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 χR(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 SR(ω), which is the Fourier transform of the autocorrelation function, characterises the frequency components of the noise.
Clausznitzer and Endres BMC Systems Biology 2011 5:151 doi:10.1186/1752-0509-5-151