Question

The new pole locations due to truncation of coefficient to 4 bit including sign bit in the cascade realization \[ H(z) = \frac{1}{(1-0.95z^{-1})(1-0.25z^{-1})} \]

• A. 0.5, 0.25
• B. 0.875, 0.25
• C. 0.95, 0.5
• D. 0.75, 0.125

Hint:

The effect of quantization should always be taken into account when using digital values to represent analog systems. Quantization will alter the pole positions.

Answer 1

The Correct Option is B

Truncating the coefficients to 4 bits including the sign bit, means that only a limited set of numbers can be used for the coefficients. For example, a decimal 0.95 in 4-bit with sign form can be only be 0.875. Similarly 0.25 which is 0.01 in binary will remain the same. Thus the new pole locations will be 0.875 and 0.25.