Enum FourierConvention 

pub enum FourierConvention {
    NonUnitaryAngular,
    UnitaryAngular,
    Ordinary,
}

Normalisation convention of the Fourier transform pair.

See the module documentation for the defining integrals.

use symplex::prelude::*;
use symplex::fourier_transform::FourierConvention;

let ctx = Context::new();
let t = ctx.symbol("t");
let w = ctx.symbol("w");
let f = (-t.abs()).exp();
// Non-unitary angular (default): 2/(1 + w²)
let fa = f.fourier_transform(&t, &w).unwrap();
assert_eq!(format!("{fa}"), "2/(w^2 + 1)");
// Unitary angular: √(2/π)/(1 + w²)
let fu = f
    .fourier_transform_with(&t, &w, FourierConvention::UnitaryAngular)
    .unwrap();
let ratio = (&fu / &fa).subs(&w, &ctx.int(1)).eval_f64().unwrap();
assert!((ratio - 1.0 / (2.0 * std::f64::consts::PI).sqrt()).abs() < 1e-12);

Variants

NonUnitaryAngular

F(ω) = ∫ f(t) e^{−iωt} dt, f(t) = (1/2π) ∫ F(ω) e^{iωt} dω. The convention of most engineering and physics texts; the default.

UnitaryAngular

F(ω) = (1/√(2π)) ∫ f(t) e^{−iωt} dt with the symmetric inverse.

Ordinary

F(ν) = ∫ f(t) e^{−2πiνt} dt, f(t) = ∫ F(ν) e^{2πiνt} dν (ordinary frequency ν in hertz).

Trait Implementations

impl Clone for FourierConvention

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for FourierConvention

impl Debug for FourierConvention

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

Formats the value using the given formatter.

impl Default for FourierConvention

fn default() -> Self

Returns the “default value” for a type.

impl Eq for FourierConvention

impl Hash for FourierConvention

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl PartialEq for FourierConvention

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for FourierConvention