The Development of Fast DST-I Algorithms for Short-Length Input Sequences

The subject of this paper is the development of rationalized algorithms of discrete sinusoidal transform of type I for short sequences of length N = 2, 3, 4, 5, 6, 7, and 8. Here, by the word “rationalization”, we mean the reduction of the number of arithmetic operations required to implement the algorithms. The arithmetic complexity of the developed algorithms is presented in the final table. For each algorithm, we also provide data flow graphs demonstrating the space–time structure of the computational processes. The algorithms were tested to verify their validity using MATLAB software (version R2023).