# Choosing sampling frequency in Digital Filter Design

#### Xavier Pacheco Paulino

Joined Oct 21, 2015
728
Hi,

I designed a Butterworth second order bandstop filter on Matlab with the following parameters:

Notch frequency: 150 Hz (the frequency I want to remove)
Bandwidth = 8 Hz, that is
Fc1=146 Hz
Fc2=154 Hz
Fs (sampling frequency) = 10000 Hz

According to Nyquist Criterion, 0.5xFs > Fm
where Fm is my signal’s highest frequency. Let's say that my signal frequency ranges from 0 to 3 kHz, so my sampling frequency should be 6 kHz or higher. As you saw, I chose a samplig frequency of 10 kHz.

MATLAB gave me the filter coefficients for my difference equation, that is

y[n]=b0x[n]+b1x[n−1]+b2x[n−2]−a1y[n−1]−a2y[n−2] (IIR Filter).

I implemented this equation in a STM32F767 Nucleo Board. The input signal goes to the ADC, the signal is processed and then go to the DAC for output. I used a timer interrupt every 100 us for this. I mean, the process takes place in the timer interrupt loop.

The problem is this:

My filter works, but it's no filtering the frequency I chose to filter. I wanted to remove the 150Hz, but it's removing a frequency of 298~300Hz.

What could be happening here? Does the sampling frequency have to do with this? Should I choose a lower sampling frequency? If it's needed I can attach my C code. But this is the basic idea:

struct difference_equation
{
// coefficients
double b0;
double b1;
double b2;
double a1;
double a2;
// input history
double x1;
double x2;
// output history
double y1;
double y2;

double process(double x0)
{
double y0 = b0 * x0 + b1 * x1 + b2 * x2
- a1 * y1 - a2 * y2;

x2 = x1;
x1 = x0;

y2 = y1;
y1 = y0;

return y0;
}
}