Partial Fraction Decomposition Example This is probably a very easy question, but can someone how in this example how X(z) was simplified from having z squared in the numerator to having 1 in the numerator? And how the terms in the denominator are also simplified? Partial fraction expansion • In case this direct formula is not useful, we can use the partial fraction expansion technique

Partial Fraction Decomposition Example

This is probably a very easy question, but can someone how in this example how X(z) was simplified from having z squared in the numerator to having 1 in the numerator? And how the terms in the denominator are also simplified?

Partial fraction expansion • In case this direct formula is not useful, we can use the partial fraction expansion technique. • Example: Find x[n] if X(z) = 7 (z – 1)(z- 2) with ROC: [z] > 2 • Solution: ? ? X(z) = (1 – z-1)(1 – 2z-1) - 1-z-1 * 1 – 2z-1 A(1 – 2z-1) + B(1 – 7-) A + B = 1 (1 – z-1)(1 – 2z-1) 2A + B = 0 A = -1, B= 2