X (t) = A, cos (t + 0) %3D Where A, is a real constant, 2 is a random variable with density function fo(), and 0 is a random variable uniformly distributed on the interval (0,2n) independent of 2. Show that the power spectrum of X(1) is Sx (1m) = "[ Sa(@) + Sa(-w)]

X (t) = A, cos (t + 0) %3D Where A, is a real constant, 2 is a random variable with density function fo(), and 0 is a random variable uniformly distributed on the interval (0,2n) independent of 2. Show that the power spectrum of X(1) is Sx (1m) = "[ Sa(@) + Sa(-w)]

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Q: Electrical Engineering 1) A 90° degree corner reflector, in conjunction with a /2 dipole feed, is…

A: Given: A 90° degree corner reflector, in conjunction with a λ/2 dipole feed, is used in a radar…

Q: The region z 0 that would provide

A: It is given that: εr'=μr=1εr''=0Ex=150 e-j10z ax+50∠20° ej10zaxV/mSo, Ei=150 and Er=50∠20°

Q: An electric dipole of 100 a, pC m is located at the origin. Find V and E at poin (a) (0, 0, 10) (h)…

A: P=Qd =100 pcm =(100×10-12cm)azAt point (0,0,10)Electric field (V) due to electric dipole centred…

Q: 1. Assuming the spherical D- layer has a refractive index of 0.8, and the frequency of transmitted…

A: As per the rules we can answer only 3 sub-parts, please post the remaining sub-parts as the separate…

Q: If you know that the electric field component in the YZ plane of a short annulus (side length I) is…

Q: 27.16 For the galaxy NGC 5585, the quantity 2v, / sin i = 218 km s-, and its apparent H magnitude is…

Q: Q1) Answer by true or false for ten of the following items, and correct the false one 4- The smooth…

A: Since you have posted a question with multiple sub-parts, we will solve first Three subparts for…

Q: 7

Q: The Voyager 1 spacecraft, now in interstellar space, radios data back to Earth using a 22.4-W…

A: The antenna is broadcasting in all direction, the practical power of the transmitter will be…

Q: The PCB monopole antenna shown in figure below is required to be designed for Bluetooth Low Energy…

A: Given: The PCB monopole antenna shown in the figure below is required to be designed for Bluetooth…

Q: A standard air-filled rectangular waveguide with dimensions a = is fed by a 4-GHz carrier from a…

A: Given a=8.636b=4.318f=4GHz

Q: 3948887715217948[1] 9.3-6 Pulse Propagation. A pulse of initial temporal width To is transmitted…

Q: As shown in the right figure, an imaging system includes 2 thin lenses separating by a distance (L),…

Q: A distortionless line has Z, = 60 , a = 20 mNp/m, u = 0.6c, where c is the speed of light in a…

A: Given that distortion line Z0=60ohm alpha= 20 mNp/m, u = 0.6c, where c is the speed of light in…

Q: A perpendicularly polarized uniform plane in air is obliquely incident on a lossless medium…

A: Figure: Oblique incidence at a plane dielectric interface

Q: Find the far-field condition of a satellite dish antenna of dimension 60 cm operating at 12 GHz.

Q: 1) The electric field component of a uniform plane VLF electromagnetic field vertically down in the…

A: Given

Q: 1. State or name one example of wired transmission media. 2. A type of transmission line that is…

A: 1. One of wire transmission media is telephone network, Telephone network : By this network…

Q: Transmitting and receiving antennas operating at 1 GHz with gains (over isotropic) of 20 and 15 dB,…

Q: Design a uniform linear scanning array whose maximum of the array factor is 30° from the axis of the…

A: Given: An uniform linear scanning array, The maximum array factor is 30° from the axis of the array…

Q: In space wave propagation, the maximum Line-of- Sight distance (d) in miles between a transmitting…

A: The given question is as follows

Q: D9.3. Find the amplitude of the displacement current density: (a) adjacent to an automobile antenna…

Q: 1 Let A = pcos o a, + pz² sin o a, (a) Transform A into the rectangular coordinates and calculate…

Q: D3.9. Given the field D = 6p sin oa, +1.5p cos oa, C/m2, evaluate both sides of the divergence…

Q: The signal received by a parabolic antenna is concentrated in its receiver, which is placed,…

A: Communication systems play a major role in connecting peoples, The transmitter is a device where…

Q: A mobile is located 5 km away from a base station and uses a vertical 2/4 monopole antenna with a…

A: It is given that: d=5kmG=2.55 dBE.F.=10-3Vmf=900MHzλ=0.333

Q: An optical system with multiple lenses is placed in the air. Experiment results find that (1) when…

Q: 4.1 I P,= 10 W, G, = 0 dB, G,= 0 dB, and ſe = 900 MHz, find P, in Watts at a free space distance %3D…

A: As per the Bartleby guidelines we are allowed to solve only one question at a time, I am very sorry…

Q: Coupling Efficiency. (a) A source emits light with optical power Po and a distribution I(0) (1/7)Po…

A: Given n1=1.46n2=1.455n3=3.5

Q: Large radio telescopes, like the one in Arecibo, Puerto Rico, can detect extremely weak signals.…

Q: 2) Consider the function A (z, t) = (z – vt)? + 1 where A is a constant. Show that it is a solution…

A: Given data:

Q: An air-filled X-band rectangular waveguide has dimensions a= 2.286 cm and b = 1.016 cm. If the…

A: Given: An air filled rectangular waveguide with a=2.286 cmb=1.016 cm Waveguide has copper walls with…

Q: (Only the last part) Write the expressions for E and B in the form ? = 10 sin(?? − ??) and ? = ????…

Q: Design a 5-ELEMENT YAGI-UDA antenna for a 545 GHz frequency, with the following contents: a.…

A: 5 Element YAGI-UDA antenna is an antenna which are fixed on a pole with 5 perpendicular metal rods…

Q: A short dipole-carrying current I, cos wt in the a̟ direction is located at the origin in free…

Q: D9.3. Find the amplitude of the displacement current density: (a) adjacent to an automobile antenna…

Q: The radial component of the radiated power density of an infinitesimal linear dipole of length 1<< 1…

A: Given data, The value of peak value of power density is Am. The value of spherical co-ordinate is .…

Q: Given that D = 10sinϴar + 2 cosϴaϴ .Evaluate both sides of the divergence theorem for the volume…

Q: This is the optical transmission function of a material. 90 80 S 70 60 50 40 30 20 10 0.1 0.2 0.3…

A: The Transmission percentage is an property of optical materials which helps us to judge the…

Q: 2.1) A parabolic reflector antenna used for radio astronomy to observe a certain patch in the sky,…

A: Given: A parabolic reflector antenna used for radio astronomy to observe a certain patch in the sky…

Q: Modal Dispersion. A step-index fiber of numerical aperture NA = 0.16, core radius a 45 um, and core…

A: According to question we have to sketch the shape of the received pulse (a) using ray optics and…

Q: A parabolic antenna with a dish diameter of 4.5 m operates at frequency of 2.5 GHz (assumed uniform…

A: The detail solution in the image

Q: PRACTICE EXERCISE A C-band radar with an antenna 1.8 m in radius transmits 60 kW at a frequency of…

A: According to the question we have to find the value of maximum range in nautical miles.

Q: as both transmitter and receiver, is at the operating frequency of 5GHz. It has a gain of 150…

Q: (b) dry earth (E (c) seawater (ɛ = 8lɛ,,o = 4 S/m) 10.9 Alumina is a ceramic material used in making…

Concept explainers

Antenna Characteristics

The antenna is an important concept in the domain of electronics and communication engineering. An antenna forms an integral part of many commonly used devices such as wireless modems, routers, game controllers, mobile phones, bluetooth devices, and so on. In simple terms, any wireless communication makes use of antennas to serve the purpose. An antenna, also known by the term 'arial', is an electrical device that converts electrical signals into electromagnetic waves or electromagnetic waves into electrical signals. An antenna contains a transmission line usually made up of co-axial cable, it then receives the signals and converts them into electromagnetic waves, which are then transmitted via space into their required destination. A communication system essentially makes use of two antennas, a transmission antenna, which converts electrical signals into electromagnetic waves, and a receiving antenna, which receives the electromagnetic waves and converts them back into electrical signals.

Question

A random process is given by
X (t) = A, cos (2t + 0)
Where A, is a real constant, 2 is a random variable with
density function fo(), and 0 is a random variable
uniformly distributed on the interval (0,211) independent
of 2. Show that the power spectrum of X(t) is
%3D
2
[(w-)°f +(w)f]=(@) "s

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Which row represent the most stable system and why? nyquist and root locus plot attached.
Two identical loudspeakers are located at points (−10, 0, 0) and (0, 0, 10) of our coordinate system, where the numbers in the brackets correspond to the (x, y, z) coordinates of the points, expressed in meters. The loudspeakers are driven by the same oscillator with a frequency of 170 Hz. The speed of sound in air can be considered 340 m/s. a) Give the coordinates of those points located on the positive x axis where the sound waves coming from the two loudspeakers interfere constructively. b) A receiver is started to move slowly from the origin (0, 0, 0) along a path lying in the x–y plane so that it receives constant sound intensity throughout its slow motion. What is the shape of the path the receiver should take?
A system has the following characteristic equation: s + s + 3 + 2s + 2 = 0 Using the Routh-Hurwitz method, check
Enter the value of the K coefficient required for the marginally stable/unstable system of a system whose characteristic equation is given as s3+6s2+3s+K=0.
Suppose an electrical signal generated, y(t) can be modelled as follows where t, is time in second, y(t) is voltage in mv. a) Produce graphs showing the amplitude and phase spectrum of y(t). b) State whether this time-domain signal y(t) is periodical, or non-periodical and justify your answer.
In case the sound from the engine of a vehicle is modelled by the function y(t) = cos[ω(t + τ) + θ] where time delay=τ & phase=θ Determine the frequency & period of the signal u(t) whena)[ω, τ, θ] = [π/3, 1/2, π/2]b)[ω, τ, θ] = [3π/4, 1/2, π/4] N.b time should be in seconds & frequency in Hertz. c) y(t) = e-atu(t) for t≥0 & y(t) = 0 for t<0 where a>0 is a constant The function above defines the model of the decay of the vibration of a vehicle engine. i.Make a sketch of the signal y(t) & determime its fourier transform.
In the system given in the coming years, t=0 candidate election chance, F(t) candidates x(t) at the exitnever happens. Maximum Overshoot (Mp) 20%, 10 rad/s before damping (wd damped) andCalculate K and B samples at the value M=1.
If x(n)={1, 2, 0, -1} and h(n)={1, 2, 0, -1} find y(n). don't care where n=0.
Draw the root locus for the control system whose T.F. is given below,
(a) The dynamics of a discrete-time system are determined by the difference equation; 8yk+2-6y+1+yk =9 Determine the response of the system given that yo= 1 and y₁= 1.5
Communication system Let's consider a communication system where four signals with different frequencies f1, f2, f3, and f4) are combined to form a single composite signal. The composite signal is represented by the equation: s(t) = 3 sin(500m (k, x t) + T/6) + 4 sin (10007 (kz × t) + T/4) + 2 sin(1500t (k3 X t) + T/3) + 5 sin(2000m(k. X t) + /2) Given the scaling factors: kg = 0.8, kz = 1.6, k3 = 2.4, and k4 = 3.2. Determine the fundamental frequency
Derive the