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 200Fig. 1. Frequency spectrum of m(t) II. P ROBLEM 2 The signal m(t) = 8 sin(2πt), voltsis transmitted using a 4-bit binary PCM system. The quantizer is of the the mid-riser type, with a step size of 1volt. Sketch the resulting PCM wave for one complete cycle of the input. Assume a sampling rate of four samplesper 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-bitbinary 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 theappropriate 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.