Transform-Domain Representation of Discrete-Time Signals Three useful representations of discrete-time sequences in the transform domain: Discrete-time- Fourier Transform(DTFT) YDiscrete Fourier Transform(DFT) z- -Transform
Discrete-Time Systems A discrete-time system processes a given input sequence x[] to generates an output sequencey[n] with more desirable properties In most applications, the discrete-time system is a single-input, single-output system:
Phase and Group Delays The output y[n] of a frequency-selective LTI discrete-time system with a frequency response(@) exhibits some delay relative to the input x[n] caused by the nonzero phase response 0(@) =arg{()} of the system
Linear-Phase FIR Transfer Functions It is nearly impossible to design linear- phase IIR transfer function It is always possible to design an FIR transfer function with an exact linear-phase response
Stability Condition in Terms of the Pole Locations A causal lti digital filter is BIBO stable if and only if its impulse response h[n] is absolutely summable, i.e
