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Is the discrete Fourier transform matrix coherent?
Incoherence.

Discrete Fourier Transform (DFT) matrix is irrelevant because it is a matrix composed of complex exponential functions. Coherence usually refers to the correlation of signals or data, not the nature of the matrix itself.

DFT matrix is a mathematical tool to convert time domain signals into frequency domain signals, which is applied to signal processing, image processing and communication systems and other related fields. It decomposes the signal into a set of sine and cosine basis functions for analyzing the frequency spectrum characteristics of the signal.

Coherence is usually related to the relationship between signals and the nature of data, but has nothing to do with DFT matrix itself. Coherence is usually used to describe the characteristics of correlation, interference and consistency between signals.