1
$\begingroup$

Two discrete-time systems are connected in series. Their input-output difference equations are:

\begin{align} w[k]&=0.25x[k-2]\\ y[k]&=0.5w[k-1]+0.5w[k-2]. \end{align}

  1. Determine the overall input-output difference equation relating $y[k]$ to $x[k]$
  2. Determine the impulse response of the overall system

Julie.

$\endgroup$
2
$\begingroup$

You simply need to put $w[k]$ into $y[k]$:

$$w[k]=0.25x[k-2] \Rightarrow \begin{align}w[k-1]&=0.25x[k-3]\\ w[k-2]&=0.25x[k-4] \end{align}$$

\begin{align} y[k] &= 0.5w[k-1] + 0.5w[k-2]\\ &=0.5\cdot0.25x[k-3] + 0.5\cdot0.25x[k-4]\\ &= 0.125(x[k-3]+x[k-4]) \end{align}

You can directly read the impulse response from it.

$\endgroup$
2
  • $\begingroup$ okay, and then i know what the b3 and the b4 koefficients are (0.125), Okay this might be a very stupid quastion but, how do i read the impulse response from this? and Thank you $\endgroup$
    – julie
    Nov 10 '16 at 6:44
  • $\begingroup$ The impulse response is [0, 0, 0, 0.125, 0.125, 0, 0, 0, ....] $\endgroup$ Nov 10 '16 at 7:35

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.