# DT System with input initially at rest

This is the very basics of Signals but my lecturer has provided barely any notes and I cannot find answers online (not just to this, but most of signals for some reason)

Dealing with DT system:

y[n]=y[n-1]+2x[-n]

and input:

x[n]={0,1,1,-1,0,2,0} (the 3rd number is underlined as n=0 ((the second 1 that appears)) )

Questions:

1. If system y[n]=y[n-1]+2x[-n] is said to be initially at rest (so y[-1]=0), and lets say the input x[-1]=1 is applied, will y[-1] still be 0, or should you apply just the input to y[-1] in some way?

2. Should you take everything before y[-1] to be 0 too since the y[n-1] in the system makes it impossible to calculate before y[-1] (I think??? Once again my lecturer has been of no help i have no clue whats going on) or should you take everything before y[-1] to be zero because its “initially at rest” (not sure if “initially at rest” also counts the values before y[-1])

3. Ive been told to plot this. What should the highest n I go up to be? Or does it all become 0 at some point?

(All in all im clearly going to fail this module due to the most dodgy lecturer of my life but any help is still appreciated.)

• This is indeed an odd system and it's also unstable again. Look at the spreadsheet in my answer to your previous question. You can do the same thing here. Commented Apr 28 at 0:22
• @Hilmar Here is my excel plots: flic.kr/p/2pN7Qwk As far as I am aware the top one is if the system was not initially at rest, and the bottom one is when the system is initially at rest. Does this look okay to you?
– Lucy
Commented Apr 29 at 19:41