The function ab2phth transforms an input matrix
a of size $T \times p$ containing the sine and cosine
coefficients in the real Fourier series representation,
to the $T \times p$ output matrix phi according to
$\phi_{n,j} = a_{1,j} + \sum_{k=1}^{\left\lfloor T/2 \right\rfloor }(a_{2k,j} \cos(2\pi kn/T) + a_{2k+1,j} \sin(2\pi kn/T))$
for $n = 1, \ldots, T$ and $j = 1, \ldots, p$.
The inverse transformation is implemented in phth2ab function.
Usage
ab2phth(a)
phth2ab(phi)
Arguments
a
matrix of $a_{n,j}$ coefficients (size of $T \times p$).
phi
matrix of $\phi_{n,j}$ coefficients (size of $T \times p$).
Value
martix phi or a for ab2phth or phth2ab, respectively.