EMA< K, input_t, state_t > Class Template Reference

#include <AH/Filters/EMA.hpp>

Detailed Description

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>
class AH::EMA< K, input_t, state_t >

Exponential moving average filter.

Fast integer EMA implementation where the weight factor is a power of two.

Difference equation: $y[n]=\alpha ·x[n]+(1-\alpha )·y[n-1]$ where $\alpha ={\left(\frac{1}{2}\right)}^K$, $x$ is the input sequence, and $y$ is the output sequence.

An in-depth explanation of the EMA filter

Template Parameters

K	The amount of bits to shift by. This determines the location of the pole in the EMA transfer function, and therefore the cut-off frequency. The higher this number, the more filtering takes place. The pole location is $1-2^{-K}$.
input_t	The integer type to use for the input and output of the filter. Can be signed or unsigned.
state_t	The unsigned integer type to use for the internal state of the filter. A fixed-point representation with $K$ fractional bits is used, so this type should be at least $M+K$ bits wide, where $M$ is the maximum number of bits of the input.

Some examples of different combinations of template parameters:

1. Filtering the result of analogRead: analogRead returns an integer between 0 and 1023, which can be represented using 10 bits, so $M=10$. If input_t and output_t are both uint16_t, the maximum shift factor K is $16-M=6$. If state_t is increased to uint32_t, the maximum shift factor K is $32-M=22$.
2. Filtering a signed integer between -32768 and 32767: this can be represented using a 16-bit signed integer, so input_t is int16_t, and $M=16$. (2¹⁵ = 32768) Let's say the shift factor K is 1, then the minimum width of state_t should be $M+K=17$ bits, so uint32_t would be a sensible choice.

Definition at line 59 of file EMA.hpp.

Collaboration diagram for EMA< K, input_t, state_t >:

Public Member Functions
	EMA (input_t initial=input_t{0})
	Constructor: initialize filter to zero or optional given value.
void	reset (input_t value=input_t(0))
	Reset the filter to the given value.
input_t	filter (input_t input)
	Filter the input: Given $x[n]$, calculate $y[n]$.
input_t	operator() (input_t input)
	Filter the input: Given $x[n]$, calculate $y[n]$.

Static Public Member Functions
template<class T >
static constexpr bool	supports_range (T min, T max)
	Verify the input range to make sure it's compatible with the shift factor and the width of the state type.

Static Public Attributes
static constexpr state_t	max_state = std::numeric_limits<state_t>::max()
static constexpr state_t	half_state = max_state / 2 + 1
static constexpr state_t	zero = std::is_unsigned<input_t>::value ? state_t{0} : half_state
static constexpr state_t	half = K > 0 ? state_t{1} << (K - 1) : state_t{0}

Private Attributes
state_t	state

Constructor & Destructor Documentation

EMA()

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

EMA ( input_t initial = input_t{0} )

inline

Constructor: initialize filter to zero or optional given value.

Definition at line 62 of file EMA.hpp.

Member Function Documentation

reset()

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

void reset ( input_t value = input_t(0) )

inline

Reset the filter to the given value.

Parameters

value

The value to reset the filter state to.

Definition at line 70 of file EMA.hpp.

filter()

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

input_t filter ( input_t input )

inline

Filter the input: Given $x[n]$, calculate $y[n]$.

Parameters

input

The new raw input value.

Returns

The new filtered output value.

Definition at line 82 of file EMA.hpp.

operator()()

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

input_t operator() ( input_t input )

inline

Filter the input: Given $x[n]$, calculate $y[n]$.

Parameters

input

The new raw input value.

Returns

The new filtered output value.

Definition at line 91 of file EMA.hpp.

supports_range()

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

template<class T >

static constexpr bool supports_range ( T min, T max )

inlinestaticconstexpr

Verify the input range to make sure it's compatible with the shift factor and the width of the state type.

Examples:

EMA<5, int_fast16_t, uint_fast16_t> filter;
static_assert(filter.supports_range(-1024, 1023),
              "use a wider state or input type, or a smaller shift factor");

EMA<5, uint_fast16_t, uint_fast16_t> filter;
static_assert(filter.supports_range(0u, 2047u),
              "use a wider state or input type, or a smaller shift factor");

Definition at line 122 of file EMA.hpp.

Member Data Documentation

max_state

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

constexpr state_t max_state = std::numeric_limits<state_t>::max()

staticconstexpr

Definition at line 96 of file EMA.hpp.

half_state

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

constexpr state_t half_state = max_state / 2 + 1

static

Definition at line 97 of file EMA.hpp.

zero

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

constexpr state_t zero = std::is_unsigned<input_t>::value ? state_t{0} : half_state

static

Definition at line 98 of file EMA.hpp.

half

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

constexpr state_t half = K > 0 ? state_t{1} << (K - 1) : state_t{0}

static

Definition at line 99 of file EMA.hpp.

state

template<uint8_t K, class input_t = uint_fast16_t, class state_t = typename std::make_unsigned<input_t>::type>

state_t state

private

Definition at line 134 of file EMA.hpp.

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The documentation for this class was generated from the following file:

• EMA.hpp