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added discrete Hilbert transform

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Ahmet Inan 2020-03-12 10:09:06 +01:00
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README.md
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@ -60,6 +60,10 @@ Normalizers for [periodic](https://en.wikipedia.org/wiki/Periodic_function) sign
Fs/4 [Complex down conversion](https://en.wikipedia.org/wiki/Digital_down_converter)
### [hilbert.hh](hilbert.hh)
[Discrete Hilbert transform](https://en.wikipedia.org/wiki/Hilbert_transform#Discrete_Hilbert_transform)
### [fmd.hh](fmd.hh)
[Frequency modulation](https://en.wikipedia.org/wiki/Frequency_modulation) [demodulation](https://en.wikipedia.org/wiki/Demodulation) with and without [atan2](https://en.wikipedia.org/wiki/Atan2).

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hilbert.hh Normal file
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/*
Discrete Hilbert transformation
Copyright 2020 Ahmet Inan <inan@aicodix.de>
*/
#pragma once
#include "window.hh"
namespace DSP {
template <typename TYPE, int TAPS>
class Hilbert
{
static_assert((TAPS-1) % 4 == 0, "TAPS-1 not divisible by four");
typedef TYPE complex_type;
typedef typename TYPE::value_type value_type;
value_type real[TAPS];
value_type imco[(TAPS-1)/4];
value_type reco;
public:
Hilbert(value_type a = value_type(2))
{
Kaiser<value_type> win(a);
reco = win((TAPS-1)/2, TAPS);
for (int i = 0; i < (TAPS-1)/4; ++i)
imco[i] = win((2*i+1)+(TAPS-1)/2, TAPS) * 2 / ((2*i+1) * Const<value_type>::Pi());
}
complex_type operator()(value_type input)
{
value_type re = reco * real[(TAPS-1)/2];
value_type im = imco[0] * (real[(TAPS-1)/2-1] - real[(TAPS-1)/2+1]);
for (int i = 1; i < (TAPS-1)/4; ++i)
im += imco[i] * (real[(TAPS-1)/2-(2*i+1)] - real[(TAPS-1)/2+(2*i+1)]);
for (int i = 0; i < TAPS-1; ++i)
real[i] = real[i+1];
real[TAPS-1] = input;
return complex_type(re, im);
}
};
}