Question

The number of multipliers and delay elements required in the direct form II realization of \[ H(z) = \frac{1 + 0.5z^{-1} - 2z^{-2}}{1 + z^{-1} - 2z^{-2}} \]

• A. 5, 2
• B. 3, 4
• C. 6, 4
• D. 3, 2

Hint:

Remember the key parameters in a direct form II realization: the number of multipliers equals the number of coefficients and the number of delay elements equals the order of the transfer function.

Answer 1

The Correct Option is C

In the direct form II realization, the number of multipliers is equal to the number of coefficients (excluding 1) in the numerator and denominator of the transfer function. The number of delay elements is equal to the order of the transfer function. In this case the transfer function is: \[ H(z) = \frac{1+0.5z^{-1}-2z^{-2}}{1+z^{-1}-2z^{-2}} \] The number of multipliers is 2(coefficients in numerator - 0.5 and -2) + 2(coefficients in denominator - 1 and -2) = 4 The order of the transfer function is 2, hence number of delay elements = 2*2 = 4. Therefore the correct option is 6 multipliers and 4 delay elements.