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UNIVERSIDAD DE LAS AMÉRICAS-PUEBLA

SCHOOL OF ENGINEERING

DEPARTAMENT OF COMPUTING, ELECTRONICS AND MECHATRONICS

IE 392 Digital Communications – Homework 1 (Source: Digital Communications by Bernard Sklar)

1. 800 characters per second are transmitted, where each character is represented by its 7-bit ASCII codeword, followed by an eighth bit for error detection, per character. A multilevel PAM waveform with M = 16 levels is used.

a) What is the effective transmitted bit rate?

b) What is the symbol rate?

2. It is desirable to transmit a 100-character alphanumeric message in 2 seconds, using 7-bit ASCII coding, followed by an eighth bit for error detection, per character. A multilevel PAM waveform with M = 32 levels is used.

a) Calculate the effective transmitted bit rate and the symbol rate.

b) Repeat part (a) for eight-level PAM and PCM (binary) waveforms.

3. An analog signal is sampled at its Nyquist rate 1/T_s, and quantized using L quantization levels. The derived digital signal is then transmitted on some channel. What is the duration time, T, of one bit of the transmitted binary encoded signal?

4. Consider an audio signal with spectral components limited to the frequency band 300 Hz to 3300 Hz. Assume that the sampling rate of 8000 samples per second will be used to generate a PCM signal. Assume the ratio of peak signal power to average quantization noise power at the output needs to be 30 dB.

a) What is the minimum number of uniform quantization levels needed, and what is the minimum number of bits per sample needed?

b) Calculate the system bandwidth required for detection of such PCM signal.

5. A waveform, x(t) = 10 Cos(1000 t + π/3) + 20 Cos(2000 t + π/6) is to be uniformly sampled for digital transmission.

a) What is the maximum allowable time interval between sample values that will ensure perfect signal reproduction?

b) If we want to reproduce 1 hour of this waveform, how many sample values need to be stored?

6. The information in an analog waveform, whose maximum frequency f_m = 4000 Hz, is to be transmitted using a 16-level PAM system. The quantization distortion must not exceed ± 1% of the peak-to-peak analog signal.

a) What is the minimum number of bits per sample or bits per PCM word that should be used in this PAM transmission system?

b) What is the minimum required sampling rate, and what is the resulting bit rate?

c) What is the 16-ary PAM symbol transmission rate?

7. In the compact disc (CD) digital audio system, an analog signal is digitized so that the ratio of the peak-signal power to the peak-quantization noise power is at least 96 dB. The sampling rate is 44.1 kilosamples/s.

a) How many quantization levels of the analog signal are needed?

b) How many bits per sample are needed for the number of levels?

c) What is the data rate in bits/second?