I have already understood partial fraction and here is link for my relevant DSP SE question

Finding inverse z transform for two sided ROC?

But now i want to know, is there any difference between partial fraction form and factored form in signal processing context?

For example I have a z transform $$Y(z)=\frac{(z^2−z)}{(z^2+1.3z+0.3)}$$

a)What will be its partial fraction form?

b)What will be its factored form?

  • 1
    $\begingroup$ Homework? Factoring a polynomial is basic algebra; you should have hit partial fraction expansion in calculus class. These are both pretty basic operations in signal processing analysis and design. $\endgroup$
    – TimWescott
    Mar 10, 2020 at 22:55
  • $\begingroup$ @TimWescott no,it is not home work $\endgroup$
    – DSP_CS
    Mar 11, 2020 at 7:29
  • $\begingroup$ b) just factor the numerator and denominator polynomials. $\endgroup$ Mar 12, 2020 at 15:22
  • $\begingroup$ a) after factoring, express the factored form of $Y(z)$ as the sum of partial fractions. you had to learn about that in calculus when you were integrating rational functions that look sorta like $Y(z)$. $\endgroup$ Mar 12, 2020 at 15:23

1 Answer 1


The partial fraction form helps in calculating the z-transform inverse since we can get the inverse of each term in partial fraction by inspection and hence get the inverse of the whole transfer function. The factored form can directly give poles and zeros by equating the numerator and denominator to zero.

  • $\begingroup$ Can you please kindly explain with an example,preferably with the one given in my question? $\endgroup$
    – DSP_CS
    Mar 11, 2020 at 7:28
  • $\begingroup$ You have calculated the partial fraction term in your provided link. It helps to solve the inverse transform but it does not directly provide the zeros or poles. For the factored form, Y(z) = $$Y(z)=\frac{(z(z-1))}{(z+1)(z+0.3))}$$ The roots of numerator and denominator gives zeros and poles $\endgroup$
    – DSP Novice
    Mar 11, 2020 at 8:09
  • $\begingroup$ Can you please kindly update your answer so as to also include MATLAB code for finding factored form? $\endgroup$
    – DSP_CS
    Mar 12, 2020 at 9:50
  • $\begingroup$ [z,p,k] = tf2zp(b,a) This function should help you $\endgroup$
    – DSP Novice
    Mar 12, 2020 at 10:28

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