Abstract
We present a theory of linear and bilinear/quadratic time-frequency (TF) representations that satisfy a covariance property with respect to “TF displacement operators” These operators cause TF displacements such as (possibly dispersive) TF shifts and dilations/compressions. Our covariance theory establishes a unified framework for important classes of linear TF representations (e.g., the short-time Fourier transform and continuous wavelet transform) as well as bilinear TF representations (e.g., Cohen’s class and the affine class). It yields a theoretical basis for TF analysis and allows the systematic construction of covariant TF representations.
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