In this paper we propose a new class of signal analysis tools that generalizes the popular wavelet and short-time Fourier transforms. The class allows skews and rotations of the analyzing wavelet in the time-frequency plane, in addition to the time and frequency translations and scalings employed by conventional transforms. In addition to providing a unifying framework for studying existing time-frequency representations, the general class provides a systematic method for designing new representations with properties useful for certain types of signals.