Differences

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--- inleiding_dsp:hoofdstuk_4 [2012/08/01 10:11] – jerry
+++ inleiding_dsp:hoofdstuk_4 [2022/09/01 11:44] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
-====== 4.9-4.13 (blz 117) ======
+====== 4.9-4.12 (blz 117) ======
 )
@@ Line 43: / Line 43: @@
 {2z^3 Y(z)} - {3z^2 Y(z)} + z
 \end{split}
+$$
+Dan gaan we vanuit de overdrachtsfunctie naar de ([[http://en.wikipedia.org/wiki/Recurrence_relation|Recurrence relation]]) we vervangen daarbij z met een tijdverschijving van één.
+$$
+\begin{split}
+{2z^3 Y(z)} - {3z^2 Y(z)} + z &= X(z) \\
+y[n+3] - 3y[n+2] + y[n+1] &= x[n] \\
+y[n] - 3y[n-1] + y[n-2] &= x[n-3] \space\text{(-3 bij alle indexen)} \\\
+y[n] \underbrace{- 3y[n-1] + y[n-2]}_\text{Naar rechts van = teken} &= x[n-3]
+\end{split}
+$$
+$$
+\begin{split}
+y[n] &= 3y[n-1] - y[n-2] + x[n-3] \\
+\frac{ 2y[n] }{ 2 } &= \frac{ 3y[n-1] - y[n-2] + x[n-3] }{ 2 } \\
+               y[n] &= 1.5y[n-1] - 0.5y[n-2] + 0.5x[n-3]
+\end{split}
 $$