Skip to content Skip to navigation

Connexions

You are here: Home » Content » N = 16 FFT module

Navigation

Content Actions
  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is 'My Favorites'?)
      'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.
    • A lens (What is a lens?)

      Definition of a lens

      Lenses

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

      What is in a lens?

      Lens makers point to Connexions 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 Connexions member, a community, or a respected organization.

    • External bookmarks
  • E-mail the authors

Recently Viewed

This feature requires Javascript to be enabled.

N = 16 FFT module

Module by: Howard Johnson, C. Sidney Burrus

Summary: A very efficient length N = 16 FFT module that can be use alone or with the PFA or the WFTA.

N=16 FFT module

A FORTRAN implementation of a length-16 FFT module to be used in a Prime Factor Algorithm program.

C
C-------------------WFTA N=16----------------------------
C
  116   R1 = X(I(1)) + X(I(9))
    R2 = X(I(1)) - X(I(9))
    S1 = Y(I(1)) + Y(I(9))
    S2 = Y(I(1)) - Y(I(9))
    R3 = X(I(2)) + X(I(10))
    R4 = X(I(2)) - X(I(10))
    S3 = Y(I(2)) + Y(I(10))
    S4 = Y(I(2)) - Y(I(10))
    R5 = X(I(3)) + X(I(11))
    R6 = X(I(3)) - X(I(11))
    S5 = Y(I(3)) + Y(I(11))
    S6 = Y(I(3)) - Y(I(11))
    R7 = X(I(4)) + X(I(12))
    R8 = X(I(4)) - X(I(12))
    S7 = Y(I(4)) + Y(I(12))
    S8 = Y(I(4)) - Y(I(12))
    R9 = X(I(5)) + X(I(13))
    R10= X(I(5)) - X(I(13))
    S9 = Y(I(5)) + Y(I(13))
    S10= Y(I(5)) - Y(I(13))
    R11 = X(I(6)) + X(I(14))
    R12 = X(I(6)) - X(I(14))
    S11 = Y(I(6)) + Y(I(14))
    S12 = Y(I(6)) - Y(I(14))
    R13 = X(I(7)) + X(I(15))
    R14 = X(I(7)) - X(I(15))
    S13 = Y(I(7)) + Y(I(15))
    S14 = Y(I(7)) - Y(I(15))
    R15 = X(I(8)) + X(I(16))
    R16 = X(I(8)) - X(I(16))
    S15 = Y(I(8)) + Y(I(16))
    S16 = Y(I(8)) - Y(I(16))
    T1 = R1 + R9
    T2 = R1 - R9
    U1 = S1 + S9
    U2 = S1 - S9
    T3 = R3 + R11
    T4 = R3 - R11
    U3 = S3 + S11
    U4 = S3 - S11
    T5 = R5 + R13
    T6 = R5 - R13
    U5 = S5 + S13
    U6 = S5 - S13
    T7 = R7 + R15
    T8 = R7 - R15
    U7 = S7 + S15
    U8 = S7 - S15
    T9 = C81 * (T4 + T8)
    T10= C81 * (T4 - T8)
    U9 = C81 * (U4 + U8)
    U10= C81 * (U4 - U8)
    R1 = T1 + T5
    R3 = T1 - T5
    S1 = U1 + U5
    S3 = U1 - U5
    R5 = T3 + T7
    R7 = T3 - T7
    S5 = U3 + U7
    S7 = U3 - U7
    R9 = T2 + T10
    R11= T2 - T10
    S9 = U2 + U10
    S11= U2 - U10
    R13 = T6 + T9
    R15 = T6 - T9
    S13 = U6 + U9
    S15 = U6 - U9
    T1 = R4 + R16
    T2 = R4 - R16
    U1 = S4 + S16
    U2 = S4 - S16
    T3 = C81 * (R6 + R14)
    T4 = C81 * (R6 - R14)
    U3 = C81 * (S6 + S14)
    U4 = C81 * (S6 - S14)
    T5 = R8 + R12
    T6 = R8 - R12
    U5 = S8 + S12
    U6 = S8 - S12
    T7 = C162 * (T2 - T6)
    T8 = C163 * T2 - T7
    T9 = C164 * T6 - T7
    T10 = R2 + T4
    T11 = R2 - T4
    R2 = T10 + T8
    R4 = T10 - T8
    R6 = T11 + T9
    R8 = T11 - T9
    U7 = C162 * (U2 - U6)
    U8 = C163 * U2 - U7
    U9 = C164 * U6 - U7
    U10 = S2 + U4
    U11 = S2 - U4
    S2 = U10 + U8
    S4 = U10 - U8
    S6 = U11 + U9
    S8 = U11 - U9
    T7 = C165 * (T1 + T5)
    T8 = T7 - C164 * T1
    T9 = T7 - C163 * T5
    T10 = R10 + T3
    T11 = R10 - T3
    R10 = T10 + T8
    R12 = T10 - T8
    R14 = T11 + T9
    R16 = T11 - T9
    U7 = C165 * (U1 + U5)
    U8 = U7 - C164 * U1
    U9 = U7 - C163 * U5
    U10 = S10 + U3
    U11 = S10 - U3
    S10 = U10 + U8
    S12 = U10 - U8
    S14 = U11 + U9
    S16 = U11 - U9
C
    X(I( 1)) = R1 + R5
    X(I( 9)) = R1 - R5
    Y(I( 1)) = S1 + S5
    Y(I( 9)) = S1 - S5
    X(I( 2)) = R2 + S10
    X(I(16)) = R2 - S10
    Y(I( 2)) = S2 - R10
    Y(I(16)) = S2 + R10
    X(I( 3)) = R9 + S13
    X(I(15)) = R9 - S13
    Y(I( 3)) = S9 - R13
    Y(I(15)) = S9 + R13
    X(I( 4)) = R8 - S16
    X(I(14)) = R8 + S16
    Y(I( 4)) = S8 + R16
    Y(I(14)) = S8 - R16
    X(I( 5)) = R3 + S7
    X(I(13)) = R3 - S7
    Y(I( 5)) = S3 - R7
    Y(I(13)) = S3 + R7
    X(I( 6)) = R6 + S14
    X(I(12)) = R6 - S14
    Y(I( 6)) = S6 - R14
    Y(I(12)) = S6 + R14
    X(I( 7)) = R11 - S15
    X(I(11)) = R11 + S15
    Y(I( 7)) = S11 + R15
    Y(I(11)) = S11 - R15
    X(I( 8)) = R4 - S12
    X(I(10)) = R4 + S12
    Y(I( 8)) = S4 + R12
    Y(I(10)) = S4 - R12
C
    GOTO 20
C
 
Figure. Length-16 FFT Module

References

    Comments, questions, feedback, criticisms?

    Send feedback