The document discusses problems related to analogue and digital communications. It contains 5 problems: 1) Drawing the spectrum of a message signal sampled at different rates and specifying the cutoff frequency to fully recover the original signal from its sampled version. 2) Sketching the resulting pulse code modulation (PCM) wave for one cycle of an input signal that is quantized using a 4-bit binary system. 3) Determining the number of quantizing levels, quantizer step size, average quantizing noise power, and output signal-to-noise ratio for a sinusoidal modulating wave quantized using an n-bit code word. 4) Finding the Nyquist sampling rate for two signals.

1. 1
TELE3113 Analogue and Digital Communications
Tutorial 4
I. P ROBLEM 1
Fig. 1 shows the idealized spectrum of a message signal m(t).
1) If the signal is sampled at a period equal to 2 ms, 2.5 ms, and 5 ms, respectively, sketch the spectrum of the
resulting signal correspondingly.
2) If the sampling period is 2 ms, specify the cutoff frequency of the ideal reconstruction filter so as to recover
m(t) fully from its sampled version.
M( f )
f (Hz )
− 200 200
Fig. 1. Frequency spectrum of m(t)
II. P ROBLEM 2
The signal
m(t) = 8 sin(2πt), volts
is transmitted using a 4-bit binary PCM system. The quantizer is of the the mid-riser type, with a step size of 1
volt. Sketch the resulting PCM wave for one complete cycle of the input. Assume a sampling rate of four samples
per second, with samples taken at t = 8 , 3 , 5 , 7 seconds.
1
8 8 8
III. P ROBLEM 3
Consider a sinusoidal modulating wave of amplitude Am at the quantizer input and assume the use of an n-bit
binary code word at each quantizing level, determine
1) the number of quantizing levels L;
2) the quantizer step size;
3) the average quantizing noise power;
4) the output signal-to-noise ratio of the PCM system.
IV. P ROBLEM 4
Find the Nyquist sampling rate for each of the following signals:
1) m(t) = 5 cos(1000πt) cos(4000πt).
2) m(t) = sin(200πt)/(πt).
V. P ROBLEM 5
A binary channel with bit rate R = 36000 bits per second is available for PCM voice transmission. Find the
appropriate values of the sampling rate fs , the number of quantized levels, L, and the length of the code, n,
assuming the voice bandwidth is B = 3.2 kHz.