Skip to content Skip to navigation


You are here: Home » Content » Split-radix FFT Algorithm


Recently Viewed

This feature requires Javascript to be enabled.

Split-radix FFT Algorithm

Module by: Douglas L. Jones. E-mail the author

Note: You are viewing an old version of this document. The latest version is available here.

The split-radix algorithm has the lowest M+A M A operations of any known power-of-two algorithm. Most FFT experts believe it to be optimum in this respect.

Figure 1
Motivation for S-R algorithm
(a) (b)
radix-2 (image1.bmp)radix-4 (image2.bmp)
Figure 2: Alternatively, note that these two butterflies are equivalent
(a) (b)
Figure 2(a) (image3.bmp)Figure 2(b) (image4.bmp)

Split-radix algorith muses part radix-2 decomposition and part radix-4 decomposition.

DIT Split-radix derivation

Xk= n =0N21x2ne(i2π×(2n)kN)+ n =0N21x4n+1e(i2π(4n+1)kN)+ n =0N21x4n+3e(i2π(4n+3)kN)= DFT N 2 x2n+ W N k DFTx4n+1+ W N 3 k DFTx4n+3 X k n N 2 1 0 x 2 n 2 2 n k N n N 2 1 0 x 4 n 1 2 4 n 1 k N n N 2 1 0 x 4 n 3 2 4 n 3 k N DFT N 2 x 2 n W N k DFT x 4 n 1 W N 3 k DFT x 4 n 3
Figure 3
Butterfly (image5.bmp)
Figure 4: Transform has L-shaped butterflies
Figure 4 (image6.bmp)
Table 1: Operation Counts
Complex M/As Real M/As (4/2) Real M/As (3/3)
ON3log 2 N O N 3 2 N 43Nlog 2 N389N+6+291M 4 3 N 2 N 38 9 N 6 2 9 1 M Nlog 2 N3N+4 N 2 N 3 N 4
ONlog 2 N O N 2 N 83Nlog 2 N169N+2+291M 8 3 N 2 N 16 9 N 2 2 9 1 M 3Nlog 2 N3N+4 3 N 2 N 3 N 4


  • Split-radix algorithm has an irregular structure. Successful progams have been written (Sorensen) for uni-processor machines, but its not good for multi processors.
  • D. Braun's algorithm has split-radix counts N2 N 2 , has a regular structure, and is thus appealing for multiprocessors or special-purpose hardware. (Contact me if you ever need the references)


  1. H.V. Sorensen, M.T. Heideman, and C.S. Burrus. (1986). On computing the split-radix FFT. ASSP, 34(1), 152-156.
  2. P. Duhamel and H. Hollman. (1984, Jan 5). Split-radix FFT algorithms. Electronics Letters, 20, 14-16.

Content actions

Download module as:

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens


A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks