Digital Signal Processing (DSP) applications in Bioinformatics have received great attention in recent years, where new effective methods for genomic sequence analysis, such as the detection of coding regions, have been developed. The use of DSP principles to analyze genomic sequences requires defining an adequate representation of the nucleotide bases by numerical values, converting the nucleotide sequences into time series. Once this has been done, all the mathematical tools usually employed in DSP are used in solving tasks such as identification of protein coding DNA regions, identification of reading frames, and others. In this article we present an overview of the most relevant applications of DSP algorithms in the analysis of genomic sequences, showing the main results obtained by using these techniques, analyzing their relative advantages and drawbacks, and providing relevant examples. We finally analyze some perspectives of DSP in Bioinformatics, considering recent research results on algebraic structures of the genetic code, which suggest other new DSP applications in this field, as well as the new field of Genomic Signal Processing.