Syöttökerroin

Syöttökerroin, literally “input coefficient” in Finnish, is a coefficient that determines how strongly an input signal affects the output of a system. In control theory, signal processing, and mathematical modeling, it denotes the gain or scaling applied to an input channel.

In a simple scalar linear system, the relation between input u(t) and output y(t) can be written as y(t) = k · u(t) for continuous time or y[n] = k · u[n] for discrete time, where k is the syöttökerroin (input gain). In more complex, multi-input systems, the scalar coefficient extends to matrices or vectors B in y = A y + B u; here the elements of B collectively define the input gains for each channel.

For linear time-invariant systems, the overall input gain may vary with frequency; the magnitude of the transfer function |G(jω)| serves as the transfer gain at frequency ω, sometimes referred to as the syöttökerroin at that frequency.

Syöttökerroin can be estimated from data via system identification, regression, or optimization, and is essential in designing controllers and filters, tuning amplifiers, or modeling dynamic processes where an input signal is scaled to produce a desired response.

It is distinct from the overall system gain or sensitivity, which may depend on state, operating point, or feedback structure. The term is general and usage varies between disciplines; in some contexts, “input gain” or “input coefficient” may be more common.