DSP IIR Realtime C++ filter library

• High performance
• Realtime sample in - sample out processing
• Butterworth, RBJ, Chebychev filters
• Lowpass, highpass, bandpass and bandstop filters
• Template based header-only filter functions
• Cross platform: Linux, Windows and Mac

An infinite impulse response (IIR) filter library for Linux, Mac OSX and Windows which implements Butterworth, RBJ, Chebychev filters and can easily import coefficients generated by Python (scipy).

The filter processes the data sample by sample for realtime processing.

It uses templates to allocate the required memory so that it can run without any malloc / new commands. Memory is allocated at compile time so that there is never the risk of memory leaks.

All realtime filter code is in the header files which guarantees efficient integration into the main program and the compiler can optimise both filter code and main program at the same time.

C++ code

Add the following include statement to your code:

#include "Iir.h"

The general coding approach is that first the filter is instantiated specifying its order, then the parameters are set with the function setup and then it's ready to be used for sample by sample realtime filtering.

Instantiating the filter

The idea is to allocate the memory of the filter at compile time with a template argument to avoid any new commands. This prevents memory leaks and can be optimised at compile time. The order provided to the template (for example here for a lowpass filter):

Iir::Butterworth::LowPass<order> f;

is used as the default order by the setup command below but can be overridden by a lower order if required.

Setting the filter parameters: setup

All filters are available as lowpass, highpass, bandpass and bandstop/notch filters. Butterworth / Chebyshev offer also low/high/band-shelves with specified passband gain and 0dB gain in the stopband.

The frequencies can either be analogue ones against the sampling rate or normalised ones between 0..1/2 where 1/2 is the Nyquist frequency. Note that normalised frequencies are simply f = F/Fs and are in units of 1/samples. Internally the library uses normalised frequencies and the setup commands simply divide by the sampling rate if given. Choose between:

1. setup: sampling rate and the analogue cutoff frequencies
2. setupN: normalised frequencies in 1/samples between f = 0..1/2 where 1/2 = Nyquist.

By default setup uses the order supplied by the template argument but can be overridden by lower filter orders.

See the header files in \iir or the documentation for the arguments of the setup commands.

The examples below are for lowpass filters:

1. Butterworth -- Butterworth.h Standard filter suitable for most applications. Monotonic response.

const int order = 4; // 4th order (=2 biquads)
Iir::Butterworth::LowPass<order> f;
const float samplingrate = 1000; // Hz
const float cutoff_frequency = 5; // Hz
f.setup (samplingrate, cutoff_frequency);

or specify a normalised frequency between 0..1/2:

f.setupN(norm_cutoff_frequency);

2. Chebyshev Type I -- ChebyshevI.h With permissible passband ripple in dB.

Iir::ChebyshevI::LowPass<order> f;
const float passband_ripple_in_db = 5;
f.setup (samplingrate,
         cutoff_frequency,
         passband_ripple_in_dB);

or specify a normalised frequency between 0..1/2:

f.setupN(norm_cutoff_frequency,passband_ripple_in_dB);

3. Chebyshev Type II -- ChebyshevII.h With worst permissible stopband rejection in dB.

Iir::ChebyshevII::LowPass<order> f;
double stopband_ripple_in_dB = 20;
f.setup (samplingrate,
         cutoff_frequency,
         stopband_ripple_in_dB);

or specify a normalised frequency between 0..1/2:

f.setupN(norm_cutoff_frequency,stopband_ripple_in_dB);

4. RBJ -- RBJ.h 2nd order filters with cutoff and Q factor.

Iir::RBJ::LowPass f;
const float cutoff_frequency = 100;
const float Q_factor = 5;
f.setup (samplingrate, cutoff_frequency, Q_factor);

or specify a normalised frequency between 0..1/2:

f.setupN(norm_cutoff_frequency, Q_factor);

5. Designing filters with Python's scipy.signal -- Custom.h

########
# Python
# See "elliptic_design.py" for the complete code.
from scipy import signal
order = 4
sos = signal.ellip(order, 5, 40, 0.2, 'low', output='sos')
print(sos) # copy/paste the coefficients over & replace [] with {}

///////
// C++
// part of "iirdemo.cpp"
const double coeff[][6] = {
		{1.665623674062209972e-02,
		 -3.924801366970616552e-03,
		 1.665623674062210319e-02,
		 1.000000000000000000e+00,
		 -1.715403014004022175e+00,
		 8.100474793174089472e-01},
		{1.000000000000000000e+00,
		 -1.369778997100624895e+00,
		 1.000000000000000222e+00,
		 1.000000000000000000e+00,
		 -1.605878925999785656e+00,
		 9.538657786383895054e-01}
	};
const int nSOS = sizeof(coeff) / sizeof(coeff[0]); // here: nSOS = 2 = order / 2
Iir::Custom::SOSCascade<nSOS> cust(coeff);

Realtime filtering sample by sample

Samples are processed one by one. In the example below a sample x is processed with the filter command and then saved in y. The types of x and y can either be float or double (integer is also allowed but is still processed internally as floating point):

y = f.filter(x);

This is then repeated for every incoming sample in a loop or event handler.

Error handling

Invalid values provided to setup() will throw an exception. Parameters provided to setup() which result in coefficients being NAN will also throw an exception.

You can switch off exeption handling by defining IIR1_NO_EXCEPTIONS via cmake or in your program.

Linking

CMake setup

If you use cmake as your build system then just add to your CMakeLists.txt the following lines for the dynamic library:

find_package(iir)
target_link_libraries(... iir::iir)

or for the static one:

find_package(iir)
target_link_libraries(... iir::iir_static)

Generic linker setup

Link it against the dynamic library (Unix/Mac: -liir, Windows: iir.lib) or the static library (Unix/Mac: libiir_static.a, Windows: libiir_static.lib).

Pre compiled packages for Ubuntu LTS (PPA):

If you are using Ubuntu LTS then you can install this library as a pre-compiled package.

Add this repository to your system:

sudo add-apt-repository ppa:berndporr/dsp

Then install the packages:

• Library files: sudo apt install iir1
• Development files: sudo apt install iir1-dev

It's available for 64 bit Intel and 32,64 bit ARM (Raspberry PI etc). The documentation of the development package and the example programs are in:

/usr/share/doc/iir1-dev/

Compilation from source

The build tool is cmake which generates the make- or project files for the different platforms. cmake is available for Linux, Windows and Mac. It also compiles directly on a Raspberry PI.

Linux / Mac

Run

cmake .

which generates the Makefile. Then run:

make
sudo make install

which installs it under /usr/local/lib and /usr/local/include.

Both gcc and clang have been tested.

Windows

cmake -G "Visual Studio 16 2019" -A x64 .

See cmake for the different build-options. Above is for a 64 bit build. Then start Visual C++ and open the solution. This will create the DLL and the LIB files. Under Windows it's highly recommended to use the static library and link it into the application program.

Unit tests

Run unit tests by typing make test or just ctest. These test if after a delta pulse all filters relax to zero, that their outputs never become NaN and if the Direct Form I&II filters calculate expected sequences by comparing them from results created by the output of scipy's sosfilt.

You can disable the generation of tests by setting IIR1_BUILD_TESTING to off.

Documentation

Learn from the demos

The easiest way to learn is from the examples which are in the demo directory. A delta pulse as a test signal is sent into the different filters and saved in a file. With the Python script plot_impulse_fresponse.py you can then plot the frequency responses.

You can disable the compilation of the demos by setting IIR1_BUILD_DEMO to off.

Also the directory containing the unit tests provides examples for every filter type.

Detailed documentation

A PDF of all classes, methods and in particular setup functions is in the docs/pdf directory.

The online documentation is here: http://berndporr.github.io/iir1

Example filter responses

These responses have been generated by iirdemo.cpp in the /demo/ directory and then plotted with plot_impulse_fresponse.py.

Credits

This library has been further developed from Vinnie Falco's great original work which can be found here:

https://github.com/vinniefalco/DSPFilters

While the original library processes audio arrays this library has been adapted to do fast realtime processing sample by sample. The setup command won't require the filter order and instead remembers it from the template argument. The class structure has been simplified and all functions documented for doxygen. Instead of having assert() statements this libary throws exceptions in case a parameter is wrong. Any filter design requiring optimisation (for example Ellipic filters) has been removed and instead a function has been added which can import easily coefficients from scipy.

Bernd Porr -- http://www.berndporr.me.uk