value. In discrete-time applications, one only examines the region of frequencies between 0 and the Nyquist frequency, because of periodicity and symmetry. Depending on the frequency units, the Nyquist frequency may be 0.5, 1.0, π, or ½ of the actual sample-rate. Some examples of linear and non-linear phase are shown below. A discrete-time filter with linear phase may be achieved by an FIR filter which is either symmetric or anti-symmetric. A necessary but not sufficient condition is: for some . Generalized linear phase Systems with generalized linear phase have an additional frequency-independent constant added to the phase. In the discrete-time case, for example, the frequency response has the form: for Because of this constant, the phase of the system is not a strictly linear function of frequency, but it retains many of the useful properties of linear phase systems. See also Minimum phase Notes Citations Digital signal processing