Time-Domain Representation Signals are represented as sequences of numbers, called samples Sample value of a typical signal or sequence denoted as x[n] with n being an integer in the range x[n] defined only for integer values of n and undefined for non-integer values of n
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
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)