Amplitudrespons

Amplitudrespons, or amplitude response, is a characterization of how the magnitude of a system’s output varies with input frequency for linear time-invariant systems. It is the magnitude of the system’s frequency response, denoted H(jω) in continuous time or H(e^(jω)) in discrete time. If an input signal with spectrum X(jω) passes through the system, the output spectrum is Y(jω) = H(jω) X(jω), and the amplitude response is A(ω) = |H(jω)|. Often, the amplitude response is expressed in decibels as 20 log10 A(ω).

The amplitude response is closely related to the phase response, which describes how the phase of each frequency component is shifted by the system. Together, they form the full frequency response. The amplitude response can be computed from the impulse response h(t) via a Fourier transform: H(jω) = ∫ h(t) e^(-jωt) dt. In discrete time, H(e^(jω)) is obtained from the discrete impulse response.

Commonly, the magnitude is plotted against frequency (a Bode magnitude plot) to show how different frequencies are attenuated or amplified. A typical example is a first-order RC filter, where for a low-pass configuration H(jω) = 1/(1 + jωRC) and A(ω) = 1/√(1 + (ωRC)²).

Applications include filter design, signal processing, acoustics, and control systems. Amplitudrespons is defined for linear, time-invariant systems and may not apply or vary for nonlinear or time-varying systems, where the response can depend on input level or time.