Question: Prove analytically that the convolution of any function (x) with a delta function, (x), generates the original function (X).

Prove analytically that the convolution of any function ƒ(x) with a delta function, δ(x), generates the original function ƒ(X).

Step by Step Solution

★★★★★

3.34 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

see section ... 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:

Prove analytically that the entropy of a two-statesystem? is maximized when p + = p ? = 1/2. S = -kB (p+ In p+ +p_ In p_) = -kB (P+ In p4 + (1 P+) In(1 P+))

Q:

Show that radiation at a distribution of temperatures decreases the estimate (34.34) of the uniform temperature radiative response 0 by proving the result in the case where the radiation comes from...

Q:

Prove analytically that carrier reinsertion with envelope detection can be used for demodulation of VSB.

Q:

A seismic probe bores itself into the seabed, going as deep as it can before running out of fuel. This takes about five minutes. It rotates its spiral drill head at rate R(t) that follows a...

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:

WRITE MATLAB PROGRAM PLEASE Assignment: 1. Assume we define a new random variable as X-g(e) V2cos() with . Analytically determine the PDF of the new variable fX(x) as a function of the as-of-yet...

Q:

(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...

Q:

Jupyter Notebook Now that we have tried our hand at some single-layer nets, let's see how they stack up compared to multi-layer nets. :) We will be exploring the basic concepts of learning non-linear...

Q:

Looking for help with question 1 part c and all of question 3. MATH353: Engineering Mathematics III Problem Set 2 Questions with asterisks (*) should be solved numerically using MATLAB 1. (a) Use...

Q:

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Q:

Exercise 2 Verify the correctness of the closing balance sheet of company ALFA and prepare a proper version. ASSETS 1. Share capital 2. Tax liabilities 3. Treasury bonds with maturity of 5 4....

Q:

Given FR SR = FE SE, find each missingquantity. FE SR 20.0 N 5.00 N 176N 12.0 N 9.80 lb 3.70 cm 49.2 cm cmm cm 76.3 cm 112 cm 53.9 in 67.4 cm 3. 4. 37.0 N 23.4 lb 119 N in N 29.7 cm

Q:

General Company's Cash account shows a $5,800 debit balance and its bank statement shows $5,370 cash on deposit at the close of business on August 31. Additional information follows. August 31 cash...

Q:

A tall Starbucks coffee costs $1.65 a day. If the banks quoted interest rate is 6% per annum and coffee prices increased at a 3% annual rate of inflation, what would an endless, inheritable free...

Q:

Consider an optically thick hydrogen gas in statistical equilibrium at temperature T. (Optically thick means that photons can travel only a small distance compared to the size of the system before...

Q:

Consider a gigantic container of gas made of identical particles that might or might not interact. Regard this gas as a bath, with temperature T b and pressure P b . Pick out at random a sample of...

Q:

Exercise 5.5 explored the enthalpy representation of thermodynamics for an equilibrium ensemble of systems in contact with a volume bath. Here we extend that analysis to an ensemble out of...

Q:

Teeswater Corp. shows the following information on its 2 0 2 0 statement of comprehensive income: sales = $ 2 4 2 , 0 0 0 ; costs = $ 1 4 6 , 0 0 0 ; other expenses = $ 8 , 4 0 0 ; depreciation...

Q:

Using Rstudio We will use a logistic regression to predict the probability ofdefaultusing income andbalanceon theDefaultdata set in the ISLR package. We will now estimate the test error of this...

Q:

Help A random survey of 75 death row inmates revealed that the mean length of tim deviation of 6.8 years. Conduct a hypothesis test to determine if the population years. + Part (a) Part (b) + Part...