Recursive type-iv discrete cosine transform system

A recursive type-IV discrete cosine transform system, comprising:

• a first permutation device for receiving N digital input signals and performing a two-dimensional order permutation operation on the N digital signals to generate N two-dimensional first temporal signals, where N is a positive integer;
• a recursive type-III discrete cosine/sine transform device which is an m-point recursive type-III discrete cosine/sine transform device connected to the first permutation device for receiving the N first temporal signals and repeating a type-III discrete cosine/sine transform c times on the N first temporal signals to generate c second temporal signals each with m points, where N=m×c, and m, c are each a positive integer;
• a cosine/sine factor generation device connected to the recursive type-III discrete cosine/sine transform device for sequentially performing cosine/sine factor multiplication and corresponding addition operations on the m-point second temporal signals to generate c third temporal signals each with m points;
• a recursive type-II discrete cosine/sine transform device which is a c-point recursive type-II discrete cosine/sine transform device connected to the cosine/sine factor generation device for receiving the third temporal signals and repeating a type-II discrete cosine/sine transform m times to generate m fourth temporal signals each with c points;
• and
• a second permutation device connected to the recursive type-II discrete cosine/sine transform device for receiving the fourth temporal signals and performing a one-dimensional order permutation operation on the fourth temporal signals for generating N one-dimensional output signals,
• wherein the N one-dimensional output signals are obtained by performing a type-IV discrete cosine transform on the N digital input signals.