Discrete-Time Signals Week 2

Continuous-Time Versus Discrete-Time Signals Continuous-time signal: a signal defined by a function of a continuous-time variable. Discrete-time Signal: a signal defined by specifying the value of the signal only at discrete times, called sampling instants.

Continuous-Time Versus Discrete-Time Signals

Distinction between Discrete- Time and Quantized Signals Quantized Signal: A quantized signal is one whose values may assume only a countable number of values, or levels, but the changes from level to level may occur at any time.

Periodic and Aperiodic Signals Periodic: a signal x(t) is periodic if and only if x(t+T 0 )=x(t), -  <t<  (1) where the constant T 0 is the period. Aperiodic: Any deterministic signal not satisfying (1) is called aperiodic.

Periodic Signals

Aperiodic Signals

Some Elementary Discrete-Time Signals Unit sample: Unit step:

Some Elementary Discrete-Time Signals Exponential sequence Sinusoidal sequence

Some Elementary Discrete-Time Signals (1) Unit sample (2) Unit step (3) Exponential sequence(4) Sinusoidal sequence

Energy and Power Signals Total energy Average power 1. X(t) is an energy signal if and only if 0<E< , so that P=0. 2. X(t) is an power signal if and only if 0<P< , thus implying that E= . 3. Signals that satisfy neither property are therefore neither energy nor power signals.

Addition, Multiplication, and Scaling Addition Multiplication Scaling

Convolution of Two Discrete- Time Signals Convolution Properties 1. Commutative property 2. Associative property 3. Distributive property

Correlation of Two Discrete- Time Signals Cross-correlation function Autocorrelation function p=0 maximum