FAST TRANSFORMS Algorithms Analyses Applications by Douglas F. Elliott K. Ramamohan Rao

Fast transforms are playing an increasingly important role in applied  engineering practices. No t only do they  provide spectral analysis in speech, sonar, radar, and vibration detection,  but also they provide bandwidth reduction in video transmission and  signal filtering. Fast transforms are used directly to filter signals in the  frequency domain and indirectly to  design digital filters for time domain  processing. They are also used for  convolution evaluation and signal decomposition. Perhaps the reader can anticipate other applications, and as time passes  the list of applications will  doubtlessly grow.