README.md

DSP filters in C++

This repo contains some DSP biquad filters used in audio. I've extracted those filters from the Designing Audio Effect Plug-Ins in C++: With Digital Audio Signal Processing Theory book that you can find here.

I've also implemented a real-time testing on a Cortex-M4 MCU, using the on-chip ADC and DAC. You can find the post here.

This is the formula I'm using for the digital biquad filter in the source code:

y(n) = a0*x(n) + a1*x(n-1) + a2*x(n-2) - b*y(n-1) + b2*y(n-2)

• First order all-pass filter (fo_apf)
• First order high-pass filter (fo_hpf)
• First order low-pass filter (fo_lpf)
• First order high-shelving filter (fo_shelving_high)
• First order low-shelving filter (fo_shelving_low)
• Second order all-pass filter (so_apf)
• Second order band-pass filter (so_bpf)
• Second order band-stop filter (so_bsf)
• Second order Butterworth band-pass filter (so_butterworth_bpf)
• Second order Butterworth band-stop filter (so_butterworth_bsf)
• Second order Butterworth high-pass filter (so_butterworth_hpf)
• Second order Butterworth low-pass filter (so_butterworth_lpf)
• Second order high-pass filter (so_hpf)
• Second order Linkwitz-Riley high-pass filter (so_linkwitz_riley_hpf)
• Second order Linkwitz-Riley low-pass filter (so_linkwitz_riley_lpf)
• Second order Low-pass filter (so_lpf)
• Second order parametric/peaking boost filter with constant-Q (so_parametric_cq_boost)
• Second order parametric/peaking cut filter with constant-Q (so_parametric_cq_cut)
• Second order parametric/peaking filter with non-constant-Q (so_parametric_ncq)

All the filters are now header files and they are located in the lib/ folder. In order to use them just copy the lib/ folder (and rename it if needed) into your project folder. There's an example how to build later in the README.

Build & run tests

You can use cmake to build the tests. On Linux, you can just run this:

./build_tests.sh

The above command will build the tests and run them.

Note: Tests are a bit naive in this case, since it doesn't make much sense for testing using unit-tests, but anyways, I've added them

Usage:

The filters can be used in your C++ code in the part where the audio sample is about to be processed. You need to include the filter_common.h and filter_includes.h files and the create an object with filter(s) you want to apply and calculate the coefficients with the calculate_coeffs() function. Then in the sample processing function run the filter() function with the current sample as a parameter.

I've used RackAFX to test these filters.

Code example

For example, to use the so-LPF filter then first create a main.cpp file in the top directory of this repo.

touch main.cpp

Then add this code inside:

#include <iostream>
#include <memory>
#include "filter_common.h"
#include "filter_includes.h"

int main() {
    std::unique_ptr<SO_LPF> filter (new SO_LPF);

    auto coeffs = filter->calculate_coeffs(1.0, 5000, 96000);
    auto yn = filter->process(0.303);

    std::cout << "Coeffs: " << std::endl;
    std::cout << "a0: " << coeffs.a0 << std::endl;
    std::cout << "a1: " << coeffs.a1 << std::endl;
    std::cout << "a2: " << coeffs.a2 << std::endl;
    std::cout << "b1: " << coeffs.b1 << std::endl;
    std::cout << "b2: " << coeffs.b2 << std::endl;

    std::cout << "yn: " << yn << std::endl;
    return 0;
}

Now to build the file run:

g++ main.cpp -I./lib

And then run the executable:

./a.out

This is will print the filter coefficients and then will process a sample with the value 0.303. You should see an output similar to this:

Coeffs: 
a0: 0.0228608
a1: 0.0457215
a2: 0.0228608
b1: -1.63163
b2: 0.723069
yn: 0.00692681