Group delay and phase delay

In signal processing, group delay and phase delay are two related ways of describing how a signal's frequency components are delayed in time when passing through a linear time-invariant (LTI) system (such as a microphone, coaxial cable, amplifier, loudspeaker, telecommunications system, ethernet cable, digital filter, or analog filter). Phase delay describes the time shift of a sinusoidal component (a sine wave in steady state). Group delay describes the time shift of the envelope of a wave packet, a "pack" or "group" of oscillations centered around one frequency that travel together, formed for instance by multiplying (amplitude modulation) a sine wave by an envelope (such as a tapering function). These delays are usually frequency dependent, which means that different frequency components experience different delays. As a result, the signal's waveform experiences distortion as it passes through the system. This distortion can cause problems such as poor fidelity in analog video and analog audio, or a high bit-error rate in a digital bit stream. However, for the ideal case of a constant group delay across the entire frequency range of a bandlimited signal and flat frequency response, the waveform will experience no distortion. Sine waveFourier analysis and Linear time-invariant system Fourier analysis reveals how signals in time can alternatively be expressed as the sum of sinusoidal frequency components, each based on the trigonometric function with a fixed amplitude and phase and no beginning and no end. Linear time-invariant systems process each sinusoidal component independently; the property of linearity means they satisfy the superposition principle. The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.