The paper gives an introductory description of novel classes of fast orthogonal transforms (Phi Transforms) which are defined, described and exploited by the team of authors during the recent three years. The main goal of the paper is the presentation of open collection of MATLAB functions and the library of SIMULINK blocks (Phi Transforms Toolbox/Blockset). Presently, the toolbox contains almost 50 units and supplements existing Signal Processing, Communication, Image Processing and other toolboxes/blocksets of MATLAB/SIMULINK. Here are several categories of the units – basis functions generators, spectrum analyzers, signal synthesizers, parametrical orthogonal filters, parametrical communication engines, GUI based interactive tools, demo tools, and others. The units are developed for both the 1 D and 2 D case. The preliminary comparison with orthogonal wavelets is provided. Advantages of Phi Transforms are demonstrated by simple examples from the signal synthesis, compression and filtering. Authors treat the toolbox as a rich base for teaching of students and the development of novel DSP algorithms and devices.