Fixed-coefficient variable prime length recursive discrete fourier transform system

The invention provides a fixed-coefficient variable prime length recursive discrete Fourier transform system. A pre-processing device receives N digital input signals and performs order permutation operations on the N digital signals to generate first and second temporal signals, wherein N is a prime number. A real-part calculation device receives the real part of the first and second temporal signals and performs discrete cosine/sine transform to generate third and fourth temporal signals. An imagenary-part calculation device receives the imagenary part of the first and second temporal signals and performs discrete cosine/sine transform to generate fifth and sixth temporal signals. A pre-processing device receives the third, fourth, fifth and sixth temporal signals to perform order permutation and addition operations for generating N digital output signals, wherein the N digital output signals are the discrete Fourier transform of the N digital signals.