Using the uniqueness property of the Fourier series, find exponential Fourier series for the following signals (f 0 is an arbitrary frequency) (a) x 1 (t) sin 2 (2f 0 t) (b) x 2 (t) cos(2f 0 t) sin(4f 0 t) (c) x 3 (t) sin(4f 0 t) cos(4f 0 t) (d) x 4 (t) cos 3 (2f 0 t) (e) x 5 (t) sin(2f 0 t) cos 2 ...

a Use the exponential representation of the sine to get the Fourier coefficients as note that the pe ...

Using the uniqueness property of the Fourier series, find exponential Fourier series for the following signals (f

Question:

Using the uniqueness property of the Fourier series, find exponential Fourier series for the following signals (f₀ is an arbitrary frequency):

(a) x₁(t) = sin²(2πf₀t)

(b) x₂(t) = cos(2πf₀t) + sin(4πf₀t)

(d) x₄(t) = cos³(2πf₀t)

(e) x₅(t) = sin(2πf₀t) cos²(4πf₀t)

(f) x₆(t) = sin²(3πf₀t) cos(5πf₀t)

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 11:38 AM

See More Questions

The coefficients of the trigonometric Fourier series representation of a function are: If n = 50n, find the exponential Fourier series for the function. a,- , n = 0, 1, 2,
The Fourier series trigonometric representation of a periodic function is Find the exponential Fourier series representation of f(t). f(t) = 10-5 |-cos nT1+.sin 1 n +1
Find the exponential Fourier series for the signal shown.
Jimmy and Elizabeth plan on getting married on the 15th of August. Elizabeth decides that she would prefer to have the reception in her backyard, so she rents an event tent from CELEBRATE Ltd, a firm...
What is the relationship between the short-run Phillips curve and the long-run Phillips curve?
The following trial balance was extracted from the books of Old NV on 31 December 20X1. Note of information not taken into the trial balance data: (a) Provide for: (i) An audit fee of 38,000. (ii)...
Find the positive z-score for which 70% of the distributions area lies between -z and z. Find the indicated z-score.
Veritas Emerging Market Fund specializes in investing in emerging stock markets of the world. Mr. Henry Mobaus, an experienced hand in international investment and your boss, is currently interested...
StorSmart Company makes plastic organizing bins. The company has the following inventory balances at the beginning and end of March: S Raw materials Work in process Finished goods Beginning Inventory...
Mr. Eric Wong operates a real estate agency that specializes in selling properties that are hard to sell. He is approached one day by a prospective client who has three properties he wishes to sell....
Expand the signal x(t) = 2t 2 in a complex exponential Fourier series over the interval |t| 2. Sketch the signal to which the Fourier series converges for all t.
Find the energies and powers of the following signals (note that 0 and are possible answers). Tell which are energy signals and which are power signals. (a) x 1 (t) = cos(10Ït) u(t) u(2 - t) (b)...
Consider a process with the following streams: When \(\Delta T_{\text {min }}=10^{\circ} \mathrm{C}\), the minimum utilities for heating and cooling are \(237 \mathrm{~kW}\) and \(145 \mathrm{~kW}\),...
How did the Jacksonville, Florida, vagrancy ordinance invalidated by the Supreme Court in the Papachristou case offend the Constitution of the United States? Have the reforms in vagrancy laws at the...
The U.S. Supreme Court has recognized a constitutional right to represent oneself in a criminal trial. Could a person who insisted on self-representation at trial later challenge his or her...
Does the grand jury still play a viable role in the criminal justice system? Are the criticisms of the grand jury valid? Why or why not?
What new or revised procedures would expedite the resolution of criminal appeals? Would such procedures detract from the fair and deliberative review essential to determine whether the decision of...
Why do you think the U.S. Supreme Court has never held that the Fifth Amendment requirement of indictment by a grand jury applies to the states as well as to the federal government?
Repeat Problem 4.20 (Fig. 4.32), except that the tank is now sealed at the top with a pressure of 25.0 kPa above the fluid. 30 Orange drink (sg - 1.10) 3.0 m 4.6 m 2.4-m diameter 1.2 m Circular view...
Give codons for the following amino acids: (a) Th (b) Asp (c) Thr
In Figure 10.39, R L = Z 0 and R g = Z 0 /3. The switch is closed at t = 0. Determine and plot as functions of time (a) The voltage across R L ; (b) The voltage across R g ; (c) The current through...
A simple frozen wave generator is shown in Figure 10.38. Both switches are closed simultaneously at t = 0. Construct an appropriate voltage reflection diagram for the case in which R L = Z 0 ....
In the transmission line of Figure 10.37, the switch is located midway down the line and is closed at t = 0. Construct a voltage reflection diagram for this case, where R L = Z 0 . Plot the load...
A 5.0 g bullet moving 325 m/s is shot into a 1.25 kg block, which slides for 1.35 seconds across the surface it is on before coming to rest. What is the average force of kinetic friction between the...
Roberta Bondar is travelling in her space craft around a distant planet. The planet has a radius R' and she is at an altitude of 2R' above its surface, coasting at some constant speed in a circular...
Some enterprising physics students working on a catapult decide to have a water balloon fight in the school hallway. The ceiling is of height 3 . 4 m, and the balloons are launched at a velocity of 9...

Using the uniqueness property of the Fourier series, find exponential Fourier series for the following signals (f

Question:

Step by Step Answer:

a Use the exponential representation of the sine to get the Fourier coefficients as note that the pe...View the full answer

Principles of Communications Systems, Modulation and Noise

Students also viewed these Physics questions