Digital frequency filter

The following code uses a FIR (Finite Impulse Response) low-pass filter with a Hann window to split a signal into two components by a given frequency:

void split(const float in[], unsigned int n, float freq, float low[], float high[])
{
        unsigned int window_n = sample_rate / freq;
        float window[window_n] = {};
        float window_sum = 0.;
        for (unsigned int i = 0; i < window_n; ++i) {
                window[i] = .5 * (1. - cos(2. * i * M_PI / (window_n - 1)));
                window_sum += window[i];
        }

        for (unsigned int i = 0; i < n; ++i) {
                float sum = 0;

                for (unsigned int j = 0; j < window_n; ++j) {
                        int index = i + j - window_n / 2;

                        if (index > 0 && index < n)
                                sum += in[index] * window[j];
                }

                low[i] = sum / window_sum;
                high[i] = in[i] - low[i];
        }
}

A property of this function is that you can recombine the low and high data using plain addition to recover the original input signal (modulo floating-point errors). This also makes it suitable for splitting a signal into multiple frequency bands; for example, calling it 7 times with different frequencies results in 8 output signals which can be independently gain-controlled and recombined.

See also

• https://en.wikipedia.org/wiki/Equalization_(audio)
• https://en.wikipedia.org/wiki/Finite_impulse_response
• https://www.keil.com/pack/doc/CMSIS/DSP/html/group__FIRLPF.html
• https://www.mathworks.com/help/signal/ref/fir1.html
• https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows