Characterisation of signal and noise propagation. Signal response and fluctuations can be analysed in the time domain or frequency domain, the latter allowing for analytical treatment. Analysis of signal propagation: A small stimulus Δc(t) (Input) is applied, which results in a measurable response ΔR(t) (Output). The response ΔR(t) of the system to an impulse input represents the linear response function χ
(t) (up to a constant factor). In the frequency domain, this stimulus is a constant. The Fourier transformed linear response function can be analysed for its frequency-resolved transmission behaviour. Noise propagation: Fluctuations are characterised by their correlations over the time interval τ. The autocorrelation function K(τ) (Inset) typically decreases as a function of interval length. In the frequency domain, the noise power spectrum S
(ω), which is the Fourier transform of the autocorrelation function, characterises the frequency components of the noise.