The input to the Wiener filter is assumed to be a signal, , corrupted by additive noise, .

Our approach here is to develop a method flexible enough to allow for all sources of nonlinearity, including additive noise.

This method is optimal when a known signal is to be detected among an additive white Gaussian noise.

For example, the Wiener filter is suitable for additive Gaussian noise.

An alternative way of thinking of location families is through the concept of additive noise.

In the noisy model, an additional term, , representing additive noise, is included.

For example in wireless communications the channel is often modelled by a random attenuation (known as fading) of the transmitted signal, followed by additive noise.

This form of noise is called additive noise, with the understanding that the noise can be negative or positive at different instants of time.

Our observed signal consists of the desirable signal and additive noise :

Whatever physical media a channel consists of, the transmitted signal will be attenuated and corrupted with additive noise.