Time shifting

Continuous Time

Let’s say we have:

• Signal $x(t)$
• Signal $\varphi (t)$, which is $x(t)$ delayed by $T$ seconds

Thus:

$$\varphi (t+T)=x(t)$$

and

$$\varphi (t)=x(t-T)$$

If $T>0$, it is delayed (shift to the right)
If $T<0$, it is advanced (shift to the left)

Discrete Time

Like C.T., we have:

$$x_M[N]=x[n-M]$$

To shift a discrete time signal by $M$ units, we replace $n$ with $n-M$.
If $M>0$, it is delayed (shift to the right)
If $M<0$, it is advanced (shift to the left)