This chapter details multiresolution analysis (MRA) as a fundamental framework for wavelet-based signal decomposition. Heisenberg’s uncertainty principle, which establishes the trade-off between time and frequency resolution in signal analysis, is explained in detail. The concept of MRA is then introduced followed by a discussion of its key properties. The decomposition of signals into approximation and detail coefficients is explained, highlighting their role in capturing low- and high-frequency components. The chapter also covers subband coding, demonstrating its connection to MRA in efficient signal representation. Finally, the fast wavelet transform is introduced as an efficient algorithm for computing wavelet coefficients.