Cite D17 book

Author: blegat

docs/src/index.md

@@ -3,12 +3,18 @@
 [TrigPolys.jl](https://github.com/yuanchenyang/TrigPolys.jl) is a package for
 fast manipulation of trigonometric polynomials.
 
-
-A trignometric polynomial is defined on $$x \in [0,2\pi)$$ by
-
+A *Hermitian trigonometric polynomial*
+can be viewed as a polynomial `R(z) \\in \\mathbb{C}[z]` [D17, (1.7)]:
 ```math
-p(x) = a_0 + \sum_{k=1}^n a_k \cos(kx) + a_{-k} \sin(kx)
+R(z) = a_0 + \\frac{1}{2} \\sum_{k=1}^n a_k z^{-k} + a_k^* z^k
 ```
+On the unit circle, this becomes [D17, (1.8)]:
+```math
+R(\\omega) = a_0 + \\sum_{k=1}^n a_{c,k} \\cos(k\\omega) + a_{s,k} \\sin(k\\omega)
+```
+where ``a_{c,k}`` is `ac[k]` and ``a_{s,k}`` is `as[k]`.
+
+[D17] ...
 
 The polynomial $$p(x)$$ can be represented either by $$2n+1$$ coefficients
 $$a_k$$ or by evaluations at $$2n+1$$ distinct points in the interval

src/TrigPolys.jl

@@ -12,7 +12,14 @@ export pad_to, truncate
         as::VT   # sin coefficients
     end
 
-Represents a trigonometric polynomial by its coefficients.
+Represents a *Hermitian trigonometric polynomial* by its coefficients.
+The vectors `ac` and `as` should have the same length, that we call `n` in this
+docstring.
+This represent the following function
+```julia
+R(ω) = a0 + sum(ac[k] * cos(k * ω) + as[k] * sin(k * ω) for k in 1:n)
+```
+which is a polynomial in the variable `x = cos(ω)`.
 """
 struct TrigPoly{T<:AbstractFloat, VT<:AbstractVector{T}}
     a0::T    # Constant coefficient