Convolution with additional cosine

Question

I want to perform a convolution, but as a complication there is a cosine of the angle between any pair of vectors in the expression:

\begin{equation} f(\theta^{\prime}) = \int d\theta G(|\theta^{\prime}-\theta|)H(\theta)\cos(2\Theta(\theta^{\prime}-\theta)) \end{equation}

where $\Theta$ is an expression for the angle, and $G$ and $H$ are just some functions.

How can I efficiently compute this integral numerically?

Answer 1

Can you collapse together $\Theta$ and $G$?

$$ X(\theta) = G(|\theta|)cos(\Theta(\theta)) $$

Then just find $X * H$