firpm library
Python
The library is also available from Python, as the firpm package:
pip install firpm
Binary wheels are published for Linux (x86_64, aarch64), macOS (arm64) and Windows (x86_64). They compute in double precision only; see Building from source below for MPFR support.
The package has two design routines, which differ only in how a specification is written:
firpm.remez |
firpm.firpm |
|
|---|---|---|
| follows | scipy.signal.remez |
MATLAB's firpm |
| length | number of taps, numtaps |
filter order, n (n + 1 taps) |
| band edges | from 0 to fs / 2 (fs=1) |
from 0 to 1 (Nyquist) |
| desired amplitude | one per band | one per edge (linear in a band) |
| antisymmetric | type="hilbert" etc. |
ftype ("hilbert" etc.) |
Designing a filter
import numpy as np
import firpm
# 101-tap type I lowpass: passband [0, 0.2], stopband [0.25, 0.5] (in
# cycles/sample, so Nyquist is 0.5), with the stopband weighted 10x.
h = firpm.remez(101, [0.0, 0.2, 0.25, 0.5], [1.0, 0.0], weight=[1.0, 10.0])
# The same filter, in MATLAB's terms.
h = firpm.firpm(100, [0.0, 0.4, 0.5, 1.0], [1.0, 1.0, 0.0, 0.0], [1.0, 10.0])
H = np.fft.rfft(h, 4096)
remez takes the arguments of scipy.signal.remez, and firpm those of
MATLAB's firpm (firpm(n, f, a), firpm(n, f, a, w), and either with an
ftype). Odd numtaps (even n) gives a type I filter, and even
numtaps (odd n) a type II filter. weight and w default to 1 in each
band.
Arbitrary amplitude and weight functions
Either routine also takes the specification band by band, as a sequence of
firpm.Band(f0, f1, amplitude, weight=1.0) (plain tuples work too). The
amplitude and the weight are each a number or a callable, so the target can
vary across a band; for example, to correct the passband droop of a CIC
decimator:
import numpy as np
import firpm
R = 8 # CIC decimation ratio (third order)
def cic_inverse(f):
if f == 0:
return 1.0
w = 2 * np.pi * f
return (np.sin(w / 2) / (R * np.sin(w / (2 * R)))) ** -3
h = firpm.remez(201, [firpm.Band(0.0, 0.04, cic_inverse),
firpm.Band(0.06, 0.5, 0.0)])
Band edges, and the frequencies passed to callables, are in each routine's
own units: units of fs for remez, and normalized to Nyquist for firpm.
Callables are called with one frequency at a time; a design takes a few
thousand calls, so keep them cheap. Bands with only numeric amplitudes and
weights make no calls into Python at all. An exception raised inside a
callable is re-raised from the design routine.
Differentiators and Hilbert transformers
remez(..., type="differentiator") or type="hilbert", and
firpm(..., ftype) likewise, give an antisymmetric filter (type III for
odd numtaps, type IV for even):
import firpm
h = firpm.remez(32, [0.0, 0.45], [1.0], type="differentiator")
h = firpm.remez(31, [0.05, 0.45], [1.0], type="hilbert")
h = firpm.firpm(30, [0.1, 0.9], [1.0, 1.0], "hilbert")
These take band edges only, not Bands. A remez differentiator's
amplitude is desired * f / fs in each band; a firpm one's is given at
the band edges, as in MATLAB. For differentiators, scipy.signal.remez
divides the weight by the frequency in every band with a nonzero slope,
but this library (like MATLAB) divides only the first band's. The two
agree for the usual differentiator, whose first band is the only one with
a slope. scipy.signal.remez's maxiter and grid_density have no
counterpart here, since the library does not use a frequency grid.
Options and errors
Both routines take these keyword options:
strategyselects how the initial reference is chosen:firpm.Strategy.UNIFORM(the default),firpm.Strategy.SCALINGorfirpm.Strategy.AFP. Reference scaling (strategy=firpm.Strategy.SCALING, depth=1) usually needs far fewer iterations for long filters, and is more robust for them.depthis the number of scaling levels, and must be at least 1 forSCALINGto have any effect.epsis the convergence threshold andnmaxthe degree of the local approximations used to locate the error extrema; the defaults rarely need changing.precision="mpfr"computes in MPFR arbitrary precision (precbits, 165 by default), whenfirpmwas built with MPFR.
Both routines return the taps as a NumPy array. As in scipy.signal.remez,
an invalid specification or a failed design raises ValueError; a design
that did not fully converge emits a RuntimeWarning (use warnings.simplefilter("error") to
turn it into an exception). help(firpm.remez) and help(firpm.firpm)
have the details.
Building from source
From a checkout, pip install . builds and installs the package. The
library's own dependencies (a C++20 compiler with OpenMP, Eigen) must be
available; see the installation instructions below. The published wheels
leave out MPFR, as pip install . does; for precision="mpfr", use a CMake
build with MPFR, GMP and mpreal present. A CMake build also builds the Python
package whenever pybind11 is found, under python/ in the build directory,
and make test then runs the Python tests too (these need pytest and
numpy; with scipy installed, they also compare designs against
scipy.signal.remez).
The package's version is firpm.__version__, and it ships type
annotations.
Folder organization
Prior to November 2019, there were three different folders containing implementations with different numerical precision used for the computations:
- double (64-bit)
- long double (80-bit on x86 architectures)
- MPFR-based custom extendend precision
They have now been merged into one template version.
Installation instructions
This code has been tested on recent Mac OS X (>= 10.14) and Linux installations. In order to compile and use it, a recent C++ compiler with C++20 and OpenMP support is necessary (recent g++ and clang compilers have been shown to work). An active internet connection and some external utilities and libraries must also be installed and available on your system search paths:
- CMake version 3.16 or newer
- Eigen version 3.3 or newer
- (optional) GMP version 6.0 or newer for multiple precision support
- (optional) MPFR version 4.0 or newer for multiple precision support
- (optional) mpreal wrapper for MPFR
- (optional) doxygen to generate the accompanying code documentation
- Google gtest framework for generating the test executables will be downloaded during CMake configuration
Assuming these prerequisites are taken care of and you are located at the base folder, building the library can be done using the following commands (with the appropriate user privileges):
mkdir build
cd build
cmake ..
make all
make install
This series of steps will install the library on your system. Usually the default location is /usr/local, but this behavior can be changed when calling CMake by specifying an explicit install prefix:
cmake -DCMAKE_INSTALL_PREFIX=/your/install/path/here ..
With gtest downloaded in the build directory, the make all command should have generated three test executables:
- firpmlib_scaling_test : should contain code to generate all the example filters used in [1] and tests for subsequent bugs
- firpmlib_extensive_test : contains a more extensive set of over 50 different filters, giving an iteration count comparison for uniform initialization, reference scaling and AFP initialization, when applicable
- firpmlib_numerics_test : unit tests for the numerical kernels (barycentric weights and error evaluation, checked against MPFR when available)
The make test command will launch these test executables on your system.
The make all target also generates the documentation if Doxygen was found on your system when running CMake. It can also be generated individually by running the command
make doc
after CMake was called.
Running the test executables will print out information regarding the final reference error (i.e., final delta value) obtained when executing the Parks-McClellan exchange algorithm, along with iteration count information. Depending on your machine, these tests can take some time to finish.
An example output for one test case from firpm_scaling_test (using the long double instantiation) of the routines looks like this:
[ RUN ] firpm_scaling_test/1.combfir
START Parks-McClellan with uniform initialization
Final Delta = 1.6039185593030203561e-07
Iteration count = 13
FINISH Parks-McClellan with uniform initialization
START Parks-McClellan with reference scaling
Final Delta = 1.6066986792983147255e-07
Iteration count = 3
FINISH Parks-McClellan with reference scaling
START Parks-McClellan with AFP
Final Delta = 1.606565353078586782e-07
Iteration count = 4
FINISH Parks-McClellan with AFP
Iteration count reduction for final filter RS: 0.76923076923076916245
Iteration count reduction for final filter AFP: 0.69230769230769229061
[ OK ] firpm_scaling_test/1.combfir (378 ms)
Use
Examples of how to use the library can be found in the test folder.
Licensing
Up until April 7, 2024 the code was GPLv3+ licensed. It has since switched to a more permissive 3-Clause BSD license.
References
[1] S.-I. Filip, A robust and scalable implementation of the Parks-McClellan algorithm for designing FIR filters, ACM Trans. Math. Softw., vol. 43, no. 1, Aug. 2016, Art. no. 7.
[2] S.-I. Filip, Robust tools for weighted Chebyshev approximation and applications to digital filter design, Ph.D. dissertation, ENS de Lyon, France, 2016.
Acknowledgements
1 maintainer
Metadata
1 maintainer
Release files for firpm 0.2.2
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Transparency logRelease files / firpm-0.2.2-cp39-cp39-musllinux_1_2_x86_64.whl
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Transparency logRelease files / firpm-0.2.2-cp39-cp39-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
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Transparency logRelease files / firpm-0.2.2-cp39-cp39-manylinux_2_26_aarch64.manylinux_2_28_aarch64.whl
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| Tags | CPython 3.9 Linux glibc 2.26+ ARM64 Linux glibc 2.28+ ARM64 |
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| Download URL | firpm-0.2.2-cp39-cp39-macosx_14_0_arm64.whl |
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| Size | 529.2 kB |
| Tags | CPython 3.9 macOS 14.0+ ARM64 |
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Transparency logSecurity for firpm 0.2.2
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