Grundphase

Grundphase, literally meaning fundamental phase, is a term used in German-language discussions of signal processing and vibration analysis to denote the phase angle associated with the fundamental frequency component of a periodic signal. It corresponds to the phase of the first harmonic in a Fourier expansion or Fourier transform representation of the signal.

In a real-valued periodic signal x(t) with fundamental angular frequency ω0, the signal can be expressed as a sum of harmonics: x(t) = A1 cos(ω0 t + φ1) + Σk≥2 Ak cos(k ω0 t + φk). Here, φ1 is the Grundphase, the phase of the k = 1 term. The higher-harmonic phases (φ2, φ3, ...) influence the detailed shape of the waveform, while φ1 largely determines where the waveform starts at t = 0.

Calculation and interpretation: From Fourier analysis, one extracts the complex coefficient X1 corresponding to the fundamental component; the argument (angle) of X1 gives the Grundphase. For discrete signals, the discrete Fourier transform provides the same information, with the indexing adjusted to align with the fundamental frequency.

Applications: Grundphase is relevant in acoustics, mechanical vibrations, and digital signal processing. It matters for accurate waveform reconstruction, phase alignment across channels, and modal or vibration analysis. In some processing approaches, controlling or preserving the Grundphase helps maintain natural timbre or impulse response characteristics.

See also: Fourier analysis, harmonic content, phase, phase reconstruction, phase vocoder.