EE 444: Digital Signal Processing
Chapter 2: Discrete-time Signals and Systems
• Discrete-time Signals
– Elementary discrete-time signals: unit impulse, unit step, unit ramp, exponential
– Classifications: energy & power signals, periodic & aperiodic signals, even & odd
signals
– Basic signal manipulations: time-shift, folding, down-sampling, scaling, addition,
multiplication
• Discrete-time Systems
– Block diagram representation: adder, constant multiplier, signal multiplier, unit
delay, unit advance, cascade & parallel interconnections
– Classifications: static vs dynamic systems, time-invariant vs time-variant systems, linear vs nonlinear systems, causal vs noncausal systems, stable vs unstable
systems
• Linear Time-invariant (LTI) Systems
– Input-output relationship of LTI systems: convolution & its properties (communitivity, associativity, distributivity)
– Properties of LTI systems: causality, stability, FIR vs IIR, constant-coefficient
difference equation
– Implementation of LTI systems: direct form I & II structures, nonrecursive &
recursive structures
• Correlation of Discrete-time Signals
– Definitions of crosscorrelation & autocorrelation for energy signals, power signals
and periodic signals
– Properties of correlation
– Relationship between correlation and convolution
– Input-output correlation of LTI systems