  Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have
a natural matricial characterization. Consequently, these operators are
difficult to study numerically. In this note we provide criteria for a matrix
with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz
operator having an analytic symbol. This test is constructive and we illustrate
it with several examples. As a byproduct, we also prove that every complex
symmetric operator on a Hilbert space of dimension $\leq 3$ is unitarily
equivalent to a direct sum of truncated Toeplitz operators.
