Magnitudrespons

Magnitudrespons, commonly referred to as magnitude response, describes how the amplitudes of different frequency components of an input signal are scaled by a linear time-invariant system. It is the magnitude of the system’s frequency response, derived from the transfer function H(jω) for continuous-time systems or H(e^{jΩ}) for discrete-time systems.

Mathematically, for a continuous-time system, the frequency response is H(jω) = ∫ h(t) e^{-jωt} dt, where h(t) is the impulse response. The magnitudrespons is |H(jω)|, representing how each frequency ω is attenuated or amplified. In many contexts, the magnitude is expressed in decibels as 20 log10|H(jω)|. In discrete time, the corresponding expression uses H(e^{jΩ}). The magnitude response is often plotted alongside the phase response φ(ω) = arg(H(jω)); together they constitute the full frequency response. Notably, the magnitude aspect is independent of the phase.

Interpretation and applications: the magnitudrespons indicates whether a filter or system passes, attenuates, or rejects specific frequencies. Common shapes include low-pass, high-pass, band-pass, and notch responses. In practice, the magnitude response is determined from the system’s impulse response, from differential or difference equations, or from a known transfer function. It is measured experimentally with equipment such as a network analyzer or via Fourier analysis of measured impulse responses.

Uses span audio processing, telecommunications, control systems, and signal filtering, where designing and analyzing how a system scales frequency components is essential.