  We show that a new unitary transform with characteristics almost similar to
those of the finite Fourier transform can be defined in any finite-dimensional
Hilbert space. It is defined by using the Kravchuk polynomials, and we call it
Kravchuk transform. Some of its properties are investigated and used in order
to obtain a simple alternative description for the irreducible representations
of the Lie algebra su(2) and group SU(2). Our approach offers a deeper insight
into the structure of the linear representations of SU(2) and new possibilities
of computation, very useful in applications in quantum mechanics, quantum
information, signal and image processing.
