Contents
Linear and non-linear examples
Linear system: y(t)=2x(t)+ 3 Non-linear system: y(t)=x(t)^2 + x(t) + 3
Causal and non-causal
Causal system: y(t)=2x(t-21) Non-causal: y(t)=4x(t+11)
Time invariant and time variant
Time invariant: y(t)=5cosx(t)+1 Time variant: y(t)=x(t)sin(t)
With and without memory
With memory: y[n]=4x[n-5]+2x[n-2] Without memory: y[n]=x[n]^2+x[n]+2
Invertible and non-invertible
Invertible: y[n]=x[n]+y[n-22] Non-invertible: y[n]=4x[n]^2-11x[n]
Stable and non-stable
Stable: y[n]=x[n]^2+x[n] Non-stable: y(t)=k*x(t)
Question:
$ f(t)= u(t) $ $ g(t)= 1 $ at $ 1 \le t \le 2 $ Solve for convolution.
Answer:
$ h(t)=0 $ at $ t \le 1 $ $ h(t)=t-1 $ at $ 1 \le t \le 2 $ $ h(t)=t-2 $ at $ 2 \le t $
Question
T/F? The sum of two peroid function is always a peroid function.
Answer:
False. Example: x1(t)=4cos(2t) x2(t)=5sin(2pi*t) y(t)=x1(t)+x2(t) y(t) is not a period funtction.
