FFT (Fast Fourier Transform) radix-2-4-8 mixed-radix butterfly operator and application thereof

Abstract

The invention relates to an FFT (Fast Fourier Transform) radix-2-4-8 mixed-radix butterfly operator which comprises a radix-2 unit, a radix-4 unit and a radix-8 unit. The radix-8 unit comprises a prefix operation unit, which is mainly formed by connecting a first complex number adding device with a real operation unit, and the radix-4 unit; the prefix operation unit is connected with the radix-4 unit by a first register; the radix-8 unit, the radix-4 unit and the radix-2 unit are connected in parallel to form a production line architecture. The FFT radix-2-4-8 mixed-radix butterfly operator has the beneficial effects that relative to a complete radix-8 butterfly operator, the FFT radix-2-4-8 mixed-radix butterfly operator is low in resource cost, is more flexible to use and meanwhile, has excellent parallelism for meeting the requirements of a high throughput system; the radix-2-4-8 mixed-radix structure enables the butterfly operator to support the sequence length of a point of an integer power of 2.

Description

technical field [0001] The invention relates to a fast Fourier transform digital integrated circuit design used in digital signal processing, in particular to a fast Fourier transform radix 2-4-8 mixed-base butterfly calculator. Background technique [0002] In 1965, Cooley and Tukey proposed the Fast Fourier Transform algorithm, which utilizes the periodicity and symmetry of the twiddle factors to decompose the DFT of a long sequence into a DFT with a smaller number of points, thereby reducing the number of multiplications and improving computational efficiency. Once this algorithm came out, it has received great attention, and many related algorithms have developed rapidly. In 1968, Bergland improved the base 2 and base 4 algorithms of FFT and derived the base 8 and base 16 algorithms. The FFT algorithm is widely used in radar systems, image processing, communication systems, aerospace and other fields. With the improvement of system performance index requirements, the tr...

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Problems solved by technology

Algorithms with high radix such as radix 4 and radix 8 can effectively reduce the operation techniques of long sequences and improve performance, but algorithms with high radix also have certain limitations: first, the design of butterfly calculators for high radix algorithms is relatively complicated, such as a complete The resource overhead of the radix-8 butterfly operator is more than four times greater than that of the radix-2 butterfly operator, and at the same time, the demand for memory access bandwidth is four times that of the radix-2 butterfly operator; The sequence length of the integer power of 2 supported by the radix-2 algorithm is the integer power of the radix of the selected high-radix algorithm

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