Genomics is a highly cross-disciplinary field that creates paradigm shifts in such diverse areas as medicine and agriculture. It is believed that many significant scientific and technological endeavors in the 21st century will be related to the processing and interpretation of the vast information that is currently revealed from sequencing the genomes of many living organisms, including humans. Genomic information is digital in a very real sense; it is represented in the form of sequences of which each element can be one out of a finite number of entities. Such sequences, like DNA and proteins, have been mathematically represented by character strings, in which each character is a letter of an alphabet. In the case of DNA, the alphabet is size 4 and consists of the letters A, T, C and G; in the case of proteins, the size of the corresponding alphabet is 20. As the list of references shows, biomolecular sequence analysis has already been a major research topic among computer scientists, physicists, and mathematicians. The main reason that the field of signal processing does not yet have significant impact in the field is because it deals with numerical sequences rather than character strings. However, if we properly map a character string into, one or more numerical sequences, then digital signal processing (DSP) provides a set of novel and useful tools for solving highly relevant problems. For example, in the form of local texture, color spectrograms visually provide significant information about biomolecular sequences which facilitates understanding of local nature, structure, and function. Furthermore, both the magnitude and the phase of properly defined Fourier transforms can be used to predict important features like the location and certain properties of protein coding regions in DNA. Even the process of mapping DNA into proteins and the interdependence of the two kinds of sequences can be analyzed using simulations based on digital filtering. These and other DSP-based approaches result in alternative mathematical formulations and may provide improved computational techniques for the solution of useful problems in genomic information science and technology.