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HOA Library
beta 3.0
High Order Ambisonics Library
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The class encodes a signal into the harmonics domain depending on coodinates. More...
#include <Hoa_Encoder.hpp>
Public Member Functions | |
| Encoder (const size_t order) | |
| The constructor. More... | |
| ~Encoder () hoa_noexcept | |
| The destructor. | |
| T | getRadius () const hoa_noexcept |
| Returns the radius. | |
| T | getAzimuth () const hoa_noexcept |
| Returns the azimuth. | |
| T | getElevation () const hoa_noexcept |
| Returns the elevation. | |
| void | setCoordinates (const T radius, const T azimuth, const T elevation) hoa_noexcept |
| Sets the coordinates. More... | |
| void | setRadius (const T radius) hoa_noexcept |
| Sets the radius. More... | |
| void | setAzimuth (const T azimuth) hoa_noexcept |
| Sets the azimuth. More... | |
| void | setElevation (const T elevation) hoa_noexcept |
| Sets the elevation. More... | |
| void | process (const T *input, T *outputs) hoa_noexcept hoa_override |
| The method performs the encoding of the harmonics signal. More... | |
 Public Member Functions inherited from ProcessorHarmonics< D, T > | |
| ProcessorHarmonics (const size_t order) hoa_noexcept | |
| The harmonics constructor. More... | |
| virtual | ~ProcessorHarmonics () hoa_noexcept |
| The harmonics destructor. | |
| size_t | getDecompositionOrder () const hoa_noexcept |
| Returns the order of decomposition. | |
| size_t | getNumberOfHarmonics () const hoa_noexcept |
| Returns the number of harmonics. | |
| size_t | getHarmonicDegree (const size_t index) const hoa_noexcept |
| Returns the degree of an harmonic. More... | |
| long | getHarmonicOrder (const size_t index) const hoa_noexcept |
| Returns the azimuthal order of an harmonic. More... | |
| size_t | getHarmonicIndex (const size_t degree, const long order) const hoa_noexcept |
| Returns the index of an harmonic given the degree and the azimuthal order. More... | |
| std::string | getHarmonicName (const size_t index) const hoa_noexcept |
| Returns the name of an harmonic. More... | |
| T | getHarmonicNormalization (const size_t index) const hoa_noexcept |
| Returns the normalization of an harmonic. More... | |
| T | getHarmonicSemiNormalization (const size_t index) const hoa_noexcept |
| Returns the semi-normalization of an harmonic. More... | |
| Public Member Functions inherited from Processor< D, T > | |
| virtual | ~Processor () hoa_noexcept |
| The destructor. | |
The class encodes a signal into the harmonics domain depending on coodinates.
The class generates the signals associated to the harmonics \(Y_{l,m}\) according to a radius \(\rho\), an azimuth \(\theta\) and an elevation \(\varphi\).
The coefficients of the harmonics are defined by:
\[Y_{l,m}(\theta, \varphi) = G_{l,m}(\rho) P_{l, \left|m\right|}(\sin{(\varphi)}) e^{+im\theta} k_{l, m} \]
with
\(G_{l,m}(\rho)\) the radius part of the equation,
\(e^{+im\theta}\) the azimuth part with \(i\) the imaginary,
\(P_{l, \left|m\right|}(\cos{(\varphi)})\) the elevation part of the equation with \(P_{l, \left|m\right|}(x)\) the associated Legendre polynomials,
\(k_{l, m}\) the normalization and
\(N\) the order of decomposition, \(l\) the degree, \(m\) the azimuthal order, \(\rho\) the radius, \(\theta\) the azimuth and \(\varphi\) the elevation in radian.
The radius \(\rho\) is included between \(0\) and \(+\infty\). \(0\) is the center of the soundfield, \(1\) is the radius of the ambisonics circle or sphere, beyond this limit the gains \(G\) of the harmonics decrease globally and before the gains \(G\) decrease independently:
if \(\rho\ge1\)
\[G_{l,m}(\rho) = \frac{1}{\rho}\]
else
\[G_{l,m}(\rho) = \rho^l((1-\rho)(N-l)+1)\]
The azimuth \(\theta\) in radian is included between \(0\) and \(2\pi\). The direction of rotation is counterclockwise. The \(0\) radian is \(\frac{\pi}{2}\) phase shifted relative to a mathematical representation of a circle, then the \(0\) radian is at the "front" of the soundfield. The azimuth part in the imaginary form of the equation \(e^{+im\theta}\) can be expressed with the real form :
if \(m\geq0\)
\[e^{+im\theta} = \cos{(\left|m\right|\theta)}\]
else
\[e^{+im\theta} = \sin{(\left|m\right|\theta)}\]
The elevation \(\varphi\) is included between \(-\pi\) and \(\pi\). The direction of rotation is from bottom to the top. The \(0\) radian is centered at the "front" of the soundfield, then \(\frac{\pi}{2}\) is at the top, \(-\frac{\pi}{2}\) is at the bottom and \(\pi\) is behind. Note that if the angle of elevation is between \(\frac{\pi}{2}\) and \(\frac{3\pi}{2}\), the azimuth is reversed. The elevation part \(P_{l, \left|m\right|}(x)\) of the formula can be expressed with the recursives formulas:
\[P_{l+1,l+1}(x) = -(2l+1)\sqrt{(1-x^2)}P_{(l,l)}(x) \]
\[P_{l+1,l}(x) = x(2l+1)P_{(l,l)}(x) \]
\[P_{l+1,m}(x) = \frac{x(2l+1)P_{(l,m)}(x) - (l+m)P_{(l-1,m)}(x)}{l-m+1} \]
and with
\[P_{0, 0}(x) = 1\]
The normalization part \(k_{l, m}\) is equivalent to :
if \(m = 0\) then
\[k_{l, m} = 1\]
else
\[k_{l, m} = \sqrt{\frac{(l - \left|m\right|)!}{(l + \left|m\right|)!}}\sqrt{2} \]
Definition at line 66 of file Hoa_Encoder.hpp.
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The constructor.
| order | The order of decomposition. |
Definition at line 72 of file Hoa_Encoder.hpp.
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Sets the coordinates.
| radius | The new radius. |
| azimuth | The new azimuth. |
| elevation | The new elevation. |
Definition at line 103 of file Hoa_Encoder.hpp.
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Sets the azimuth.
| azimuth | The new azimuth. |
Definition at line 133 of file Hoa_Encoder.hpp.
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Sets the elevation.
| elevation | The new elevation. |
Definition at line 179 of file Hoa_Encoder.hpp.
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The method performs the encoding of the harmonics signal.
The input pointer must be the sample to encode and the outputs array contains the spherical harmonics samples thus the minimum size of the array must be the number of harmonics.
| input | The input pointer. |
| outputs | The outputs array. |
Reimplemented from Processor< D, T >.
Definition at line 252 of file Hoa_Encoder.hpp.
1.8.11
