Frequentieresponst

Frequentieresponst is a term used to describe the frequency response of a system in signal processing and related fields. It characterizes how the system processes input signals as a function of frequency, revealing how different frequencies are amplified or attenuated and how their phases are shifted.

In linear time-invariant systems, a sinusoidal input at frequency ω produces an output that is also a sinusoid at the same frequency, but with a changed amplitude and phase. The frequency response is often denoted H(jω) for continuous-time systems, defined as H(jω) = ∫ h(t) e^{-jωt} dt, where h(t) is the impulse response. For discrete-time systems, H(e^{jω}) = ∑ h[n] e^{-jωn}. The magnitude |H(jω)| indicates how much the amplitude is scaled, and the phase ∠H(jω) indicates the phase shift. Magnitude is commonly expressed in decibels as 20 log10|H(jω)|.

The frequency response is related to the transfer function H(s) in the Laplace domain; evaluating on the imaginary axis (s = jω) yields the steady-state response to sinusoidal inputs. It assumes linearity and time-invariance, and, for causal systems, stability.

Common shapes include low-pass, high-pass, band-pass, band-stop, and all-pass. Design goals include achieving a flat magnitude in the desired band and adequate attenuation elsewhere, along with consideration of phase characteristics and group delay.

Measurement and estimation can be performed via impulse or swept-sine tests, deconvolution of step responses, or spectral analysis with FFT. Applications span filter design, audio engineering, room acoustics, and control systems.