(a) Use the Fourier transform of x(t) = exp (-t) u (t) - exp (t) u (-t)...

Question:

(a) Use the Fourier transform of x(t) = exp (-Î±t) u (t) - exp (Î±t) u (-t) where Î± > 0

t > 0 1, sgn (t) = -1, t< 0

(b) Use the result above and the relation u(t) = 1/2[sgn (t) + 1] to find Fourier transform of the unit step.

(c) Use the integration theorem and the Fourier transform of the unit impulse function to find the Fourier transform of the unit step. Compare the result with part (b).

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

Step by Step Answer:

Related Book For book-img-for-question

Principles of Communications Systems, Modulation and Noise

ISBN: 978-8126556793

7th edition

Authors: Rodger E. Ziemer, William H. Tranter

See More Books

Question Posted: Sep 13, 2018 11:29 AM

See More Questions

Let X(e j? ) denote the Fourier transform of x[n].Using the Fourier transform syntheses or analyses equations (Eqs. (2.133) and (2.134)), show that (a) The Fourier transform of x*[n] is X*(e ?j? ),...
Given that F{(x)} = F(), introduce a constant scaling factor 1/ and determine the Fourier transform of (x/). Show that the transform of (-x) is F(-).
A simple model of a multipath communication channel is indicated in Figure. Assume that s c (t) is band limited such that S c (j?) = 0 for |?| ? ? / T and that x c (t) is sampled with a sampling...
Assume that n is a positive integer. For each of the following algorithm segments, how many times will the innermost loop be iterated when the algorithm segment is implemented and run? 1) for k:=1 to...
What does it mean to say that workers and firms have rational expectations?
Find the present value of an annuity that pays $1,000 at the end of each year for 5 years if the appropriate discount rate is 15%. Calculate the future value of that same annuity. How would the PV /...
Assume the training heart rates of all 20-year-old athletes are normally distributed, with a mean of 135 beats per minute and a standard deviation of 18 beats per minute, as shown in the figure....
Use the following data, compute 1. Cost of goods manufactured for both Garcia Company and Culpepper Company. (Omit the "$" sign in your response.) 2. Cost of goods sold for both Garcia Company and...
Nordstrom, the apparel company has the following data from their annual reports. Calculate the customer lifetime value for Nordstrom. i ) Monthly revenue per customer - $ 8 7 ii ) Profit per customer...
A 200-pound steer can be sustained on a diet calling for various proportions of grass and grain. These combinations are shown in the table. Pounds of Grass Pounds of Grain 50 ..........80 56...
(a) Given II(t) sinc(f), find the Fourier transforms of the following signals using the frequency-translation followed by the time-delay theorem. (i) x 1 (t) = II (t - 1) exp [j4(t - 1)] (ii) x 2...
Sketch each signal given below and find its Fourier transform. Plot the amplitude and phase spectra of each signal (A and are positive constants). (a) x 1 (t) = A exp (-t/) u(t) (b) x 2 (t) = A exp...
The four employees for JackWorks are paid on an hourly basis. During the week of December 25-31, 2016, these employees worked the hours indicated. Information about their hourly rates, marital...
During the late afternoon, police were called to quell a disturbance at a motel where the management had reported some disorderly conduct and apparent drug use. Outside the motel, the police observed...
What, if any, constitutional objections could be raised against a city ordinance making it a criminal offense to use profane language in a public place?
Why has it been necessary for American courts to interpret laws proscribing breach of peace and vagrancy more strictly than did the English common-law courts?
How does RICO define enterprise, and what is its significance in prosecution of RICO offenses?
Hoss Tile is arrested after police are called to the scene of a private social club where Tile is a member. The police are called because Tile refuses to extinguish his cigarette in the dining room...
Use Fig. 4.53. The surface is 1.50 m long. 2.80 m 1.20 m +: Water
Separate variables and use partial fractions to solve the initial value problems in Problems 18. Use either the exact solution or a computer-generated slope field to sketch the graphs of several...
Two equal but opposite-sign point charges of 3 C are held x meters apart by a spring that provides a repulsive force given by F sp = 12(0.5 x) N. Without any force of attraction, the spring would be...
A semiconductor sample has a rectangular cross section 1.5 by 2.0 mm, and a length of 11.0 mm. The material has electron and hole densities of 1.8 10 18 and 3.0 10 15 m 3 , respectively. If e =...
Electron and hole concentrations increase with temperature. For pure silicon, suitable expressions are h = e = 6200T 1.5 e 7000 /T C/m 3 . The functional dependence of the mobilities on temperature...
Dollar-Value LIFO On January 1, 2018, Sato Company adopted the dollar-value LIFO method of inventory costing. Sato's ending inventory records appear as follows: Year Current Cost Index 2018 $31,600...
How many standards are included in the ELP accreditation standards? What stands out to you about the different areas? What are the topic areas under administration and leadership? What are the...
What is performance management systems? Do the companies where you (or others you know) have worked used performance management systems rather than performance appraisal systems? If yes, what kind of...

(a) Use the Fourier transform of x(t) = exp (-t) u (t) - exp (t) u (-t)...

Question:

t > 0 1, sgn (t) = -1, t< 0

Step by Step Answer:

a Using a table of Fourier transforms and the time reversal theorem the Fourier transfo...View the full answer

Principles of Communications Systems, Modulation and Noise

Students also viewed these Physics questions