The concepts of basis and frame are studied in the classical literature of functional analysis, Fourier analysis, and wavelet theory in a wide range. In this paper, we consider an operator‐theoretic approach to discrete frame theory on a separable Hilbert space. For this purpose, we define a special type of frames and bases, called wavelet‐type frames and wavelet‐type bases, obtained by acting with a family of bounded linear operators on some vectors, and then investigate the elementary properties of these concepts.