Struct Symlet 

pub struct Symlet { /* private fields */ }

Symlet wavelet family

Symlets are a family of wavelets that are nearly symmetrical, designed by Ingrid Daubechies as modifications of the Daubechies wavelets with increased symmetry. They have the same number of vanishing moments as Daubechies wavelets but with better symmetry properties.

Mathematical Foundation

Symlets were designed by Ingrid Daubechies to be as symmetric as possible while maintaining the same orthogonality and compact support properties as standard Daubechies wavelets. They minimize the phase nonlinearity of the transfer function.

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(‘symN’).dec_lo)
• Daubechies, I. (1992). “Ten Lectures on Wavelets”, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, SIAM, Philadelphia, Chapter 8 (Symmetry for Compactly Supported Wavelet Bases).
• Percival, D.B. and Walden, A.T. (2000). “Wavelet Methods for Time Series Analysis”, Cambridge University Press, Table 114.

Properties

All coefficients satisfy:

• Σh[n] = √2 (DC gain normalization)
• Σh[n]² = 1 (energy normalization)
• Near-symmetry (improved phase linearity compared to Daubechies)

Supported Orders

This implementation includes SYM2-SYM10.

Implementations

impl Symlet

pub fn new(order: usize) -> Self

Create a Symlet wavelet of given order

pub fn sym2() -> Self

pub fn sym3() -> Self

pub fn sym4() -> Self

pub fn sym5() -> Self

pub fn sym6() -> Self

pub fn sym7() -> Self

pub fn sym8() -> Self

pub fn sym9() -> Self

pub fn sym10() -> Self

Trait Implementations

impl Clone for Symlet

fn clone(&self) -> Symlet

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Symlet

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

Formats the value using the given formatter.

impl Wavelet for Symlet

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