Q3 Determine the closed-loop transfer function of the system shown in Figure Q3a. The plant transfer functions are: (a) 1 g1(s) = 52 + 1 4 92(s) = s+2 and the feedback transfer functions are: h1(s) = 0.25s h2(s) = s+1 R(s) C(s) g1(s) 82(s) h(s) h2(s) Figure Q3a Please see overleaf for part (b)... Continued overleaf Page 3 of 11 (b) (i) Using the Routh-Hurwitz criterion, find the range of values of parameter 'a' for which the system shown in Figure Q3b is stable. Is the system stable for a = 30? If not, how many positive (unstable) poles does it have? (ii) R(s) E(s) C(s) s+4 s2 +s+9 Figure Q3b

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Quantization and Resolution

Quantization is a methodology of carrying out signal modulation by the process of mapping input values from an infinitely long set of continuous values to a smaller set of finite values. Quantization forms the basic algorithm for lossy compression algorithms and represents a given analog signal into digital signals. In other words, these algorithms form the base of an analog-to-digital converter. Devices that process the algorithm of quantization are known as a quantizer. These devices aid in rounding off (approximation) the errors of an input function called the quantized value.

Probability of Error

This topic is widely taught in many undergraduate and postgraduate degree courses of: