the Transform Domain An LTI discrete-time system is completely characterized in the time-domain by its impulse response {h[n]} We consider now the use of the DTFT and the z-transform in developing the transformdomain representations of an LTI system
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., We now develop a stability condition in terms of the pole locations of the transfer function H(z)
It is nearly impossible to design a linearphase IIR transfer function It is always possible to design an FIR transfer function with an exact linear-phase response Consider a causal FIR transfer function H(z) of length N+1, i.e., of order N:
Later in the course we shall review various methods of designing frequency-selective filters satisfying prescribed specifications We now describe several low-order FIR and IIR digital filters with reasonable selective frequency responses that often are satisfactory in a number of applications
The simple filters discussed so far are characterized either by a single passband and/or a single stopband There are applications where filters with multiple passbands and stopbands are required The comb filter is an example of such filters