1
0
mirror of https://github.com/TomHarte/CLK.git synced 2024-12-24 12:30:17 +00:00
CLK/SignalProcessing/FIRFilter.cpp
2018-11-26 22:34:04 -05:00

173 lines
5.4 KiB
C++

//
// LinearFilter.c
// Clock Signal
//
// Created by Thomas Harte on 01/10/2011.
// Copyright 2011 Thomas Harte. All rights reserved.
//
#include "FIRFilter.hpp"
#include <cmath>
using namespace SignalProcessing;
/*
A Kaiser-Bessel filter is a real time window filter. It looks at the last n samples
of an incoming data source and computes a filtered value, which is the value you'd
get after applying the specified filter, at the centre of the sampling window.
Hence, if you request a 37 tap filter then filtering introduces a latency of 18
samples. Suppose you're receiving input at 44,100Hz and using 4097 taps, then you'll
introduce a latency of 2048 samples, which is about 46ms.
There's a correlation between the number of taps and the quality of the filtering.
More samples = better filtering, at the cost of greater latency. Internally, applying
the filter involves calculating a weighted sum of previous values, so increasing the
number of taps is quite cheap in processing terms.
Original source for this filter:
"DIGITAL SIGNAL PROCESSING, II", IEEE Press, pages 123-126.
*/
/*! Evaluates the 0th order Bessel function at @c a. */
float FIRFilter::ino(float a) {
float d = 0.0f;
float ds = 1.0f;
float s = 1.0f;
do {
d += 2.0f;
ds *= (a * a) / (d * d);
s += ds;
} while(ds > s*1e-6f);
return s;
}
void FIRFilter::coefficients_for_idealised_filter_response(short *filter_coefficients, float *A, float attenuation, std::size_t number_of_taps) {
/* calculate alpha, which is the Kaiser-Bessel window shape factor */
float a; // to take the place of alpha in the normal derivation
if(attenuation < 21.0f) {
a = 0.0f;
} else {
if(attenuation > 50.0f)
a = 0.1102f * (attenuation - 8.7f);
else
a = 0.5842f * powf(attenuation - 21.0f, 0.4f) + 0.7886f * (attenuation - 21.0f);
}
std::vector<float> filter_coefficients_float(number_of_taps);
/* work out the right hand side of the filter coefficients */
std::size_t Np = (number_of_taps - 1) / 2;
float I0 = ino(a);
float Np_squared = static_cast<float>(Np * Np);
for(unsigned int i = 0; i <= Np; ++i) {
filter_coefficients_float[Np + i] =
A[i] *
ino(a * sqrtf(1.0f - (static_cast<float>(i * i) / Np_squared) )) /
I0;
}
/* coefficients are symmetrical, so copy from right hand side to left side */
for(std::size_t i = 0; i < Np; ++i) {
filter_coefficients_float[i] = filter_coefficients_float[number_of_taps - 1 - i];
}
/* scale back up so that we retain 100% of input volume */
float coefficientTotal = 0.0f;
for(std::size_t i = 0; i < number_of_taps; ++i) {
coefficientTotal += filter_coefficients_float[i];
}
/* we'll also need integer versions, potentially */
float coefficientMultiplier = 1.0f / coefficientTotal;
for(std::size_t i = 0; i < number_of_taps; ++i) {
filter_coefficients[i] = static_cast<short>(filter_coefficients_float[i] * FixedMultiplier * coefficientMultiplier);
}
}
std::vector<float> FIRFilter::get_coefficients() const {
std::vector<float> coefficients;
for(const auto short_coefficient: filter_coefficients_) {
coefficients.push_back(static_cast<float>(short_coefficient) / FixedMultiplier);
}
return coefficients;
}
FIRFilter::FIRFilter(std::size_t number_of_taps, float input_sample_rate, float low_frequency, float high_frequency, float attenuation) {
// we must be asked to filter based on an odd number of
// taps, and at least three
if(number_of_taps < 3) number_of_taps = 3;
if(attenuation < 21.0f) attenuation = 21.0f;
// ensure we have an odd number of taps
number_of_taps |= 1;
// store instance variables
filter_coefficients_.resize(number_of_taps);
/* calculate idealised filter response */
std::size_t Np = (number_of_taps - 1) / 2;
float two_over_sample_rate = 2.0f / input_sample_rate;
// Clamp the high cutoff frequency.
high_frequency = std::min(high_frequency, input_sample_rate * 0.5f);
std::vector<float> A(Np+1);
A[0] = 2.0f * (high_frequency - low_frequency) / input_sample_rate;
for(unsigned int i = 1; i <= Np; ++i) {
float i_pi = static_cast<float>(i) * static_cast<float>(M_PI);
A[i] =
(
sinf(two_over_sample_rate * i_pi * high_frequency) -
sinf(two_over_sample_rate * i_pi * low_frequency)
) / i_pi;
}
FIRFilter::coefficients_for_idealised_filter_response(filter_coefficients_.data(), A.data(), attenuation, number_of_taps);
}
FIRFilter::FIRFilter(const std::vector<float> &coefficients) {
for(const auto coefficient: coefficients) {
filter_coefficients_.push_back(static_cast<short>(coefficient * FixedMultiplier));
}
}
FIRFilter FIRFilter::operator+(const FIRFilter &rhs) const {
std::vector<float> coefficients = get_coefficients();
std::vector<float> rhs_coefficients = rhs.get_coefficients();
std::vector<float> sum;
for(std::size_t i = 0; i < coefficients.size(); ++i) {
sum.push_back((coefficients[i] + rhs_coefficients[i]) / 2.0f);
}
return FIRFilter(sum);
}
FIRFilter FIRFilter::operator-() const {
std::vector<float> negative_coefficients;
for(const auto coefficient: get_coefficients()) {
negative_coefficients.push_back(1.0f - coefficient);
}
return FIRFilter(negative_coefficients);
}
FIRFilter FIRFilter::operator*(const FIRFilter &rhs) const {
std::vector<float> coefficients = get_coefficients();
std::vector<float> rhs_coefficients = rhs.get_coefficients();
std::vector<float> sum;
for(std::size_t i = 0; i < coefficients.size(); ++i) {
sum.push_back(coefficients[i] * rhs_coefficients[i]);
}
return FIRFilter(sum);
}