Filter Design

Detailed Description

Filter design tools.

Collaboration diagram for Filter Design:

Functions
template<uint8_t N, class T = float>
SOSCoefficients< T,(N+1)/2 >	butter_coeff (double f_n, bool normalize=true)
	Compute Butterworth filter coefficients. More...
template<uint8_t N, class T = float, class Implementation = BiQuadFilterDF1<T>>
SOSFilter< T,(N+1)/2, Implementation >	butter (double f_n, bool normalize=true)
	Create a Butterworth filter, implemented as Second Order Sections (SOS) filter. More...
template<class T = float>
FIRFilter< 3, T >	simpleNotchFIR (double f_n)
	Create a very simple second-order FIR notch filter. More...
template<class T , size_t N>
TransferFunction< N *2+1, N *2+1, T >	sos2tf (const SOSCoefficients< T, N > &sos)
	Convert Second Order Section (SOS) coefficients to an equivalent tranfer function representation. More...

Function Documentation

butter_coeff()

SOSCoefficients< T,(N+1)/2 > butter_coeff	(	double	f_n,
		bool	normalize = true
	)

Compute Butterworth filter coefficients.

Template Parameters

N	Order of the filter.

Parameters

f_n	Normalized cut-off frequency in half-cycles per sample. \( f_n = \frac{2 f_c}{f_s} \in \left[0, 1\right] \), where \( f_s \) is the sample frequency in \( \text{Hz} \), and \( f_c \) is the cut-off frequency in \( \text{Hz} \).
normalize	If true, normalize all coefficients such that \( a_0 = 1 \).

Template Parameters

T	The type of the coefficients.

See also

https://tttapa.github.io/Pages/Mathematics/Systems-and-Control-Theory/Digital-filters/Discretization/Discretization-of-a-fourth-order-Butterworth-filter.html#discretization-using-second-order-sections-sos

Definition at line 26 of file Butterworth.hpp.

butter()

SOSFilter< T,(N+1)/2, Implementation > butter	(	double	f_n,
		bool	normalize = true
	)

Create a Butterworth filter, implemented as Second Order Sections (SOS) filter.

Template Parameters

N	Order of the filter.

Parameters

f_n	Normalized cut-off frequency in half-cycles per sample. \( f_n = \frac{2 f_c}{f_s} \in \left[0, 1\right] \), where \( f_s \) is the sample frequency in \( \text{Hz} \), and \( f_c \) is the cut-off frequency in \( \text{Hz} \).

Template Parameters

T	The type of filter values and coefficients.

Parameters

normalize

If true, normalize all coefficients such that \( a_0 = 1 \).

Template Parameters

Implementation

The BiQuad implementation to use.

See also

https://tttapa.github.io/Pages/Mathematics/Systems-and-Control-Theory/Digital-filters/Discretization/Discretization-of-a-fourth-order-Butterworth-filter.html#discretization-using-second-order-sections-sos

Definition at line 109 of file Butterworth.hpp.

simpleNotchFIR()

FIRFilter< 3, T > simpleNotchFIR

(

double

f_n

)

Create a very simple second-order FIR notch filter.

\[ H(z) = \frac{z^2 - 2\cos\left(\omega_{c,d}\right)z + 1} {2 - 2\cos\left(\omega_{c,d}\right)} \]

where \( \omega_{c,d} = \pi f_n = 2\pi \frac{f_c}{f_n} \)

See also

https://tttapa.github.io/Pages/Mathematics/Systems-and-Control-Theory/Digital-filters/FIR-Notch.html

Parameters

f_n	Normalized notch frequency in half-cycles per sample. \( f_n = \frac{2 f_c}{f_s} \in \left[0, 1\right] \), where \( f_s \) is the sample frequency in \( \text{Hz} \), and \( f_c \) is the analog notch frequency in \( \text{Hz} \).

Examples

FIRNotch.ino.

Definition at line 27 of file Notch.hpp.

sos2tf()

TransferFunction< N *2+1, N *2+1, T > sos2tf

(

const SOSCoefficients< T, N > &

sos

)

Convert Second Order Section (SOS) coefficients to an equivalent tranfer function representation.

Definition at line 76 of file SOSFilter.hpp.