoothing system, claiming that their judgmental forecasts are much better than any computer...
For the steel countershaft specified in the table, assume the bearings have a maximum slope specification of 0.06° for good bearing life. Determine the minimum shaft diameter. Problem 3-69, A...
Consider a convergent-divergent nozzle with an exit-to-throat area ratio of 1.53. The reservoir pressure is 1atm. Assuming isentropic flow, except for the possibility of a normal shock wave inside...
A woman is emptying her aquarium at a steady rate with a small pump. The water pumped to a 12 -in.-diameter cylindrical bucket, and its depth is increasing at the rate of 4.0 in. per minute. Find the...
The Mona chino Manufacturing Company has the following budgeted overhead cost and other data for its machining department for the month of December: Budgeted Data: Indirect labor and supplies .....
Which segments of the streaming and television industry (hardware (e.g. Roku), broadcast networks (CBS, NBC), streamers (Netflix, Paramount , Disney ), cable channels (ESPN), content producers...
OO! Grace, a self-employed married woman with two children who both attend basic schools in Ghana trades as Mbrewa Din Enterprise. She commenced business on 1st January 2022 and submitted the...
Find the Fourier transforms of: (a) cos 2tu(t) (b) sin 10tu(t)
Find the Fourier transform of f(t) = cos 2 t[u(t) - u(t - 1)]
Following are income statement data for Mylin Corporation for the companys most recent ï¬scal year: At the beginning of the year, Mylin had 252,000 shares of common stock outstanding. On...
24. A particle moves according to the displacement function s(t) = 2t^3-15t^2 + 10t + 1, where s(t) is measured in centimeters and t is measured in seconds. a) What is the initial position of the...
While the individual states have different approaches to establishing their constitutions, they all have central elements that guide the setup and management of powers of the state government. This...
4. A point source Gaussian plume model for a power plant uses 50 m as the effective stack height (see Figure P7.32). The night is overcast. (Note: This is not the same as "cloudy" in this model;...
A cosmic ray proton moving toward the Earth at 3.5 107 m/s experiences a magnetic force of 1.8 10-16 N .What is the strength of the magnetic field if there is a 45 angle between it and the proton's...
4. Beach Bums is a popular beachside store. Becky, owner of the Beach Bums, is deciding how much refrigerator space to devote to four different drinks. Pertinent data on these four drinks are as...
a. On such a night the earths surface cools by radiation. The air in contact with the surface also cools and may become saturated with water vapor, which then condenses into droplets of liquid water....
What mass of H2 will be produced when 122 g of Zn are reacted? Zn(s) + 2HCl(aq) ( ZnCl2(aq) + H2(g)
A hot-air balloon consists of a bas-t ket, one passenger, and some cargo. Let the total mass be M. Even though there is an upward lift force on the balloon, the balloon is initially accelerating...
A student tries to raise a chain consisting of three identical links. Each link has a mass of 300 g. The three-piece chain is connected to a string and then suspended vertically, with the student...
The position of a 2.75 X 102 N training helicopter under test isgivenby1 = (0.020 m/s2)t2 + (2.2m/s)tj- (0.060m}S2)t2k, Find the net force on the helicopter at t = 5.0 s
The articles of partnership for Pal - Trotter Partnership provide for a salary allowance of $ 5 , 3 0 0 per month for partner Trotter, with the balance of net income to be divided equally. If Trotter...
The City of Piglet reported property tax revenues in 2020 in the amount of $10 million. The deferred inflow-property taxes reported in the General Fund's balance sheet was $300,000 on December 31,...
Texas Roadhouse is expecting to earn $ 5 million in revenue for the next fiscal year. How much net income would the company need to generate from that revenue to achieve a net profit margin ratio of...

Given that F() = F[f(t)], prove the following results, using the definition of Fourier transform: (a) F[f(t

Question:

Step by Step Answer:

a b Given that c This is a special case o...View the full answer

Fundamentals Of Electric Circuits

Students also viewed these Electricity and Magnetism questions