Let $G$ be a deterministic polynomial-time function from $\mathbb{N}^{{<\omega}}$ to $\mathbb{N}^{{<\omega}}$ with stretch function $l:\mathbb{N}\rightarrow\mathbb{N}$, so that if $x$ has length $n$ then $G(x)$ has length $l(n)$. Then let $G_{n}$ be the distribution on strings of length $l(n)$ defined by the output of $G$ on a randomly selected string of length $n$ selected by the uniform distribution.

Then we say $G$ is pseudorandom generator if $\{G_{n}\}_{{n\in\mathbb{N}}}$ is pseudorandom.

In effect, $G$ translates a random input of length $n$ to a pseudorandom output of length $l(n)$. Assuming $l(n)>n$, this expands a random sequence (and can be applied multiple times, since $G_{n}$ can be replaced by the distribution of $G(G(x))$).