Struct FFTEnhanced 

pub struct FFTEnhanced;

Enhanced Fast Fourier Transform (FFT) implementation supporting arbitrary-sized inputs

This module extends the FFT functionality to support:

1. Non-power-of-2 input sizes
2. Additional window functions
3. Optimized implementation for real-valued inputs
4. Implementation of the Stockwell transform (S-transform)

FFTEnhanced provides extended FFT functionality

Implementations

impl FFTEnhanced

pub fn fft_any_size<T>(x: &Array<T>) -> Result<Array<Complex<T>>>

where T: Float + Clone + Debug + Into<f64> + From<f64>,

Compute the FFT of an array with any size (not limited to powers of 2)

This function implements the Chirp-Z transform to handle arbitrary sizes

Parameters

• x - The input array

Returns

• The FFT of the input array

pub fn ifft_any_size<T>(x: &Array<Complex<T>>) -> Result<Array<Complex<T>>>

where T: Float + Clone + Debug + Into<f64> + From<f64>,

Compute the inverse FFT of a complex array with any size

Parameters

• x - The input complex array

Returns

• The inverse FFT of the input array

pub fn window<T>(window_type: &str, n: usize) -> Result<Array<T>>

where T: Float + Clone + Debug + From<f64>,

Generate a window function with any size

Parameters

• window_type - The type of window function
• n - The size of the window

Returns

• The window function as an array

pub fn apply_window<T>(x: &Array<T>, window_type: &str) -> Result<Array<T>>

where T: Float + Clone + Debug + From<f64>,

Apply a window function to a signal

Parameters

• x - The input signal
• window_type - The type of window function

Returns

• The windowed signal

pub fn window_energy_concentration<T>( window_types: &[&str], n: usize, ) -> Result<Vec<(String, T)>>

where T: Float + Clone + Debug + From<f64> + Into<f64>,

Calculate the energy concentration of different window functions in frequency domain

Parameters

• window_types - List of window function types to compare
• n - The size of the window

Returns

• A map of window type to its energy concentration in dB

pub fn stockwell_transform<T>( x: &Array<T>, min_freq: Option<usize>, max_freq: Option<usize>, ) -> Result<Array<Complex<T>>>

where T: Float + Clone + Debug + Into<f64> + From<f64>,

Compute the Stockwell Transform (S-Transform) of a signal

The S-transform is a time-frequency spectral localization method similar to the short-time Fourier transform, but with a Gaussian window whose width scales with frequency.

Parameters

• x - The input signal
• min_freq - Minimum frequency index to compute (optional)
• max_freq - Maximum frequency index to compute (optional)

Returns

• The S-transform of the input signal (2D array)

pub fn real_fft_optimized<T>(x: &Array<T>) -> Result<Array<Complex<T>>>

where T: Float + Clone + Debug + Into<f64> + From<f64>,

Optimized FFT for real-valued inputs (Hermitian optimized FFT)

This implementation takes advantage of the conjugate symmetry of the FFT of real-valued signals. For now, it uses the standard FFT approach to ensure correctness, with potential optimizations to be added later.

Parameters

• x - The real-valued input array

Returns

• The FFT of the input array