WM8941
Pre Production
+0
-5
T
-10
-15
-20
-25
-30
-35
R
E
S
P
O
N
S
E
(dB)
-40
20
50
100
200
500
1k
2k
5k
10k
20k
Frequency (Hz)
Figure 56 Cumulative Notch + Low Pass Filters Responses (48kHz); NF0 fc = 1kHz; NF1 fc = 5kHz; NF2 fc = 10kHz;
LPF fc = 11kHz; fb = 100Hz, 600Hz, 2kHz
Notch Filter Worked Example
The following example illustrates how to calculate the a0 and a1 coefficients for a desired centre frequency and -3dB
bandwidth.
fc = 1000 Hz
fb = 100 Hz
fs = 48000 Hz
= 2π x (1000 / 48000) = 0.1308996939 rads
= 2π x (100 / 48000) = 0.01308996939 rads
w
w
= 2πf / f
c
0
b
s
= 2πf / f
b
s
1− tan(w / 2)
1− tan(0.01308996939/ 2)
1+ tan(0.01308996939 / 2)
b
=
= 0.9869949627
a
=
0
1+ tan(w / 2)
b
a = −(1+ a )cos(w ) = −(1+ 0.9869949627)cos(0.1308996939) = -1.969995945
1
0
0
NFn_A0 = -a0 x 213 = -8085 (rounded to nearest whole number)
NFn_A1 = -a1 x 212 = 8069 (rounded to nearest whole number)
These values are then converted to a 14-bit sign / magnitude notation:
NFn_A0[13] = 1; NFn_A0[12:0] = 13’h1F95; NFn_A0 = 14’h3F95 = 14’b11111110010101
NFn_A1[13] = 0; NFn_A1[12:0] = 13’h1F85; NFn_A1 = 14’h1F85 = 14’b01111110000101
PP, Rev 3.3, December 2007
92
w
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