Sequence alignment is the positioning of primary biological sequences, such as DNA, RNA and protein sequences, to identify regions of similarity in large databases. Common signal processing techniques include cross-correlations in time or frequency. However, these techniques can result in many misalignments when capturing a grouping in local or repetitive portions of the sequence. We propose a time-frequency based alignment technique using the matching pursuit decomposition method and a mapping algorithm. The aim of this alignment technique is to identify local and global alignments more efficiently and with greater precision than existing methods. Its success is based on the fact that sequence elements are mapped to unique Gaussian basis atoms that uniformly sample the time-frequency plane.