O'Reilly logo

Signals and Systems by Smarajit Ghosh

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

6.18 INVERSE z-TRANSFORM USING PARTIAL FRACTION EXPANSION

In partial fraction expansion method, the function X(z) is expressed as follows:

 

X(z) = α1X1(z) + α2X2(z) + α3X3(z) + ....... + αmXm(z)

 

where α1, α2, α3, ............ and αm are the constants and X1(z), X2(z), X3(z), ........., Xm(z) are the standard z-transforms. The inverse transform of these standard z-transform are known. Using linearity property we can write

 

x(n) = α1x1(n) + α2x2(n) + α3x3(n) + ....... + αmxm(n)    (6.72)

 

If the z-transform is rational in nature which can be expressed as the ratio of two polynomials as follows

 

image

 

Let b0 = 1. If b0 ≠ 1, the polynomials ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required