Analog and Digital Filters 563
Transform a prototype to any fi lter specs (denormalized process)
Understand the concept of distortion (magnitude, phase, or delay)
Understand the concepts of linear phase
Understand the difference between active and passive fi lters
Understand the difference between analog and digital fi lters
Understand the differences between fi nite impulse response (FIR) and infi nite
impulse response (IIR) digital fi lter
Understand the (practical) importance of using windows in the design of fi lters
Understand that there is a trade-off when windows are used, such as ripple ampli-
tude and the transition time
Develop simple fi lter prototype sections such as T and π (used in electrical
communications)
Understand the effects of using polynomials in the process of modeling and sys-
tem implementation
Use MATLAB® in the analysis and synthesis process involving fi lters6.3 Background
R.6.1 Filters are devices that are specifi ed in the frequency domain. The synthesis and
analysis process is generally done in the frequency domain.
R.6.2 An ideal fi lter displays two main bands in the frequency domain
A pass band
A stop band
R.6.3 Any sinusoidal input with any one of the frequencies of the pass-band region
emerges or is present in the output with its magnitude almost (little attenuation)
unchanged if the fi lter is implemented with passive elements (RLC).
R.6.4 Any applied sinusoidal input with frequencies in the stop-band region is not pres-
ent in its output or if it is its magnitude is drastically attenuated.
R.6.5 In the pass-band region, the magnitude frequency response of an ideal passive
fi lter is unity, whereas in the stop band it is zero.
R.6.6 An ideal fi lter allows any sinusoidal input to either pass or be rejected.
R.6.7 Assuming the inputs to a fi lter are sinusoidals and its frequencies are in the pass-
band region of the fi lter, then they emerge as outputs. If the output is amplifi ed by a
constant k > 1 over the pass band, then the fi lter presents a gain. The type of fi lters
with a gain k > 1 is called active.
R.6.8 Assuming the inputs to a fi lter are sinusoidals and its frequencies are in the pass-
band region of the fi lter, and if they emerge as outputs with different gains, then
the output suffers from amplitude distortion and the output is a distorted version
of its input.
R.6.9 Strictly, ideal fi lters that present two regions (pass band and stop band) cannot be
implemented in practice, since they are noncasual devices (the output is returned
before the input is applied).