Module transforms 

Integral & discrete transforms (Gap analysis §3.4) — Fourier, Laplace, Z.

• fourier — discrete Fourier transform / inverse over complex samples. The forward dft is the f64-exact CPU reference; dft_accelerated is an opt-in f32 fast path that uses the WGSL forge FFT when an accelerator is present (for spectral callers that accept f32 precision).
• laplace — numerical Laplace transform by quadrature (general), plus a symbolic table transform over the CAS Expr for the cases the current expression algebra can represent (constants, powers tⁿ, and their linear combinations) — fail-closed on the rest.
• ztransform — Z-transform of a finite sequence + the standard closed forms.

Complex numbers are (re, im) tuples (Cplx). Fail-closed throughout.

Re-exports

pub use fourier::dft;

pub use fourier::dft_accelerated;

pub use fourier::idft;

pub use fourier::Cplx;

pub use laplace::laplace_numeric;

pub use laplace::laplace_table;

pub use laplace::LaplaceError;

pub use ztransform::geometric_z;

pub use ztransform::unit_step_z;

pub use ztransform::z_transform_finite;

Modules

fourier

Discrete Fourier transform and its inverse over complex samples.

laplace

Laplace transform L{f}(s) = ∫₀^∞ e^{−st} f(t) dt.

ztransform

Z-transform X(z) = Σ_{n≥0} x[n] z^{−n} of a finite causal sequence, evaluated at a complex z, plus the standard closed forms for the unit step and the geometric sequence.