# Lecture 1: Useful Signal Models for Discrete-Time

### Some Useful Signal Models for Discrete-Time

**Discrete-time unit impulse**:

**Discrete-time unit step**:

**Discrete-time exponential**

grows when , and decays when . Plot on unit circle.

What about when ? We can write this as for some . This is a rotating phasor.

**Discrete-time sinusoid**.

Note: Not all discrete-time sinusoids are periodic (unlike in the continuous-time
case):

This is only possible if is an integral multiple of :

iff

Must therefore have be a

**rational**number.

Note: There is non-uniqueness of discrete-time sinusoids. For example:

All these frequencies 'look' the same!

**Exponentially damped sinusoid**