Struct Daubechies 

pub struct Daubechies { /* private fields */ }

Daubechies wavelets - a family of orthogonal wavelets

Daubechies wavelets are a family of orthogonal wavelets with compact support. They are characterized by a maximal number of vanishing moments for a given support width.

Mathematical Foundation

Daubechies wavelets were developed by Ingrid Daubechies in 1988. They are constructed to have the maximum number of vanishing moments for a given filter length, making them optimal for representing polynomial signals.

Coefficient Sources

All coefficients are canonical PyWavelets values, ensuring machine-precision accuracy (~2e-16 sum error) and cross-library compatibility.

References:

• PyWavelets - Primary source for canonical coefficients (pywt.Wavelet(‘dbN’).dec_lo)
• Daubechies, I. (1992). “Ten Lectures on Wavelets”, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, SIAM, Philadelphia.

Properties

All coefficients satisfy:

• sum_n(h[n]) = √2 (DC gain normalization)
• sum_n(h[n]²) = 1 (energy normalization)
• sum_n(h[n] * h[n+2k]) = 0 for k ≠ 0 (orthogonality)

Supported Orders

This implementation includes DB2, DB4, DB6, DB8, and DB10.

Implementations

impl Daubechies

pub fn new(wavelet_type: DaubechiesType) -> Self

Create a new Daubechies wavelet of the specified type

pub fn db2() -> Self

Create a Daubechies 2 wavelet (4 coefficients)

pub fn db4() -> Self

Create a Daubechies 4 wavelet (8 coefficients)

pub fn db6() -> Self

Create a Daubechies 6 wavelet (12 coefficients)

pub fn db8() -> Self

Create a Daubechies 8 wavelet (16 coefficients)

pub fn db10() -> Self

Create a Daubechies 10 wavelet (20 coefficients)

pub fn wavelet_type(&self) -> DaubechiesType

Get the wavelet type

Trait Implementations

impl Clone for Daubechies

fn clone(&self) -> Daubechies

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Daubechies

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Wavelet for Daubechies

fn as_any(&self) -> &dyn Any

Allow downcasting to concrete types

fn name(&self) -> &str

Get the name of the wavelet

fn vanishing_moments(&self) -> usize

Get the number of vanishing moments

fn support_width(&self) -> usize

Get the support width (filter length)

fn low_pass_decomposition(&self) -> &[f64]

Get the low-pass decomposition filter coefficients

fn high_pass_decomposition(&self) -> &[f64]

Get the high-pass decomposition filter coefficients

fn low_pass_reconstruction(&self) -> &[f64]

Get the low-pass reconstruction filter coefficients

fn high_pass_reconstruction(&self) -> &[f64]

Get the high-pass reconstruction filter coefficients

fn is_orthogonal(&self) -> bool

Check if the wavelet is orthogonal

fn is_biorthogonal(&self) -> bool

Check if the wavelet is biorthogonal