phase-spectrum

The phase spectrum of a signal is the function that assigns, to each frequency component in a spectral decomposition, the phase angle (argument) of the corresponding complex-valued spectral coefficient. It is obtained by applying a frequency-domain transform (Fourier, Laplace, or Z-transform) and extracting the argument of the resulting complex output — complementing the magnitude spectrum, which records the amplitude of each component. The phase spectrum encodes the timing and alignment relationships among frequency components; it determines how those components superpose to reconstruct the original signal's waveform. Without the phase spectrum, the magnitude spectrum alone cannot recover the signal's temporal structure. The concept persists as a theoretical construct in signal analysis, system identification, and audio processing, where phase information is essential for tasks such as phase retrieval, group-delay analysis, and coherent signal reconstruction. [formal: spectrum phase | substrate: mind | horizon: hours | explicit: yes | epoch: 0.01]