In this paper, basic forms of Fourier analysis considered − harmonic series, integrals and discrete transforms with respect to engineering approach. Quantum uncertainty relation introduced for bound time-frequency metrics in harmonic function presentation. Generalized Fourier transforms determined on the basis of unified summation-integration operator. This extends the scope of harmonic analysis application. Figs.: 2. Refs.: 11 titles.

The methods of quantum physics penetrate today into various fields of theoretical disciplines. In this paper, based on quantum mechanics principles, a uniform geometric model of a quantum system experiment introduced. A phase space determined for quantum system experiment in the form of two-dimensional topological torus. On this torus, the math expectation of quantum system track defined as the wave function, along with the tensor of quantum states entanglement. The tensor of quantum entanglement interpreted as the vector basis of a local Euclidian space. The work intends the complex many-body system applications. Refs.: 22 titles.