Question: Consider the function and first check that the exponents are unitless. Then show that the Fourier transform of E(t) is You might want to use

Consider the function

,-ίωρ! E(t) = Ege-i@ote-7/27²

and first check that the exponents are unitless. Then show that the Fourier transform of E(t) is

E(@) = V2E0TE(w-ww°/2 w-w²/2

You might want to use the integral identity

,-! E(t) = Ege-i@ote-7/27 E(@) = V2E0TE(w-ww/2 w-w/2

,-! E(t) = Ege-i@ote-7/27 E(@) = V2E0TE(w-ww/2 w-w/2

Step by Step Solution

★★★★★

3.30 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

E E expt27 expiwt ex... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Optics Questions!

Q:

Show that (10.26) and (10.27) are Fourier transform pairs. In 2 (f (10.26) (f) xp 2? 2 -B exp In 2 h(t) = (10.27) In 2

Q:

Use the Fourier transform method to obtain vo(t) in the circuit of Fig. 18.51. 1 H 2 H 1 H cos t V (2) 2

Q:

Use the Fourier transform to find i(t) in the circuit of Fig. 18.47 if v s (t) = 10e2t u(t). 2 2 1 H

Q:

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

Q:

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Q:

Describe how to construct the function cpo ((D E), v) of two cpos (D, vD) and (E, vE). Prove that ((D E), v) is a cpo. (You may use facts about least upper bounds provided you state them clearly.)...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

5. (16 pts) In the previous homework, we looked at a quantum algorithm for performing a Fourier transform, which is a part of Shor's algorithm for factoring numbers. Now we will look at another...

Q:

Show the parse trees for the two parses that the grammar assigns for sentence S1. S1: the train station bus rumbles [3 marks] (b) Give an algorithm for a bottom-up passive chart parser without...

Q:

Q1. How many wuld Signals expect to se in tre normal broad band decoupled BC NMR Spectry you Of the following compaunds A#of )Sgnal's Q2 Draw an acleptable structure for The following campoure): 3-...

Q:

New equipment purchase, income taxes. Innovation, Inc. is considering the purchase of a new industrial electric motor to improve efficiency at its Fremont plant The motor has an estimated useful life...

Q:

True or False: Securitization in the shadow banking system usually takes place within a single financial institution. Question 6 Answer True False

Q:

What are the most important organizational buyer behavior trends, and how might these trends affect sales strategies in the future?

Q:

A rectangular container measuring 25 cm x 35cm x 55 cm is filled with water. What is the mass of this volume of water?

Q:

The outside dimensions of a cylindrical soda can are reported as 12.559 cm for the diameter and 5.62 cm for the height. (a) How many significant figures will the total outside area have: (1) two, (2)...

Q:

In doing a problem, a student adds 46.9 m and 5.72 m and then subtracts 38 m from the result. (a) How many decimal places will the final answer have: (1) zero, (2) one, or (3) two? Why? (b) What is...

Q:

Fama's Llamas has a weighted average cost of capital of 11 percent. The company's cost of equity is 16 percent, and its pretax cost of debt is 7.5 percent. The tax rate is 34 percent. What is the...

Q:

Consider the following portfolio: a newly entered - into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and...

Q:

John will reitre next month and has $ 6 5 0 , 0 0 0 in Registered Retirement Savings Plan ( RRSP ' s ) . He wants a monthly payment at the beginning of each month and expects to earn 7 % , compounded...