Ryhmäviiveen

Ryhmäviiveen, or group delay in English, is a fundamental concept in signal processing, communications engineering, and acoustics. It describes how the phase of a signal’s frequency components is shifted as the signal propagates through a medium or component. The group delay is defined as the negative derivative of the phase response with respect to angular frequency, τ_g(ω) = –dφ(ω)/dω, where φ(ω) is the phase shift introduced by the system. This quantity represents the time delay experienced by the envelope of a narrowband signal or a group of frequencies.

Group delay differs from phase delay, which is the simple phase shift divided by frequency, and from group velocity in wave mechanics, which relates to energy transport. In electronic filter design, a constant group delay across the passband is desirable because it preserves the waveform shape of modulated signals, avoiding distortion known as dispersion. Non‐constant group delay can cause frequency components to arrive at different times, which is critical in broadband communications, digital transmission, and audio equalization.

Typical values of group delay in a low‑pass RC filter can be derived analytically; for a first‑order system τ_g = R C. In multi‑stage filters, group delay is obtained by summing the contributions of each stage. In fiber‑optic communication links, chromatic dispersion causes frequency dependence of group delay, directly impacting pulse broadening and limiting data rates.

Measurement of group delay is performed using vector network analyzers or time‑domain reflectometers by launching known signals and observing the phase shift across frequencies. Engineers often plot the group delay versus frequency to diagnose filter performance or to tune the dispersion compensation in optical networks.

Historically, the term originates from group velocity in physics and was adopted in electronics in the 1940s to describe signal integrity. The concept remains essential to modern digital signal processing, where careful control of group delay enables high‑fidelity audio reproduction, efficient data transmission, and precise instrumentation.