Page 394 - Analog and Digital Filter Design

Digital FIR Filter Design 39

band frequencies. In bandpass and bandstop filter designs there are
two slopes, one on either side of the passband or stopband. In these
designs the smaller of the two values (the steepest slope) should be
chosen.
2 Find the filter ratio.
Using the value of the slope obtained by the method outlined above,
a ratio can be obtained. This ratio is dependent on whether the
response is lowpass, highpass, bandpass, or bandstop. The ratio
required for all filters to determine the number of taps is:
ratio = (clock frequency - slope)/slope.
3 Decide on the window.

The number of taps required also depends upon the window function
used. A rectangular window requires the least number of taps. In
order of increasing number of taps required we have: Von Hann
(or Hanning), Hamming, Bartlett (triangular window), and finally
Blackman.
4 Calculate the number of taps.
The number of taps required for a rectangular window is:
N = 1 + (integer) 0.95 x ratio.
For example, if the clock frequency is 1 kHz and the filter cutoff fre-
quency is 80 Hz, the ratio = (1000 - 80)/80 = 11.5, then 0.95 x 11.5 =
10.925. The ratio equals (integer) 10
N= 1 + 10= 11.
In Table 16.2 are empirical formulae for the number of taps required
for some basic types of fixed window.

Window Function
Rectangular
Bartlett (Triangular) 1 i (int) 4.15 x ratio
Von Hann 1 i (int) 3.3 x ratio I
Hamming 1 + (int) 3.44 x ratio I
Blackman 1 + (int) 6.0 x ratio 1
Exact Blackman 1 + (int) 6.8 x ratio 1 1
3-term Blackman Harris 1 + (int) 6.0 x ratio 1
ble 16.2 I-term Blackman Harris 1 + (inti 5.8 x ratio 1
3-term Harris Nutall I + (int) 6.8 x ratio 1
Empirical Formulae for I-term Harris Nutall 1 + (int) 6.8 x ratio 1
Number of Taps