  The Hamiltonian of the harmonic oscillator is usually defined as a
differential operator, but an integral representation can be obtained by using
the coherent state quantization. The finite frame quantization is a finite
counterpart of the coherent state quantization and it allows us to define a
finite oscillator by starting from the integral representation of the harmonic
oscillator. Our purpose is to investigate the oscillator obtained in this way,
and to present a possible application to the discrete fractional Fourier
transform.
