Applications and other transformations

Abstract

This chapter illustrates application of the FFT to the processes of convolution and correlation. As described previously, these two processes play an important part in image processing. However, because the microprocessor is limited by its capacity to process most real images, of size generally at least 256 x 256 picture elements, we have restricted our illustration of these processes to one-dimensional situations. For example, the correlation process is important for aligning sequences, or for providing a measure of how closely related two given sequences are. This situation often occurs in biology where we are frequently required to match sequences made up of nucleic or amino acid components which play an important part in the biological growth process. An example is given to illustrate the application of sequence alignment on nucleic acid data using the FFT approach.