Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 271

3. Calculate the absolute values of the passband ripple and stopband attenuation if they are given in
terms if dB values:

d p dB
20

d p ¼ 10 1 (7.34)

d s dB
20

d s ¼ 10 (7.35)

Then calculate the ratio and put it into fraction form:

d p
d s ¼ fraction form ¼ denominator ¼ W s

numerator

(7.36)

W p

Next, set the error weight factors for passband and stopband, respectively:

W s ¼ numerator

W p ¼ denominator (7.37)

4. Apply the Remez algorithm to calculate filter coefficients.
5. If the specifications are not met, then increase the filter order and repeat steps 1 to 4.

The following two examples are given to illustrate the design procedure.

EXAMPLE 7.15
Design a lowpass filter with the following specifications:
DSP system sampling rate ¼ 8,000 Hz
Passband ¼ 0e800 Hz
Stopband ¼ 1,000e4,000 Hz
Passband ripple ¼ 1dB
Stopband attenuation ¼ 40 dB
Filter order ¼ 53
Solution:
From the specifications, we have two bands: a lowpass band and a stopband. We perform normalization and specify
ideal magnitudes as follows:
Folding frequency:

f s =2 ¼ 8; 000=2 ¼ 4; 000 Hz

For 0 Hz: 0=4; 000 ¼ 0 magnitude: 1

For 800 Hz: 800=4; 000 ¼ 0:2 magnitude: 1

For 1,000 Hz: 1; 000=4; 000 ¼ 0:25 magnitude: 0

For 4,000 Hz: 4; 000=4; 000 ¼ 1 magnitude: 0

Next, let us determine the weights: