Find maximum bit rate that can be supported by pcm system

Assignment Help Other Engineering
Reference no: EM131281103

Assignment

Question 1

(a) A computer terminal has 128 characters on its keyboard and each character is transmitted using binary words. How fast can the characters be sent (characters/s) over a telephone line having a bandwidth of 3.2 kHz and an SNR of 20 dB?

(b) A source transmits binary words of length 10 bits. One fourth of the possible words have a probability of being transmitted that is ½12 for each word. The remaining three fourths have probabilities equal to 5½12. Find the entropy of the source.

(c) A waveform, 0.23 + 1.69 sin(300t + 30o), is to be sampled and reproduced from these values. Determine the maximum allowable interval between the sample values.

Question 2

(a) The power spectral density (PSD) of a zero-mean ergodic process y(t) is given by

2336_Power Spectral Density.jpg

Find the variance of y(t) in terms of B, where B > 0.

(b) An analog signal is to be converted into a PCM signal that is a binary polar NRZ line code. The signal is transmitted over a channel that is absolutely bandlimited to 8 kHz. The PCM quantizer has 32 steps. The overall equivalent transfer function is of the raised cosine-rolloff type with r = 0.25 .

(i) Find the maximum bit rate that can be supported by the above PCM system without introducing intersymbol interference (ISI).

(ii) Find the maximum bandwidth that can be permitted for the analog signal.

(c) The input signal r(t) = s(t) + n(t) is given as input to a matched filter with impulse response h(t). The input noise n(t) is white noise whose power spectral density (PSD) is given by Pn(f) = 1. The Fourier transform of signal s(t) is given by

S(f) = T[{sin (πfT)} / (πfT)]2

The matched filter output signal attains the peak value at t0 = 2T. Determine the impulse response h(t) of the matched filter and sketch it out for T = 1 ms and assuming the matched filter's real-valued constant K is equal to 1.

Question 3

(a) Represent the data sequence 0 1 1 0 1 0 1 using Manchester NRZ signaling. Assume the duration of each bit to be 4 ms.

(b) A transmitter generates signal s(t) given by

s(t) = 10 cos[2πfct + 6 sin(2000πt)]
where fc = 100 MHz.

(i) If the phase deviation constant is 50 rad/V, find the mathematical expression for the corresponding phase modulation voltage m(t) . Specify the peak value and frequency of this phase modulation voltage.

(ii) If the frequency deviation constant is 105 rad/V-s, find the mathematical expression for the corresponding FM voltage m(t). Specify the peak value and frequency of this FM voltage.

Question 4

The following baseband signaling waveforms are used for the transmission of binary data generated by a digital source

s1(t) = a, 0 < t ≤ T (binary 1)
s2(t) = b, 0 < t ≤ T (binary 0)

where a, b are real-valued constants and a > b. The signal at the output of the receiver filter is a sum of baseband signal and white Gaussian noise whose mean and variance are 0 and σ2, respectively.

(a) Show that the optimum detection threshold level (VT) for detecting the transmitted data is given by

VT = [2σ2 ln(P2/P1) + a2 - b2] / 2(a - b)

(b) Find the BER for the above baseband signaling system when a = 10, b = 5, p1 = 3/4 , p2 = 1/4 and σ2 = 0.5. Refer to Appendix A for the Q function table.

(c) Find the entropy of the digital source, if the optimum detection threshold level (VT) given in part(a) is

VT = (a + b)/2

APPENDIX A

Tabulation of the Q-function

z

Q(z)

z

Q(z)

0.0

0.50000

2.0

0.02275

0.1

0.46017

2.1

0.01786

0.2

0.42074

2.2

0.01390

0.3

0.38209

2.3

0.01072

0.4

0.34458

2.4

0.00820

0.5

0.30854

2.5

0.00621

0.6

0.27425

2.6

0.00466

0.7

0.24196

2.7

0.00347

0.8

0.21186

2.8

0.00256

0.9

0.18406

2.9

0.00187

1.0

0.15866

3.0

0.00135

1.1

0.13567

3.1

0.00097

1.2

0.11507

3.2

0.00069

1.3

0.09680

3.3

0.00048

1.4

0.08076

3.4

0.00034

1.5

0.06681

3.5

0.00023

1.6

0.05480

3.6

0.00016

1.7

0.(11157

3.7

0.00011

1.8

0.03593

3.8

0.00007

1.9

0.02872

3.9

0.00005

The definition of Q function is:

Q(z) = z (1/√2π) e-y^2/2 dy

Reference no: EM131281103

Questions Cloud

Basic objectives of monetary policy : What are the basic objectives of monetary policy? Comment on the cause-effect chain through which monetary policy is made effective. What are the major strengths of monetary policy? 200 words
Determine the maximum slope allowed : For such surface material it is recommended that to prevent scouring of the surface the average velocity be no more than 1.75 ft/s. Determine the maximum slope allowed.
Skilled and unskilled unit labor requirements : The technology is such that at any factor prices, cars are intensive in their use of skilled labor. You can alternatively use the skilled and unskilled unit labor requirements in the two goods, cars and food, given in the table below.
Find the channel slope needed to maintain this depth : The depth downstream of a sluice gate in a rectangular wooden channel of width 5 m is 0.60 m. If the flowrate is 18 m3 /s, determine the channel slope needed to maintain this depth.
Find maximum bit rate that can be supported by pcm system : Find the maximum bit rate that can be supported by the above PCM system without introducing intersymbol interference (ISI). Find the maximum bandwidth that can be permitted for the analog signal.
What is the difference in a per se violation : What is the difference in a “per se” violation and one that requires the rule of reason? How does the “Maricopa” case explain the application of “per se” and the rule of reason? Explain how the “Jefferson” case establishes guidelines for understandin..
Provide a long-term sustainable food supply : The characteristics that will enable your land to provide a long-term sustainable food supply.
Should the nlrb issue the bargaining order : Is the company's conduct within the company's rights under the NLRA? Explain. Should the NLRB issue the bargaining order requested by the union? Explain.
Exhaust administrative remedies : What does it mean that a provider is required to “exhaust administrative remedies” before it can challenge an administrative decision in court? Name and describe the four federal laws that compose the foundation for antitrust legislation. List and de..

Reviews

Write a Review

Other Engineering Questions & Answers

  Characterization technology for nanomaterials

Calculate the reciprocal lattice of the body-centred cubic and Show that the reciprocal of the face-centred cubic (fcc) structure is itself a bcc structure.

  Calculate the gasoline savings

How much gasoline do vehicles with the following fuel efficiencies consume in one year? Calculate the gasoline savings, in gallons per year, created by the following two options. Show all your work, and draw boxes around your answers.

  Design and modelling of adsorption chromatography

Design and modelling of adsorption chromatography based on isotherm data

  Application of mechatronics engineering

Write an essay on Application of Mechatronics Engineering

  Growth chracteristics of the organism

To examine the relationship between fermenter design and operating conditions, oxygen transfer capability and microbial growth.

  Block diagram, system performance and responses

Questions based on Block Diagram, System Performance and Responses.

  Explain the difference in a technical performance measure

good understanding of Mil-Std-499 and Mil-Std-499A

  Electrode impedances

How did this procedure affect the signal observed from the electrode and the electrode impedances?

  Write a report on environmental companies

Write a report on environmental companies

  Scanning electron microscopy

Prepare a schematic diagram below of the major parts of the SEM

  Design a pumping and piping system

creating the pumping and piping system to supply cool water to the condenser

  A repulsive potential energy should be a positive one

Using the data provided on the webvista site in the file marked vdw.txt, try to develop a mathematical equation for the vdW potential we discussed in class, U(x), that best fits the data

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd