2021-10-14 13:47:35 +02:00

1124 lines
33 KiB
C++

//$ nobt
/**
* @file r8bbase.h
*
* @brief The "base" inclusion file with basic classes and functions.
*
* This is the "base" inclusion file for the "r8brain-free-src" sample rate
* converter. This inclusion file contains implementations of several small
* utility classes and functions used by the library.
*
* r8brain-free-src Copyright (c) 2013-2014 Aleksey Vaneev
* See the "License.txt" file for license.
*
* @mainpage
*
* @section intro_sec Introduction
*
* Open source (under the MIT license) high-quality professional audio sample
* rate converter (SRC) (resampling) library. Features routines for SRC, both
* up- and downsampling, to/from any sample rate, including non-integer sample
* rates: it can be also used for conversion to/from SACD sample rate and even
* go beyond that. SRC routines were implemented in multi-platform C++ code,
* and have a high level of optimality.
*
* The structure of this library's objects is such that they can be frequently
* created and destroyed in large applications with a minimal performance
* impact due to a high level of reusability of its most
* "initialization-expensive" objects: the fast Fourier transform and FIR
* filter objects.
*
* The SRC algorithm at first produces 2X oversampled (relative to the source
* sample rate, or the destination sample rate if the downsampling is
* performed) signal and then performs interpolation using a bank of short
* (14 to 28 taps, depending on the required precision)
* polynomial-interpolated sinc function-based fractional delay filters. This puts the
* algorithm into the league of the fastest among the most precise SRC
* algorithms. The more precise alternative being only the whole
* number-factored SRC, which can be slower.
*
* @section requirements Requirements
*
* C++ compiler and system with the "double" floating point type (53-bit
* mantissa) support. No explicit code for the "float" type is present in this
* library, because as practice has shown the "float"-based code performs
* considerably slower on a modern processor, at least in this library.
* However, if the "double" type really represents the "float" type (24-bit
* mantissa) in a given compiler, on a given system, the library won't become
* broken, only the conversion quality may become degraded. This library
* always uses the "sizeof( double )" operator to obtain "double" floating
* point type's size in bytes. This library does not have dependencies beside
* the standard C library, the "windows.h" on Windows and the "pthread.h" on
* Mac OS X and Linux.
*
* @section usage Usage Information
*
* The sample rate converter (resampler) is represented by the
* r8b::CDSPResampler class, which is a single front-end class for the whole
* library. You do not basically need to use nor understand any other classes
* beside this class. Several derived classes that have varying levels of
* precision are also available.
*
* The code of the library resides in the "r8b" C++ namespace, effectively
* isolating it from all other code. The code is thread-safe. A separate
* resampler object should be created for each audio channel or stream being
* processed.
*
* Note that you will need to compile the "r8bbase.cpp" source file and
* include the resulting object file into your application build. This source
* file includes definitions of several global static objects used by the
* library. You may also need to include to your project: the "Kernel32"
* library (on Windows) and the "pthread" library on Mac OS X and Linux.
*
* The library is able to process signal of any scale and loudness: it is not
* limited to just a "usual" -1.0 to 1.0 range.
*
* The code of this library was commented in the Doxygen style. To generate
* the documentation locally you may run the "doxygen ./other/r8bdoxy.txt"
* command from the library's directory.
*
* Preliminary tests show that the r8b::CDSPResampler24 resampler class
* achieves 15.6*n_cores Mflops when converting 1 channel of audio from 44100
* to 96000 sample rate, on a typical Intel Core i7-4770K processor-based
* system without overclocking. This approximately translates to a real-time
* resampling of 160*n_cores audio streams, at 100% CPU load.
*
* @section dll Dynamic Link Library
*
* The functions of this SRC library are also accessible in simplified form
* via the DLL file on Windows, requiring a processor with SSE2 support.
* Delphi Pascal interface unit file for the DLL file is available. DLL and
* C LIB files are distributed in a separate ZIP file on the project's home
* page. On non-Windows systems it is preferrable to use the C++ library
* directly.
*
* @section realtime Real-time Applications
*
* The resampler class of this library was designed as asynchronous processor:
* it may produce any number of output samples, depending on the input sample
* data length and the resampling parameters. The resampler must be fed with
* the input sample data until enough output sample data was produced, with
* any excess output samples used before feeding the resampler with more input
* data. A "relief" factor here is that the resampler removes the initial
* processing latency automatically, and that after initial moments of
* processing the output becomes steady, with only minor output sample data
* length fluctuations.
*
* Note that the r8b::CDSPResampler::getInLenBeforeOutStart() function can be
* used to estimate the number of input samples that should be provided to the
* resampler before the actual output starts.
*
* @section notes Notes
*
* When using the r8b::CDSPResampler<> class directly, you may select the
* transition band/steepness of the low-pass (reconstruction) filter,
* expressed as a percentage of the full spectral bandwidth of the input
* signal (or the output signal if the downsampling is performed), and the
* desired stop-band attenuation in decibel.
*
* The transition band is specified as the normalized spectral space of the
* input signal (or the output signal if the downsampling is performed)
* between the low-pass filter's -3 dB point and the Nyquist frequency, and
* ranges from 0.5% to 45%. Stop-band attenuation can be specified in the
* range 49 to 218 decibel.
*
* This SRC library also implements a faster "power of 2" resampling (e.g. 2X,
* 4X, 8X, 16X, etc. upsampling and downsampling).
*
* This library was tested for compatibility with GNU C++, Microsoft Visual
* C++ and Intel C++ compilers, on 32- and 64-bit Windows, Mac OS X and CentOS
* Linux.
*
* All code is fully "inline", without the need to compile many source files.
* The memory footprint is quite modest.
*
* @section users Users
*
* This library is used by:
*
* * http://www.martinic.com/combov/ Combo Model V VSTi instrument
* * http://midithru.net/Home/AsioLink WDM Asio Link Driver
*
* @section license License
*
* The MIT License (MIT)
*
* r8brain-free-src Copyright (c) 2013-2014 Aleksey Vaneev
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
* DEALINGS IN THE SOFTWARE.
*
* Please credit the creator of this library in your documentation in the
* following way: "Sample rate converter designed by Aleksey Vaneev of
* Voxengo"
*
* @version 1.6
*/
#pragma once
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "r8bconf.h"
#if defined( R8B_WIN )
#include <windows.h>
#else // R8B_WIN
#include <pthread.h>
#endif // R8B_WIN
/**
* @brief The "r8brain-free-src" library namespace.
*
* The "r8brain-free-src" sample rate converter library namespace.
*/
namespace r8b
{
#if !defined( M_PI )
/**
* The macro equals to "pi" constant, fits 53-bit floating point mantissa.
*/
#define M_PI 3.14159265358979324
#endif // M_PI
#if !defined( M_2PI )
/**
* The M_2PI macro equals to "2 * pi" constant, fits 53-bit floating point
* mantissa.
*/
#define M_2PI 6.28318530717958648
#endif // M_2PI
#if !defined( M_3PI )
/**
* The M_3PI macro equals to "3 * pi" constant, fits 53-bit floating point
* mantissa.
*/
#define M_3PI 9.42477796076937972
#endif // M_3PI
#if !defined( M_4PI )
/**
* The M_4PI macro equals to "4 * pi" constant, fits 53-bit floating point
* mantissa.
*/
#define M_4PI 12.56637061435917295
#endif // M_4PI
#if !defined( M_PId2 )
/**
* The macro equals to "pi divided by 2" constant, fits 53-bit floating
* point mantissa.
*/
#define M_PId2 1.57079632679489662
#endif // M_PId2
/**
* A special macro that defines empty copy-constructor and copy operator with
* the "private:" prefix. This macro should be used in classes that cannot be
* copied in a standard C++ way.
*
* This macro does not need to be defined in classes derived from a class
* where such macro was already used.
*
* @param ClassName The name of the class which uses this macro.
*/
#define R8BNOCTOR( ClassName ) \
private: \
ClassName( const ClassName& ) { } \
ClassName& operator = ( const ClassName& ) { return( *this ); }
/**
* @brief The default base class for objects created on heap.
*
* Class that implements "new" and "delete" operators that use standard
* malloc() and free() functions.
*/
class CStdClassAllocator
{
public:
/**
* @param n The size of the object, in bytes.
* @param p Pointer to object's pre-allocated memory block.
* @return Pointer to object.
*/
void* operator new(size_t, void* p) { return (p); }
/**
* @param n The size of the object, in bytes.
* @return Pointer to the allocated memory block for the object.
*/
void* operator new(size_t n) { return (malloc(n)); }
/**
* @param n The size of the object, in bytes.
* @return Pointer to the allocated memory block for the object.
*/
void* operator new[](size_t n) { return (malloc(n)); }
/**
* Operator frees a previously allocated memory block for the object.
*
* @param p Pointer to the allocated memory block for the object.
*/
void operator delete(void* p) { free(p); }
/**
* Operator frees a previously allocated memory block for the object.
*
* @param p Pointer to the allocated memory block for the object.
*/
void operator delete[](void* p) { free(p); }
};
/**
* @brief The default base class for objects that allocate blocks of memory.
*
* Memory buffer allocator that uses "stdlib" standard memory functions.
*/
class CStdMemAllocator : public CStdClassAllocator
{
public:
/**
* Function allocates memory block.
*
* @param Size The size of the block, in bytes.
* @result The pointer to the allocated block.
*/
static void* allocmem(const size_t Size) { return (malloc(Size)); }
/**
* Function reallocates a previously allocated memory block.
*
* @param p Pointer to the allocated block, can be NULL.
* @param Size The new size of the block, in bytes.
* @result The pointer to the (re)allocated block.
*/
static void* reallocmem(void* p, const size_t Size) { return (realloc(p, Size)); }
/**
* Function frees a previously allocated memory block.
*
* @param p Pointer to the allocated block, can be NULL.
*/
static void freemem(void* p) { free(p); }
};
/**
* @brief Templated memory buffer class for element buffers of fixed capacity.
*
* Fixed memory buffer object. Supports allocation of a fixed amount of
* memory. Does not store buffer's capacity - the user should know the actual
* capacity of the buffer. Does not feature "internal" storage, memory is
* always allocated via the R8B_MEMALLOCCLASS class's functions. Thus the
* object of this class can be moved in memory.
*
* This class manages memory space only - it does not perform element class
* construction nor destruction operations.
*
* @param T The class of the stored elements (e.g. "double").
*/
template <class T>
class CFixedBuffer : public R8B_MEMALLOCCLASS
{
R8BNOCTOR(CFixedBuffer)
public:
CFixedBuffer() : Data(nullptr) { }
/**
* Constructor allocates memory so that the specified number of elements
* of type T can be stored in *this buffer object.
*
* @param Capacity Storage for this number of elements to allocate.
*/
CFixedBuffer(const int Capacity)
{
R8BASSERT(Capacity > 0 || Capacity == 0);
Data = (T*)allocmem(Capacity * sizeof(T));
R8BASSERT(Data != nullptr || Capacity == 0);
}
~CFixedBuffer() { freemem(Data); }
/**
* Function allocates memory so that the specified number of elements of
* type T can be stored in *this buffer object.
*
* @param Capacity Storage for this number of elements to allocate.
*/
void alloc(const int Capacity)
{
R8BASSERT(Capacity > 0 || Capacity == 0);
freemem(Data);
Data = (T*)allocmem(Capacity * sizeof(T));
R8BASSERT(Data != nullptr || Capacity == 0);
}
/**
* Function deallocates a previously allocated buffer.
*/
void free()
{
freemem(Data);
Data = NULL;
}
/**
* @return Pointer to the first element of the allocated buffer, nullptr if
* not allocated.
*/
T* getPtr() const { return (Data); }
/**
* @return Pointer to the first element of the allocated buffer, nullptr if
* not allocated.
*/
operator T*() const { return (Data); }
private:
T* Data = nullptr; ///< Element buffer pointer.
///<
};
/**
* @brief Pointer-to-object "keeper" class with automatic deletion.
*
* An auxiliary class that can be used for keeping a pointer to object that
* should be deleted together with the "keeper" by calling object's "delete"
* operator.
*
* @param T Pointer type to operate with, must include the asterisk (e.g.
* "CDSPFIRFilter*").
*/
template <class T>
class CPtrKeeper
{
R8BNOCTOR(CPtrKeeper)
public:
CPtrKeeper() : Object(NULL) { }
/**
* Constructor assigns a pointer to object to *this keeper.
*
* @param aObject Pointer to object to keep, can be NULL.
*/
template <class T2>
CPtrKeeper(T2 const aObject) : Object(aObject) { }
~CPtrKeeper() { delete Object; }
/**
* Function assigns a pointer to object to *this keeper. A previously
* keeped pointer will be reset and object deleted.
*
* @param aObject Pointer to object to keep, can be NULL.
*/
template <class T2>
void operator =(T2 const aObject)
{
reset();
Object = aObject;
}
/**
* @return Pointer to keeped object, nullptr if no object is being kept.
*/
T operator ->() const { return (Object); }
/**
* @return Pointer to keeped object, nullptr if no object is being kept.
*/
operator T() const { return (Object); }
/**
* Function resets the keeped pointer and deletes the keeped object.
*/
void reset()
{
T DelObj = Object;
Object = NULL;
delete DelObj;
}
/**
* @return Function returns the keeped pointer and resets it in *this
* keeper without object deletion.
*/
T unkeep()
{
T ResObject = Object;
Object = NULL;
return (ResObject);
}
private:
T Object; ///< Pointer to keeped object.
///<
};
/**
* @brief Multi-threaded synchronization object class.
*
* This class uses standard OS thread-locking (mutex) mechanism which is
* fairly efficient in most cases.
*
* The acquire() function can be called recursively, in the same thread, for
* this kind of thread-locking mechanism. This will not produce a dead-lock.
*/
class CSyncObject
{
R8BNOCTOR(CSyncObject)
public:
CSyncObject()
{
#if defined( R8B_WIN )
InitializeCriticalSectionAndSpinCount(&CritSec, 4000);
#else // R8B_WIN
pthread_mutexattr_t MutexAttrs;
pthread_mutexattr_init( &MutexAttrs );
pthread_mutexattr_settype( &MutexAttrs, PTHREAD_MUTEX_RECURSIVE );
pthread_mutex_init( &Mutex, &MutexAttrs );
pthread_mutexattr_destroy( &MutexAttrs );
#endif // R8B_WIN
}
~CSyncObject()
{
#if defined( R8B_WIN )
DeleteCriticalSection(&CritSec);
#else // R8B_WIN
pthread_mutex_destroy( &Mutex );
#endif // R8B_WIN
}
/**
* Function "acquires" *this thread synchronizer object immediately or
* waits until another thread releases it.
*/
void acquire()
{
#if defined( R8B_WIN )
EnterCriticalSection(&CritSec);
#else // R8B_WIN
pthread_mutex_lock( &Mutex );
#endif // R8B_WIN
}
/**
* Function "releases" *this previously acquired thread synchronizer
* object.
*/
void release()
{
#if defined( R8B_WIN )
LeaveCriticalSection(&CritSec);
#else // R8B_WIN
pthread_mutex_unlock( &Mutex );
#endif // R8B_WIN
}
private:
#if defined( R8B_WIN )
CRITICAL_SECTION CritSec; ///< Standard Windows critical section
///< structure.
///<
#else // R8B_WIN
pthread_mutex_t Mutex; ///< pthread.h mutex object.
///<
#endif // R8B_WIN
};
/**
* @brief A "keeper" class for CSyncObject-based synchronization.
*
* Sync keeper class. The object of this class can be used as auto-init and
* auto-deinit object for calling the acquire() and release() functions of an
* object of the CSyncObject class. This "keeper" object is best used in
* functions as an "automatic" object allocated on the stack, possibly via the
* R8BSYNC() macro.
*/
class CSyncKeeper
{
R8BNOCTOR(CSyncKeeper)
public:
CSyncKeeper() { }
/**
* @param aSyncObj Pointer to the sync object which should be used for
* sync'ing, can be NULL.
*/
CSyncKeeper(CSyncObject* const aSyncObj) : SyncObj(aSyncObj) { if (SyncObj != nullptr) { SyncObj->acquire(); } }
/**
* @param aSyncObj Reference to the sync object which should be used for
* sync'ing.
*/
CSyncKeeper(CSyncObject& aSyncObj) : SyncObj(&aSyncObj) { SyncObj->acquire(); }
~CSyncKeeper() { if (SyncObj != nullptr) { SyncObj->release(); } }
protected:
CSyncObject* SyncObj = nullptr; ///< Sync object in use (can be NULL).
///<
};
/**
* The synchronization macro. The R8BSYNC( obj ) macro, which creates and
* object of the r8b::CSyncKeeper class on stack, should be put before
* sections of the code that may potentially change data asynchronously with
* other threads at the same time. The R8BSYNC( obj ) macro "acquires" the
* synchronization object thus blocking execution of other threads that also
* use the same R8BSYNC( obj ) macro. The blocked section begins with the
* R8BSYNC( obj ) macro and finishes at the end of the current C++ code block.
* Multiple R8BSYNC() macros may be defined from within the same code block.
*
* @param SyncObject An object of the CSyncObject type that is used for
* synchronization.
*/
#define R8BSYNC( SyncObject ) R8BSYNC_( SyncObject, __LINE__ )
#define R8BSYNC_( SyncObject, id ) R8BSYNC__( SyncObject, id )
#define R8BSYNC__( SyncObject, id ) CSyncKeeper SyncKeeper##id( SyncObject )
/**
* @brief Sine signal generator class.
*
* Class implements sine signal generator without biasing.
*/
class CSineGen
{
public:
CSineGen() { }
/**
* Constructor initializes *this sine signal generator.
*
* @param si Sine function increment, in radians.
* @param ph Starting phase, in radians. Add 0.5 * M_PI for cosine
* function.
*/
CSineGen(const double si, const double ph) : svalue1(sin(ph)), svalue2(sin(ph - si)), sincr(2.0 * cos(si)) { }
/**
* Constructor initializes *this sine signal generator.
*
* @param si Sine function increment, in radians.
* @param ph Starting phase, in radians. Add 0.5 * M_PI for cosine
* function.
* @param g The overall gain factor, 1.0 for unity gain (-1.0 to 1.0
* amplitude).
*/
CSineGen(const double si, const double ph, const double g) : svalue1(sin(ph) * g), svalue2(sin(ph - si) * g), sincr(2.0 * cos(si)) { }
/**
* Function initializes *this sine signal generator.
*
* @param si Sine function increment, in radians.
* @param ph Starting phase, in radians. Add 0.5 * M_PI for cosine
* function.
*/
void init(const double si, const double ph)
{
svalue1 = sin(ph);
svalue2 = sin(ph - si);
sincr = 2.0 * cos(si);
}
/**
* Function initializes *this sine signal generator.
*
* @param si Sine function increment, in radians.
* @param ph Starting phase, in radians. Add 0.5 * M_PI for cosine
* function.
* @param g The overall gain factor, 1.0 for unity gain (-1.0 to 1.0
* amplitude).
*/
void init(const double si, const double ph, const double g)
{
svalue1 = sin(ph) * g;
svalue2 = sin(ph - si) * g;
sincr = 2.0 * cos(si);
}
/**
* @return Next value of the sine function, without biasing.
*/
double generate()
{
const double res = svalue1;
svalue1 = sincr * res - svalue2;
svalue2 = res;
return (res);
}
private:
double svalue1 = 0; ///< Current sine value.
///<
double svalue2 = 0; ///< Previous sine value.
///<
double sincr = 0; ///< Sine value increment.
///<
};
/**
* @param v Input value.
* @return Calculated bit occupancy of the specified input value. Bit
* occupancy means how many significant lower bits are necessary to store a
* specified value. Function treats the input value as unsigned.
*/
inline int getBitOccupancy(const int v)
{
static const char OccupancyTable[] =
{
1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
};
const int tt = v >> 16;
if (tt != 0)
{
const int t = v >> 24;
return (t != 0 ? 24 + OccupancyTable[t & 0xFF] : 16 + OccupancyTable[tt]);
}
const int t = v >> 8;
return (t != 0 ? 8 + OccupancyTable[t] : OccupancyTable[v]);
}
/**
* Function calculates frequency response of the specified FIR filter at the
* specified circular frequency. Phase can be calculated as atan2( im, re ).
*
* @param flt FIR filter's coefficients.
* @param fltlen Number of coefficients (taps) in the filter.
* @param th Circular frequency [0; pi].
* @param[out] re0 Resulting real part of the complex frequency response.
* @param[out] im0 Resulting imaginary part of the complex frequency response.
* @param fltlat Filter's latency in samples.
*/
inline void calcFIRFilterResponse(const double* flt, int fltlen, const double th, double& re0, double& im0, const int fltlat = 0)
{
const double sincr = 2.0 * cos(th);
double cvalue1;
double svalue1;
if (fltlat == 0)
{
cvalue1 = 1.0;
svalue1 = 0.0;
}
else
{
cvalue1 = cos(-fltlat * th);
svalue1 = sin(-fltlat * th);
}
double cvalue2 = cos(-(fltlat + 1) * th);
double svalue2 = sin(-(fltlat + 1) * th);
double re = 0.0;
double im = 0.0;
while (fltlen > 0)
{
re += cvalue1 * flt[0];
im += svalue1 * flt[0];
flt++;
fltlen--;
double tmp = cvalue1;
cvalue1 = sincr * cvalue1 - cvalue2;
cvalue2 = tmp;
tmp = svalue1;
svalue1 = sincr * svalue1 - svalue2;
svalue2 = tmp;
}
re0 = re;
im0 = im;
}
/**
* Function calculates frequency response and group delay of the specified FIR
* filter at the specified circular frequency. The group delay is calculated
* by evaluating the filter's response at close side-band frequencies of "th".
*
* @param flt FIR filter's coefficients.
* @param fltlen Number of coefficients (taps) in the filter.
* @param th Circular frequency [0; pi].
* @param[out] re Resulting real part of the complex frequency response.
* @param[out] im Resulting imaginary part of the complex frequency response.
* @param[out] gd Resulting group delay at the specified frequency, in
* samples.
*/
inline void calcFIRFilterResponseAndGroupDelay(const double* const flt, const int fltlen, const double th, double& re, double& im, double& gd)
{
// Calculate response at "th".
calcFIRFilterResponse(flt, fltlen, th, re, im);
// Calculate response at close sideband frequencies.
const int Count = 2;
const double thd2 = 1e-9;
double ths[ Count ] = { th - thd2, th + thd2 };
if (ths[0] < 0.0) { ths[0] = 0.0; }
if (ths[1] > M_PI) { ths[1] = M_PI; }
double ph1[ Count ];
for (int i = 0; i < Count; ++i)
{
double re1;
double im1;
calcFIRFilterResponse(flt, fltlen, ths[i], re1, im1);
ph1[i] = atan2(im1, re1);
}
if (fabs(ph1[1] - ph1[0]) > M_PI)
{
if (ph1[1] > ph1[0]) { ph1[1] -= M_2PI; }
else { ph1[1] += M_2PI; }
}
const double thd = ths[1] - ths[0];
gd = (ph1[1] - ph1[0]) / -thd;
}
/**
* Function normalizes FIR filter so that its frequency response at DC is
* equal to DCGain.
*
* @param[in,out] p Filter coefficients.
* @param l Filter length.
* @param DCGain Filter's gain at DC (linear, non-decibel value).
* @param pstep "p" array step.
*/
inline void normalizeFIRFilter(double* const p, const int l, const double DCGain, const int pstep = 1)
{
R8BASSERT(l > 0);
R8BASSERT(pstep != 0);
double s = 0.0;
double* pp = p;
int i = l;
while (i > 0)
{
s += *pp;
pp += pstep;
i--;
}
s = DCGain / s;
pp = p;
i = l;
while (i > 0)
{
*pp *= s;
pp += pstep;
i--;
}
}
/**
* Function calculates coefficients used to calculate 3rd order spline
* (polynomial) on the equidistant lattice, using 8 points.
*
* @param[out] c Output coefficients buffer, length = 4.
* @param xm3 Point at x-3 position.
* @param xm2 Point at x-2 position.
* @param xm1 Point at x-1 position.
* @param x0 Point at x position.
* @param x1 Point at x+1 position.
* @param x2 Point at x+2 position.
* @param x3 Point at x+3 position.
* @param x4 Point at x+4 position.
*/
inline void calcSpline3p8Coeffs(double* c, const double xm3, const double xm2, const double xm1, const double x0, const double x1, const double x2,
const double x3, const double x4)
{
c[0] = x0;
c[1] = (61.0 * (x1 - xm1) + 16.0 * (xm2 - x2) + 3.0 * (x3 - xm3)) / 76.0;
c[2] = (106.0 * (xm1 + x1) + 10.0 * x3 + 6.0 * xm3 - 3.0 * x4 - 29.0 * (xm2 + x2) - 167.0 * x0) / 76.0;
c[3] = (91.0 * (x0 - x1) + 45.0 * (x2 - xm1) + 13.0 * (xm2 - x3) + 3.0 * (x4 - xm3)) / 76.0;
}
/**
* Function calculates coefficients used to calculate 2rd order spline
* (polynomial) on the equidistant lattice, using 8 points. This function is
* based on the calcSpline3Coeffs8() function, but without the 3rd order
* coefficient.
*
* @param[out] c Output coefficients buffer, length = 3.
* @param xm3 Point at x-3 position.
* @param xm2 Point at x-2 position.
* @param xm1 Point at x-1 position.
* @param x0 Point at x position.
* @param x1 Point at x+1 position.
* @param x2 Point at x+2 position.
* @param x3 Point at x+3 position.
* @param x4 Point at x+4 position.
*/
inline void calcSpline2p8Coeffs(double* c, const double xm3, const double xm2, const double xm1, const double x0, const double x1, const double x2,
const double x3, const double x4)
{
c[0] = x0;
c[1] = (61.0 * (x1 - xm1) + 16.0 * (xm2 - x2) + 3.0 * (x3 - xm3)) / 76.0;
c[2] = (106.0 * (xm1 + x1) + 10.0 * x3 + 6.0 * xm3 - 3.0 * x4 - 29.0 * (xm2 + x2) - 167.0 * x0) / 76.0;
}
/**
* Function calculates coefficients used to calculate 3rd order segment
* interpolation polynomial on the equidistant lattice, using 4 points.
*
* @param[out] c Output coefficients buffer, length = 4.
* @param[in] y Equidistant point values. Value at offset 1 corresponds to
* x=0 point.
*/
inline void calcInterpCoeffs3p4(double* const c, const double* const y)
{
c[0] = y[1];
c[1] = 0.5 * (y[2] - y[0]);
c[2] = y[0] - 2.5 * y[1] + y[2] + y[2] - 0.5 * y[3];
c[3] = 0.5 * (y[3] - y[0]) + 1.5 * (y[1] - y[2]);
}
/**
* Function calculates coefficients used to calculate 3rd order segment
* interpolation polynomial on the equidistant lattice, using 6 points.
*
* @param[out] c Output coefficients buffer, length = 4.
* @param[in] y Equidistant point values. Value at offset 2 corresponds to
* x=0 point.
*/
inline void calcInterpCoeffs3p6(double* const c, const double* const y)
{
c[0] = y[2];
c[1] = (11.0 * (y[3] - y[1]) + 2.0 * (y[0] - y[4])) / 14.0;
c[2] = (20.0 * (y[1] + y[3]) + 2.0 * y[5] - 4.0 * y[0] - 7.0 * y[4] - 31.0 * y[2]) / 14.0;
c[3] = (17.0 * (y[2] - y[3]) + 9.0 * (y[4] - y[1]) + 2.0 * (y[0] - y[5])) / 14.0;
}
/**
* Function calculates coefficients used to calculate 3rd order segment
* interpolation polynomial on the equidistant lattice, using 8 points.
*
* @param[out] c Output coefficients buffer, length = 4.
* @param[in] y Equidistant point values. Value at offset 3 corresponds to
* x=0 point.
*/
inline void calcInterpCoeffs3p8(double* const c, const double* const y)
{
c[0] = y[3];
c[1] = (61.0 * (y[4] - y[2]) + 16.0 * (y[1] - y[5]) + 3.0 * (y[6] - y[0])) / 76.0;
c[2] = (106.0 * (y[2] + y[4]) + 10.0 * y[6] + 6.0 * y[0] - 3.0 * y[7] - 29.0 * (y[1] + y[5]) - 167.0 * y[3]) / 76.0;
c[3] = (91.0 * (y[3] - y[4]) + 45.0 * (y[5] - y[2]) + 13.0 * (y[1] - y[6]) + 3.0 * (y[7] - y[0])) / 76.0;
}
/**
* Function calculates coefficients used to calculate 3rd order segment
* interpolation polynomial on the equidistant lattice, using 8 points.
*
* @param[out] c Output coefficients buffer, length = 3.
* @param[in] y Equidistant point values. Value at offset 3 corresponds to
* x=0 point.
*/
inline void calcInterpCoeffs2p8(double* const c, const double* const y)
{
c[0] = y[3];
c[1] = (61.0 * (y[4] - y[2]) + 16.0 * (y[1] - y[5]) + 3.0 * (y[6] - y[0])) / 76.0;
c[2] = (106.0 * (y[2] + y[4]) + 10.0 * y[6] + 6.0 * y[0] - 3.0 * y[7] - 29.0 * (y[1] + y[5]) - 167.0 * y[3]) / 76.0;
}
#if !defined( min )
/**
* @param v1 Value 1.
* @param v2 Value 2.
* @return The minimum of 2 values.
*/
template <class T>
T min(const T& v1, const T& v2) { return (v1 < v2 ? v1 : v2); }
#endif // min
#if !defined( max )
/**
* @param v1 Value 1.
* @param v2 Value 2.
* @return The maximum of 2 values.
*/
template <class T>
T max(const T& v1, const T& v2) { return (v1 > v2 ? v1 : v2); }
#endif // max
/**
* Function "clamps" (clips) the specified value so that it is not lesser than
* "minv", and not greater than "maxv".
*
* @param Value Value to clamp.
* @param minv Minimal allowed value.
* @param maxv Maximal allowed value.
* @return "Clamped" value.
*/
inline double clampr(const double Value, const double minv, const double maxv)
{
if (Value < minv) { return (minv); }
if (Value > maxv) { return (maxv); }
return (Value);
}
/**
* @param x Value to square.
* @return Squared value of the argument.
*/
inline double sqr(const double x) { return (x * x); }
/**
* @param v Input value.
* @param p Power factor.
* @return Returns pow() function's value with input value's sign check.
*/
inline double pows(const double v, const double p) { return (v < 0.0 ? -pow(-v, p) : pow(v, p)); }
/**
* @param v Input value.
* @return Calculated single-argument Gaussian function of the input value.
*/
inline double gauss(const double v) { return (exp(-(v * v))); }
/**
* @param v Input value.
* @return Calculated inverse hyperbolic sine of the input value.
*/
inline double asinh(const double v) { return (log(v + sqrt(v * v + 1.0))); }
/**
* @param x Input value.
* @return Calculated zero-th order modified Bessel function of the first kind
* of the input value. Approximate value.
*/
inline double besselI0(const double x)
{
const double ax = fabs(x);
double y;
if (ax < 3.75)
{
y = x / 3.75;
y *= y;
return (1.0 + y * (3.5156229 + y * (3.0899424 + y * (1.2067492 + y * (0.2659732 + y * (0.360768e-1 + y * 0.45813e-2))))));
}
y = 3.75 / ax;
return (exp(ax) / sqrt(ax) * (0.39894228 + y * (0.1328592e-1 + y * (
0.225319e-2 + y * (
-0.157565e-2 + y * (
0.916281e-2 + y * (
-0.2057706e-1 + y * (0.2635537e-1 + y * (-0.1647633e-1 + y * 0.392377e-2)))))))));
}
} // namespace r8b