Tiddomänen

Tiddomänen is a term used in some Scandinavian technical contexts to denote the time domain, the representation of signals as a function of time. The time-domain description contrasts with other representations such as the frequency domain, where signals are described by their spectral content. In continuous-time systems, signals are functions x(t) defined for all real numbers t; in discrete-time systems they are sequences x[n] defined for integer n.

In the time domain, system behavior is often described by impulse response h(t) or h[n]. For a linear time-invariant system, the output y is the convolution of input x with the system impulse response: y(t) = ∫ x(τ) h(t−τ) dτ in continuous time, or y[n] = sum_k x[k] h[n−k] in discrete time. Other common time-domain descriptions include step response, differential or difference equations, and state-space representations.

Transition to other domains is achieved via transforms, most notably the Fourier transform for frequency-domain analysis X(ω), and the Laplace transform X(s); the Z-transform X(z) is used for discrete-time systems. Transform methods often simplify convolution into multiplication and expose stability and resonance properties.

Applications of time-domain analysis span signal processing, control engineering, communications, and physics. It emphasizes intuition about causality, time delays, and transient behavior, though some problems are more easily solved in the frequency domain.