A novel 3780-point FFT

Abstract

This paper proposes a novel 3780-point FFT algorithm for the China national broadcasting standard. This new algorithm adopts the pure PFA (prime factor algorithm) and nested Winograd FFT which can realize the identity in the circuit structure. The simulation demonstrates that the new algorithm can achieve the equal accuracy rather than other methods but with the least quantity of multiplication.

A novel overall in-place in-order prime factor FFT algorithm

“…Therefore, the structure of short DFT can be chosen flexibly, which can be replaced by other structures without influencing the global design. For example, the 27-point WFTA matrixes introduced in [8] can replace the combination of 3×9, but do not need any modification for the global design.…”

Hardware design and implementation of 3780 points FFT based on FPGA in DTTB

“…The paper [5] derived the 27 point WFTA matrixes to replace the combination of 3 9 × , which can greatly reduce the multiplication quantity due to elimination of multiplication rotator and can realize the high coherence in circuit architecture. Therefore, this paper contributes to the hardware design and implementation of the proposed algorithm in paper [5].…”

“…The paper firstly in part II introduces the algorithm derived in [5] briefly. Then the hardware design and implementation based on FPGA is considered in the part III.…”

“…ALGORITHM SCHEME The paper [5] decomposed the 3780 into 4 5 7 27 × × × and adopted the 4 points WFTA, 5 points WFTA, 7 points WFTA, 27 points WFTA and PFA to compute the 3780 points DFT.…”

“…Associating the PFA [6], the proposed algorithm [5] can be expressed as = × × × . To map above equation to the hardware, a simple and more efficient indexing scheme is to consider this fourdimensional problem as a sequence of two-dimensional problem [10].…”