In this article, a new Constant-Q transform implementation is proposed together with a generalization of both the Short-Term Fourier Transform and the Constant-Q transform. The purpose of this generalization is to provide a discrete time-frequency analysis tool with arbitrary center frequency and frequency resolution for each bin of the transform. This new analysis framework is very flexible and can be related to many common time-frequency transforms. Furthermore, new interesting transforms with specific time-frequency resolutions can be defined. To illustrate and validate the corresponding approach, experimental results and examples are provided for different configurations.