Frequentieresponsen

Frequentieresponsen, commonly referred to as the frequency response in English, describes how a dynamic system responds to sinusoidal inputs over a range of frequencies. It is a foundational concept in signal processing, electronics, acoustics, and control engineering, used to characterize components such as filters, amplifiers, loudspeakers, and sensors.

For a continuous-time linear time-invariant system with impulse response h(t), the output y(t) equals the convolution of the input x(t) and h(t). The frequency response H(ω) is the Fourier transform of h(t): H(ω) = ∫ h(t) e^{-jωt} dt. In the frequency domain, Y(ω) = H(ω) X(ω). In discrete time, the frequency response is H(e^{jΩ}) = ∑ h[n] e^{-jΩ n}.

Interpretation: the magnitude |H(ω)| gives the gain at frequency ω, while the phase ∠H(ω) gives the phase shift introduced by the system. Magnitude is often expressed in decibels as 20 log10|H(ω)|. The phase information relates to linearity properties, such as group delay, which describes how waveforms are distorted in time by the system.

Measurement and visualization: Bode plots display magnitude and phase versus frequency on logarithmic scales. Practical measurements use instruments like network analyzers or swept-sine and chirp tests to estimate the frequency response, enabling analysis and design refinements of the system.

Applications: frequentieresponsen is used in filter design and tuning, audio engineering and room acoustics, telecommunications and channel characterization, sensor calibration, and system identification, providing a compact summary of how a system behaves across the frequency spectrum.