564 Practical MATLAB® Applications for Engineers
R.6.10 A real fi lter presents three bands (for an LPF), which is illustrated in Figure 6.2
Pass band, for w < wp
Stop band, for w > ws
Transition band, for wp < w < ws
The plot or sketch shown in Figure 6.2 may be used to spec a real (LP) fi lter.R.6.11 A real fi lter creates a phase shift between the input and its output (where phase
indicates the propagation delay).
R.6.12 If a phase shift (delays) of all the sinusoidals that make up the input with respect to
their output is constant in the range of frequencies defi ned by the pass band, then
all the sinusoidal inputs are delayed by the same amount of time and the fi lter is
said to present no delay distortion, and the output waveform is a replica of the input
as far as phase is concerned.
R.6.13 If the phase shift of a fi lter is linear with respect to their frequencies in the pass-
band region, then the fi lter is said to present no phase or delay distortion.
R.6.14 Filters are best described in terms of the transfer function.
Recall that the transfer function is the ratio of the output Vo(w) voltage to the input
voltage Vi(w) (in the frequency domain).
Recall that the transfer function is also known as the gain or system function.
R.6.15 Recall that the transfer function is denoted by H(w), and it is a function of the com-
plex frequency (s = jw). Therefore, H(w) or H(jw) is a complex function consisting of
two parts:
A real part
An imaginary part
The description of the transfer function H(w) translates graphically into two
plots:
Plot H(w) versus w called the magnitude or system gain plot
Plot ∠ [H(w)] versus w called the phase gain plot
• • • • • • •
FIGURE 6.2
Filter’s bands.
|H(jw)|dswp wsPass band Stop band1 + p1 − pTransition band