CButterworthLowPassFilter2 Class Reference

2nd order Butterworth low-pass filter implemented in direct form I. More...

Classes
struct	SCoefficients
struct	SFilterState

Public Member Functions
	CButterworthLowPassFilter2 ()=default
	Construct a pass-through placeholder filter.
	CButterworthLowPassFilter2 (float fCutoffFrequencyHz, float fSamplingFrequencyHz)
	Construct and configure the filter.
float	Get () const
	Get the latest filtered value.
void	Add (float fNewValue)
	Feed one new sample into the filter.
void	Reset ()
	Reset the filter state.
void	Configure (float fCutoffFrequencyHz, float fSamplingFrequencyHz)
	Reconfigure the filter coefficients.

Static Private Member Functions
static SCoefficients	computeCoefficients (float fCutoffFrequencyHz, float fSamplingFrequencyHz)
	Compute normalized IIR coefficients for the configured Butterworth filter.
static SFilterState	initializeStateWithoutTransient (float fInputValue, const SCoefficients &korCoefficients)
	Initialize the direct-form-I state to the steady state for a constant input.

Private Attributes
SCoefficients	oCoefficients_ {}
	Filter coefficients.
SFilterState	oState_ {}
	State of the direct-form-I recurrence.
float	fFilteredSignal_ { 0.0F }
	Latest filter output.
bool	bIsInitialized_ { false }
	True once the internal state has been initialized from an input sample.

Detailed Description

2nd order Butterworth low-pass filter implemented in direct form I.

Constructor & Destructor Documentation

CButterworthLowPassFilter2() [1/2]

CButterworthLowPassFilter2::CButterworthLowPassFilter2 ( )

default

Construct a pass-through placeholder filter.

The default-constructed filter uses unity gain with no filtering until Configure() is called or the configured constructor is used.

CButterworthLowPassFilter2() [2/2]

CButterworthLowPassFilter2::CButterworthLowPassFilter2	(	float	fCutoffFrequencyHz,
		float	fSamplingFrequencyHz )

Construct and configure the filter.

Function design

Normal case

The function SHALL compute the normalized IIR coefficients for a 2nd order Butterworth low-pass filter. For the formulae see the helper function documentation.

Argument checks

1. The function SHALL assert that the provided cutoff frequency is finite and positive.
2. The function SHALL assert that the provided sampling frequency is finite and positive.
3. The function SHALL assert that the provided cutoff frequency is less than half the sampling frequency (Nyquist frequency).

Parameters

fCutoffFrequencyHz	Cutoff frequency in [Hz]
fSamplingFrequencyHz	Sampling frequency in [Hz]

Member Function Documentation

Add()

void CButterworthLowPassFilter2::Add

(

float

fNewValue

)

Feed one new sample into the filter.

Parameters

fNewValue

New input sample.

Function design

Case 1: Filter is not initialized

1. IF the filter is not initialized, THEN the function SHALL initialize the filter.
2. After initialization, the function SHALL update the pre-computed filtered output.
3. After updating the pre-computed filtered output, the function SHALL update the filter's state.

For the filter initialization procedure see the helper function documentation.

Case 2: Filter is initialized

1. WHEN the filter is initialized, THEN the function SHALL update the pre-computed filtered output.
2. After updating the pre-computed filtered output, the function SHALL update the filter's state.

Computation of the filtered output

The latest filtered output is given by the direct-form-I recurrence

\[y[k] = b_0 x[k] + b_1 x[k - 1] + b_2 x[k - 2] - a_1 y[k - 1] - a_2 y[k - 2] \]

where \( x[k] = \) fNewValue, and the coefficients are given by the current filter configuration.

computeCoefficients()

SCoefficients CButterworthLowPassFilter2::computeCoefficients ( float fCutoffFrequencyHz, float fSamplingFrequencyHz )

staticprivate

Compute normalized IIR coefficients for the configured Butterworth filter.

Function design

Normal case

The function SHALL compute coefficients for the direct-form-I recurrence

\[y[k] = b_0 x[k] + b_1 x[k - 1] + b_2 x[k - 2] - a_1 y[k - 1] - a_2 y[k - 2] \]

where \( f_c = \) fCutoffFrequencyHz, \( f_s = \) fSamplingFrequencyHz.

The function SHALL return the normalized Butterworth coefficients

\[b_0 = \Omega^2 / c, \; b_1 = 2 b_0, \; b_2 = b_0, \]

\[a_1 = 2 (\Omega^2 - 1) / c, \; a_2 = (1 - \sqrt{2} \Omega + \Omega^2) / c. \]

Herein \(\Omega = \tan\left(\frac{\pi f_c}{f_s}\right)\), and \(c = 1 + \sqrt{2} \Omega + \Omega^2\).

Argument checks

1. The function SHALL NOT perform argument checks.

Parameters

fCutoffFrequencyHz	Cutoff frequency in [Hz]
fSamplingFrequencyHz	Sampling frequency in [Hz]

Returns

Coefficients of the direct-form-I recurrence.

Configure()

void CButterworthLowPassFilter2::Configure	(	float	fCutoffFrequencyHz,
		float	fSamplingFrequencyHz )

Reconfigure the filter coefficients.

Function design

Normal case

The function SHALL compute the normalized IIR coefficients for a 2nd order Butterworth low-pass filter. For the formulae see the helper function documentation.

Argument checks

1. The function SHALL assert that the provided cutoff frequency is finite and positive.
2. The function SHALL assert that the provided sampling frequency is finite and positive.
3. The function SHALL assert that the provided cutoff frequency is less than half the sampling frequency (Nyquist frequency).

Parameters

fCutoffFrequencyHz	Cutoff frequency in [Hz]
fSamplingFrequencyHz	Sampling frequency in [Hz]

Get()

float CButterworthLowPassFilter2::Get

(

)

const

Get the latest filtered value.

Returns

Latest filter output. Returns 0.0F while the filter is uninitialized, for example right after default construction or Reset().

initializeStateWithoutTransient()

SFilterState CButterworthLowPassFilter2::initializeStateWithoutTransient ( float fInputValue, const SCoefficients & korCoefficients )

staticprivate

Initialize the direct-form-I state to the steady state for a constant input.

Function design

1. The function SHALL set the states SFilterState::fInput1_ and SFilterState::fInput2_ to the provided input value.
2. The function SHALL set the states SFilterState::fOutput1_ and SFilterState::fOutput2_ to the corresponding steady-state output value.

The steady-state output value is given by

\[y_\infty = \frac{b_0 + b_1 + b_2}{1 + a_1 + a_2} x_\infty \]

where \( x_\infty = \) fInputValue.

Parameters

fInputValue	Constant input value to initialize the filter from.
korCoefficients	Filter coefficients.

Reset()

void CButterworthLowPassFilter2::Reset

(

)

Reset the filter state.

Function design

1. The function SHALL transition the filter to an uninitialized state.
2. The function SHALL NOT modify the filter coefficients.
3. The function SHALL set the pre-computed filter output to zero.

Member Data Documentation

bIsInitialized_

bool CButterworthLowPassFilter2::bIsInitialized_ { false }

private

True once the internal state has been initialized from an input sample.

fFilteredSignal_

float CButterworthLowPassFilter2::fFilteredSignal_ { 0.0F }

private

Latest filter output.

oCoefficients_

SCoefficients CButterworthLowPassFilter2::oCoefficients_ {}

private

Filter coefficients.

oState_

SFilterState CButterworthLowPassFilter2::oState_ {}

private

State of the direct-form-I recurrence.

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

• CButterworthLowPassFilter2.h