We investigate the use of time-frequency (TF) methods to query biological sequences in search of regions of similarity or critical relationships among the sequences. Existing querying approaches are insensitive to repeats, especially in low-complexity regions, and do not provide much support for efficiently querying sub-sequences with inserts and deletes (or gaps). Our approach uses highly-localized basis functions and multiple transformations in the TF plane to map characters in a sequence as well as different properties of a sub-sequence, such as its position in the sequence or number of gaps between sub-sequences. We analyze gapped query-based alignment methods using transformations in the TF plane while demonstrating the method's possible operation in real-time without pre-processing. The algorithm's performance is compared to the widely-accepted BLAST alignment approach, and a significance improvement is observed for queries with repetitive segments.