Digital Filters - Signal Processing of Random Physiological Signals - page 112

2. Chevbychev

a. Low-pass filter

b. High-pass filter, etc.

Other classifications that are also used in conjunction with the previous classification
are

1. Voltage Controlled Voltage Source (VCVS),

2. Bi Quad,

3. Elliptical, and

4. Digital.

The most common digital filters fall into one of two classes:

1. Finite Impulse Response (FIR) and

2. Infinite Impulse Response (IIR)

Filters are generally described mathematically by their “Transfer Function” in the
Time domain as differential equations, or in the Frequency domain as the ratio of two
polynomials in “s-domain” or as j in radians. The order of a filter is defined by the

degree of the denominator. The higher the order, the closer the filter approaches the ideal
filter; however, the tradeoff an engineer must make is that higher order filters require
more complex hardware, and consequently, are more expensive (costly).

ω

11.1.1 Low-Pass Butterworth Filter
In many applications, the most common low-pass filter used is referred to as an “All-Pole
Filter,” which implies that the filter contained “All poles” and “No zeros” in the s-plane.
In addition, the all pole, low-pass filter may be called a “Butterworth filter,” which means
that the filter has an “over damped” response. Figure 11.1 shows the ideal response of
a low-pass Butterworth filter with its cutoff frequency at

c and the practical response
for the same cutoff frequency. It should be noted that the low-pass Butterworth filter

ω