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--- dsp:inversezxfer [2013/04/22 09:56] – randy
+++ dsp:inversezxfer [2022/09/01 11:44] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
 ====== Inverse Z transformatie ======
+Transformeer naar tijd-domein:
 $$
 y[z] = \frac{2}{ (z-1) \cdot (z+0.5) }
 $$
+Prototype uit tabel:
+$$
+\frac{ z(1-a) }{ (z-a)(z-1) }
+$$
+A =
+$$
+a= -\frac{1}{2}
+$$
+Wordt:
+$$
+\frac{z \cdot \frac{3}{2} }{ (z+\frac{1}{2}) (z-1) }
+$$
+Volgende stap (?)
+$$
+\frac{1}{z}  \cdot  \frac{z \cdot \frac{3}{2} }{ (z+\frac{1}{2}) (z-1) } \cdot \frac{4}{3}
+$$
+Volgende stap kapt alles voor n=0 af
+$$
+y[n]  =  \frac{4}{3}  \cdot  (1-(-\frac{1}{2}) ^ {n}) \cdot  u[n]
+$$
+Volgende stap (?)
+$$
+y[n]  =  \frac{4}{3}  \cdot  (1-(-\frac{1}{2}) ^ {(n-1)}) \cdot  u[n-1]
+$$
+Blz 115 breuksplitsing