$\DeclareMathOperator\Cl{Cl}$Let $V$ be a real vector space of dimension $p+q$. Let $Q$ be a non-degenerate quadratic form on $V$ of signature $(p,q)$ where $p$ is the number of positive eigenvalues, and $q$ is the number of negative ones.

The Clifford algebra $\Cl(p,q)$ is the quotient of the tensor algebra $\oplus_{k=0}^\infty V^{\otimes k}$ modulo the two sided ideal generated by elements $v^2-Q(v)$ for any $v\in V$.

I am looking for a classification up to an isomorphism of $\Cl(p,q)$. The cases $p=1,q=3$ and $p=3,q=1$ are of special interest. A reference would be helpful.