Question: Verify the pulse width-bandwidth relationship of Equation (2.234) for the following signals. Sketch each signal and its spectrum. (a) x(t) = A exp (-t 2

Verify the pulse width-bandwidth relationship of Equation (2.234) for the following signals. Sketch each signal and its spectrum.

(a) x(t) = A exp (-t2 / 2τ2) (Gaussian pulse) 

(b) x(t) = A exp (-α |t|), (Gaussian pulse) α > 0 (double-sided exponential)

Step by Step Solution

★★★★★

3.46 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a The Fourier transform of this signal is X f A2... 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 Principles Communications Systems Questions!

Q:

Another definition of bandwidth for a signal is the 90% energy containment bandwidth. For a signal with energy spectral density G(f) = |X(f)| 2 , it is given by B 90 in the relation Obtain B 90 for...

Q:

Equation (31.14) was derived by using the relationship i = dq/dt between the current and the charge on the capacitor. In Fig. 31.9a the positive counterclockwise current increases the charge on the...

Q:

For each of the following pairs of compounds, determine the relationship between the two compounds: a. b.

Q:

A discrete-time signal x[n] is sketched below. Sketch and label carefully each of the following signals: (a) x[n - 2]; (b) x [2 -n]; (d) x[-1-2n]; (c) x [2n]; (e) xod[n] (the odd part of x[n]) 1...

Q:

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Q:

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

Q:

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

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:

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

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:

Use integration by parts, together with the techniques of this section, to evaluate the integral. 49. ( In(x - x + 2) dx x tan-'x dx 50.

Q:

Concord, a coffee-mug producer, generally conducts over half of its business in the last month of the calendar year due to holiday sales. By the end of December, its fiscal year-end, Concord had...

Q:

Which would you prefer? A 2 % annual yiold on an investment in 1 0 - year U . S . government bonds. A 4 % annual yield on a credit risk - free 1 0 - year government bond from the mythical country of...

Q:

Research has looked at emotional reactions to infidelity and found that men get homicidal and suicidal and women feel undesirable and insecure (Shackelford, LeBlanc, & Drass, 2000). Lets imagine we...

Q:

Given point P(r = 0.8, = 30, = 45) and E = 1/r 2 [cos a r + (sin / sin ) a ], find (a) E at P; (b) |E| at P; (c) A unit vector in the direction of E at P.

Q:

Express the uniform vector field F = 5a x in (a) Cylindrical components; (b) Spherical components.

Q:

The surfaces r = 2 and 4, = 30 and 50, and = 20 and 60 identify a closed surface. Find (a) The enclosed volume; (b) The total area of the enclosing surface; (c) The total length of the twelve edges...

Q:

Elsinore Electronics is a decentralized organization that evaluates divisional management based on measures of divisional contribution margin. Home Audio (Home) Division and Mobile Electronics...

Q:

6. One person found the equation y = 10x + 50 to be a good fit for the 2 points data. Use this model to predict y when x is 9. * Your answer 8. a. Estimate the slope of the line of fit. * 2 points...

Q:

Your company will generate $57,000 in annual revenue each year for the next seven years from a new information database. If the appropriate interest rate is 7.8%, what is the present value of the...