Question: Given that F() = F[f(t)], prove the following results, using the definition of Fourier transform: (a) F[f(t - t0)] = e-jt, F() (b) F[df(t)/dt] =

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)

Step by Step Solution

★★★★★

3.28 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

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

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

905-P-E-M-C (1643).docx

120 KBs Word File

Students Have Also Explored These Related Electricity and Magnetism 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 (?),...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

PLEASE DO IT IN JAVA AND USE ONE OR TWO DIMENSIONAL ARRAYS Problem Description: We would like to write a graphics program which draws a user entered triangle on a 51x51 grid. The program should be...

PLEASE DO IT IN JAVA Problem Description: We would like to write a graphics program which draws a user entered triangle on a 51x51 grid. The program should be modular and use methods for subtasks....

It should be written in Java and should be written as simply as possible. It should be written according to the 1st grade student Problem Description: We would like to write a graphics program which...

Problem Description: We would like to write a graphics program which draws a user entered triangle on a 51x51 grid. The program should be modular and use methods for subtasks. The program has three...

Determine the z -transforms of the following signals and sketch the corresponding pole-zero patterns. (a) x(n) = (l + n) u (n) (b) x(n) = (a n + a n ) u(n), a real (c) x(n) = (-1) a 2 -n u (n) (d)...

You can invest in a machine that costs $500,000. You can expect revenues net of any expense, except maintenance costs, of $150,000 at the end of each year for five years. You will subcontract the...

Estimating Share Value Using the ROPI Model Following are forecasts of ilinois Tool Works inc, sales, net operating profit after tax ( NOPAT ) , and net operating assets ( NOA ) as of December 3 1 ,...

Does keeping a childs lunch in an insulated bag, even with ice packs, protect the food from warming to temperatures where germs can proliferate? Researchers used an electric temperature gun on 235...

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

A stock has had the following year-end prices and dividends: Year Price ($) Dividend ($) 1 92.7 - 2 94.36 1.47 3 93.58 1.34 4 94.66 1.33 5 95.58 1.57 6 96.64 1.78 What is the geometric average return...

Sunland industries had sales in 2021 of $6,392,000 and gross profit of $1,034,000. Management is considering two alternative budget plans to increase its gross profit in 2022 Plan A would increase...

Question 7 (1 point) The problem faced by insurance companies because individuals who are more likely to have claims are also more likely to purchase insurance is referred to as Adverse selection...