N-Pole Roll off
In general, low-frequency signal contains main signal and hash, a term we apply to
unwanted high-frequency signals such as shrill tones, scratching sounds, or chirps is
shown in figure 1. To remove the hash, leaving only the low-frequency signal, requires
a lowpass filter capable of passing low frequencies and rejecting high frequencies.
Filters are designed such that each transmitted signal have same amplitude.
Figure 1: 2-Pole Rolloff Transfer function
Figure 2: 2- Transfer function of idea LPF and n-pole rolloff
The ideal Low Pass Filter characteristic is shown in Figure 2. The normalized frequency
of
ω0=1rad /s
, the amplitude of T(jω)) is a constant; above that frequency the value of
T(jω)) is 0. The pass band and stop band are clearly separated at
ω0=1rad /s
. Because
of its shape, this characteristic is called a brick wall; it is the ideal lowpass filter
characteristic. As shown in Figure 2, the magnitude should be nearly to constant
(T(j ω))=1¿
in the pass band. In the stop band we require n-pole rolloff, where n is a
large number, in contrast to the n = 2 rolloff for the biquad circuit.
Figure 3: 2- Product of three transfer function T1*T2*T3
