Print out Homework and Do Work on the Printed Pages

ES 442 Homework #7

(Spring 2017 – Due April 10, 2017 )

Print out homework and do work on the printed pages.

Textbook: B. P. Lathi & Zhi Ding, Modern Digital and Analog Communication Systems, 4th edition, Oxford University Press, New york, 2009.

Problem 1 Angle Modulation (20 points)

We have an angle modulated signal described by

(a) Consider jMOD(t) to be a PM signal with kp = 20; Find m(t).

(b) Consider jMOD(t) to be a FM signal with kf = 20p; Find m(t).

Problem 2 ASCII Code (20 points)

(Problem 6.1-9 in Lathi and Ding)

The American Standard Code for Information Interexchange (ASCII) has 128 binary-coded characters. If a computer generates 100,000 characters per second, determine the following:

(a) The number of bits (binary digits) required per character.

(b) The number of bits per second required to transmit the computer output, and the minimum bandwidth required to transmit this signal.

(c) For a single error detection capability, an additional bit (called a parity bit) is added to the code of each character. Modify your answers for part (a) and (b) to accommodate the addition of the parity bit for each character.

Problem 3 CD Audio (30 points)

(Problem 6.2-1 in Lathi and Dong)

A compact disc (CD) records audio signals digitally by using PCM. The audio baseband signal’s bandwidth is 15 kHz.

(a) If the Nyquist samples are uniformly quantized into L = 65,536 levels and then binary-coded; determine the number of binary digits (bits) required to encode a sample.

(b) If the audio signal has an average power of 0.1 watt and a peak voltage of 1 volt. Find the resulting ratio of signal-to-quantization (SQNR) of the uniform quantizer output in part (a).

(d) In practice CD music is actually sampled at 44,100 samples/second, which is well above the Nyquist rate. Still retaining the number of levels L to be 65,536 levels, determine the bit rate needed to support this higher sampling rate. What is the minimum bandwidth needed to support this higher data rate.

Problem 4 Bit Rate and Baud Rate (10 points)

A multi-level digital communication system sends one of 32 possible levels over a channel every 0.8 milliseconds.

(a) What is number of bits corresponding to each level?

(b) What is the Baud rate?

Problem 5 Delta Modulation (20 points)

Consider a sinusoidal signal m(t) = A×cos(wmt), where fm = 2pwm, that is applied to a delta modulator with step size D. Show that slope overload distortion will occur if

where fS = 1/TS is the sampling frequency and TS is the period between samples.

Homework 5
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