What is an "innovation filter"?
An innovations filter of a WSS process $X(t)$ is a causal and stable minimum phase filter that can be used to generate $X(t)$ from a white noise input $N(t)$:

$$X(t)=\int_0^{\infty}h(\tau)N(t-\tau)d\tau\tag{1}$$

where $h(t)$ is the impulse response of the innovations filter.

The (causal and stable) inverse filter of $h(t)$ is called the whitening filter of $X(t)$. Its response to the input $X(t)$ is white noise $N(t)$.

A process that can be represented by $(1)$ is called a regular process. Note that its power spectrum is given by

$$S(\omega)=|H(\omega)|^2\tag{2}$$

where $H(\omega)$ is the Fourier transform of the impulse response $h(t)$ of the innovations filter (assuming that $E\{N(t)N(t+\tau\}=c\delta(\tau)$ with $c=1$). The requirement of causality of the innovations filter implies that the power spectrum $S(\omega)$ of $X(t)$ satisfies the Paley-Wiener condition

$$\int_{-\infty}^{\infty}\frac{|\log S(\omega)|}{1+\omega^2}d\omega\lt\infty\tag{3}$$

This implies that $S(\omega)$ cannot contain spectral lines, and it cannot be band-limited. Unlike a singular process (consisting of spectral lines), a regular process cannot be parameterized by a finite set of random variables and it is not predictable, i.e., it is not completely determined in terms of its past.

Reference:
Probability, Random Variables, and Stochastic Processes, A.Papoulis, Athanasios 1965. McGraw-Hill.