We extend the Wigner distribution (WD) to conjugate unitary operators A, and Bp. The resulting “ABWD” is defined both as an a-b representation and as a timefrequency representation. Important properties and relations of the WD are generalized to the AB-WD.

This text describes a series of experiments performed with a machine capable of synthesizing human whistles and canary song. We call this device The Universal Whistling Machine (U.W.M). It senses the presence of living creatures in its vicinity and attracts them with a signature whistle. Given a response whistle, U.W.M. counters with its own composition, based on a time-frequency analysis of th...

We prove that the generalized Carleson operator with polynomial phase function of degree two is of weak type (2,2). For this, we introduce a new approach to the time-frequency analysis of the quadratic phase.

We estimate the U.S. New Keynesian Phillips Curve in time-frequency domain with continuous wavelet tools to provide integrated answers three controversial issues. (1) Has short-run tradeoff been stable? (2) What has role of expectations? (3) Is there a long-run tradeoff? First, we find that is limited some specific episodes and no evidence nonlinearities or structural breaks. Second, households...

The generalized entropies of Rényi inspire new measures for estimating signal information and complexity in the time–frequency plane. When applied to a time–frequency representation (TFR) from Cohen’s class or the affine class, the Rényi entropies conform closely to the notion of complexity that we use when visually inspecting time–frequency images. These measures possess several additional int...