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3-3
filters have a phase shift that is linear with respect to frequency. This linear phase shift delays
signal components of all frequencies by a constant time, independent of frequency, thereby
preserving the overall shape of the signal.
In practice, lowpass filters subject input signals to a mathematical transfer function that
approximates the characteristics of an ideal filter. By analyzing the Bode Plot, or the plot that
represents the transfer function, you can determine the filter characteristics.
Figures 3-3 and 3-4 show the Bode Plots for the ideal filter and the real filter, respectively, and
indicate the attenuation of each transfer function.
Figure 3-3.
Transfer Function Attenuation for an Ideal Filter
Figure 3-4.
Transfer Function Attenuation for a Real Filter
The cut-off frequency,
f
c
, is defined as the frequency beyond which the gain drops 3 dB.
Figure 3-3 shows how an ideal filter causes the gain to drop to zero for all frequencies greater
than
f
c
. Thus,
f
c
does not pass through the filter to its output. Instead of having a gain of absolute
zero for frequencies greater than
f
c
, the real filter has a transition region between the passband
and the stopband, a ripple in the passband, and a stopband with a finite attenuation gain.
Real filters have some nonlinearity in their phase response, causing signals at higher frequencies
to be delayed longer than signals at lower frequencies and resulting in an overall shape distortion
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