Notch filter

  • Author or source: Olli Niemitalo
  • Type: 2 poles 2 zeros IIR
  • Created: 2002-01-17 02:11:07
notes
Creates a muted spot in the spectrum with adjustable steepness. A complex conjugate pair
of zeros on the z- plane unit circle and neutralizing poles approaching at the same angles
from inside the unit circle.
code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Parameters:
0 =< freq =< samplerate/2
0 =< q < 1 (The higher, the narrower)

AlgoAlgo=double pi = 3.141592654;
double sqrt2 = sqrt(2.0);

double freq = 2050; // Change! (zero & pole angle)
double q = 0.4;     // Change! (pole magnitude)

double z1x = cos(2*pi*freq/samplerate);
double a0a2 = (1-q)*(1-q)/(2*(fabs(z1x)+1)) + q;
double a1 = -2*z1x*a0a2;
double b1 = -2*z1x*q;
double b2 = q*q;
double reg0, reg1, reg2;

unsigned int streamofs;
reg1 = 0;
reg2 = 0;

/* Main loop */
for (streamofs = 0; streamofs < streamsize; streamofs++)
{
  reg0 = a0a2 * ((double)fromstream[streamofs]
                 + fromstream[streamofs+2])
       + a1 * fromstream[streamofs+1]
       - b1 * reg1
       - b2 * reg2;

  reg2 = reg1;
  reg1 = reg0;

  int temp = reg0;

  /* Check clipping */
  if (temp > 32767) {
    temp = 32767;
  } else if (temp < -32768) temp = -32768;

  /* Store new value */
  tostream[streamofs] = temp;
}

Comments

i tried implementing it, failed,
and its wierd how it looks further in time
instead of backwards, you cant use it in
a running rendered stream cause the end of
it stuffs up....
I think it's a type, and should be
=-=-=
reg0 = a0a2 * ((double)fromstream[streamofs]
+ fromstream[streamofs-2])
+ a1 * fromstream[streamofs-1]
- b1 * reg1
- b2 * reg2;
=-=-=
In which case there is some rangechecking to be done when streamofs<2

You could just use the coeffs, and stick them into whatever biquad code you have hanging around :)

DSP
Still doesn't work. Either way its looking one each side of a centre value, so it doesn't change the maths. Not sure what the code should be. Ideas???
does this code work with float output?
I really need a notch filter, i will try the code.
yes, there are some errors in this source.

Here is the correct version:


// (C) Sergey Aleynik.   [email protected]

     // BW_Coeff is changing from 0.0 to 1.0 (excluded) and the more the narrow:
     // |  BW_Coeff   |  Real BandWidth (approxim.)  |
     // |   0.975     | 0.00907 * Sampling_Frequency |
     // |   0.95      | 0.01814 * Sampling_Frequency |
     // |   0.9       | 0.03628 * Sampling_Frequency |

void  Notch_Filter_Test(short int *Data_In,
                        short int *Data_Out,
                        long       nData_Length,
                        double     Sampling_Frequency,
                        double     CutOff_Frequency,
                        double     BW_Coeff)
{
  // If wrong parameters:
  if((NULL == Data_In)||(Data_Out)||(nData_Length <= 0))   return;
  if((Sampling_Frequency < 0.0)||(CutOff_Frequency < 0.0)) return;
  if(CutOff_Frequency > (Sampling_Frequency/2))            return;
  if((BW_Coeff <= 0.0)||(BW_Coeff >= 1.0))                 return;

  static const double  pi = 3.141592654;

  // Filter coefficients:
  double z1x = cos(2*pi*CutOff_Frequency/Sampling_Frequency);
  double b0 = (1-BW_Coeff)*(1-BW_Coeff)/(2*(fabs(z1x)+1)) + BW_Coeff;
  double b2 = b0;
  double b1 = -2*z1x*b0;
  double a1 = -2*z1x*BW_Coeff;
  double a2 = BW_Coeff*BW_Coeff;

  // Filter internal vars:
  double y=0,  y1=0, y2=0;
  double x0=0, x1=0, x2=0;

  long i;
  for(i=0; i<nData_Length; i++)
  {
    y  = b0 * x0 + b1 * x1 + b2 * x2 - a1 * y1 - a2 * y2;
    y2 = y1;
    y1 = y;
    x2 = x1;
    x1 = x0;
    x0 = Data_In[i];

    if(      y >  32767) y =  32767;
    else if (y < -32768) y = -32768;

    Data_Out[i] = (short int)y;
  }
}
Just an idea on coef notch :
 a0 = 1;
 a1 = -2 * cs;
a2 = 1;
b0 = 1 + alpha;
b1 = -2 * cs;
b2 = 1 - alpha;
 notch: H(s) = (s^2 + 1) / (s^2 + s/Q + 1);
 omega = 2*PI*cf/sample_rate;
sn = sin(omega);
cs = cos(omega);
alpha = sn/(2*Q);