Skip to content Skip to navigation

Connexions

You are here: Home » Content » Appendix: A 45 Point Circular Convolution Program

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

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.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Rice Digital Scholarship

    This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Automatic Generation of Prime Length FFT Programs"

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Automatic Generation of Prime Length FFT Programs"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • UniqU content

    This module is included inLens: UniqU's lens
    By: UniqU, LLCAs a part of collection: "Automatic Generation of Prime Length FFT Programs"

    Click the "UniqU content" link to see all content selected in this lens.

  • Lens for Engineering

    This module is included inLens: Lens for Engineering
    By: Sidney Burrus

    Click the "Lens for Engineering" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
Download
x

Download module as:

  • PDF
  • EPUB (what's this?)

    What is an EPUB file?

    EPUB is an electronic book format that can be read on a variety of mobile devices.

    Downloading to a reading device

    For detailed instructions on how to download this content's EPUB to your specific device, click the "(what's this?)" link.

  • More downloads ...
Reuse / Edit
x

Module:

Add to a lens
x

Add module to:

Add to Favorites
x

Add module to:

 

Appendix: A 45 Point Circular Convolution Program

Module by: Ivan Selesnick, C. Sidney Burrus. E-mail the authors

Appendix: A 45 Point Circular Convolution Program

As an example, we list a 45 point circular convolution program.

function y = cconv45(x,u)
% y = ccconv45(x,u)
% y : the 45 point circular convolution of x and h
% where u is a vector of precomputed multiplicative constants

x = pfp([9,5],2,x);                % prime factor permuation
x = KRED([3,5],[2,1],2,x);         % reduction operations (152 Additions)
y = zeros(45,1);
% -------------------- block : 1 -------------------------------------------------
y(1) = x(1)*u(1);             % 1 Multiplication
% -------------------- block : 3 -------------------------------------------------
v = ID2I(1,1,x(2:3));         % v = (I(1) kron D2 kron I(1)) * x(2:3)           a : 1=1*1
v = v.*u(2:4);                % 3 Multiplications
y(2:3) = ID2tI(1,1,v);        % y(2:3) = (I(1) kron D2' kron I(1)) * v          a : 2=1*2
% -------------------- block : 9 -------------------------------------------------
v = ID3I(2,1,x(4:9));         % v = (I(2) kron D3 kron I(1)) * x(4:9)           a : 14=2*7
v = ID2I(1,5,v);              % v = (I(1) kron D2 kron I(5)) * v                a : 5=5*1
v = v.*u(5:19);               % 15 Multiplications
v = ID2tI(1,5,v);             % v = (I(1) kron D2' kron I(5)) * v               a : 10=5*2
y(4:9) = ID3tI(2,1,v);        % y(4:9) = (I(2) kron D3' kron I(1)) * v          a : 18=2*9
% -------------------- block : 5 -------------------------------------------------
v = ID2I(1,2,x(10:13));       % v = (I(1) kron D2 kron I(2)) * x(10:13)         a : 2=2*1
v = ID2I(3,1,v);              % v = (I(3) kron D2 kron I(1)) * v                a : 3=3*1
v = v.*u(20:28);              % 9 Multiplications
v = ID2tI(1,3,v);             % v = (I(1) kron D2' kron I(3)) * v               a : 6=3*2
y(10:13) = ID2tI(2,1,v);      % y(10:13) = (I(2) kron D2' kron I(1)) * v        a : 4=2*2
% -------------------- block : 15 = 3 * 5 ----------------------------------------
v = ID2I(1,4,x(14:21));       % v = (I(1) kron D2 kron I(4)) * x(14:21)         a : 4=4*1
v = ID2I(3,2,v);              % v = (I(3) kron D2 kron I(2)) * v                a : 6=6*1
v = ID2I(9,1,v);              % v = (I(9) kron D2 kron I(1)) * v                a : 9=9*1
v = v.*u(29:55);              % 27 Multiplications
v = ID2tI(1,9,v);             % v = (I(1) kron D2' kron I(9)) * v               a : 18=9*2
v = ID2tI(2,3,v);             % v = (I(2) kron D2' kron I(3)) * v               a : 12=6*2
y(14:21) = ID2tI(4,1,v);      % y(14:21) = (I(4) kron D2' kron I(1)) * v        a : 8=4*2
% -------------------- block : 45 = 9 * 5 ----------------------------------------
v = ID3I(2,4,x(22:45));       % v = (I(2) kron D3 kron I(4)) * x(22:45)         a : 56=8*7
v = ID2I(1,20,v);             % v = (I(1) kron D2 kron I(20)) * v               a : 20=20*1
v = ID2I(15,2,v);             % v = (I(15) kron D2 kron I(2)) * v               a : 30=30*1
v = ID2I(45,1,v);             % v = (I(45) kron D2 kron I(1)) * v               a : 45=45*1
v = v.*u(56:190);             % 135 Multiplications
v = ID2tI(1,45,v);            % v = (I(1) kron D2' kron I(45)) * v              a : 90=45*2
v = ID2tI(10,3,v);            % v = (I(10) kron D2' kron I(3)) * v              a : 60=30*2
v = ID2tI(20,1,v);            % v = (I(20) kron D2' kron I(1)) * v              a : 40=20*2
y(22:45) = ID3tI(2,4,v);      % y(22:45) = (I(2) kron D3' kron I(4)) * v        a : 72=8*9

y = tKRED([3,5],[2,1],2,y);        % transpose reduction operations (152 Additions)
y = pfpt([9,5],2,y);               % prime factor permuation
y = y(45:-1:1);

% Total Number of Multiplications : 190
% Total Number of Additions: 839

References

    Content actions

    Download module as:

    PDF | EPUB (?)

    What is an EPUB file?

    EPUB is an electronic book format that can be read on a variety of mobile devices.

    Downloading to a reading device

    For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

    | More downloads ...

    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

    Lenses

    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

    Reuse / Edit:

    Reuse or edit module (?)

    Check out and edit

    If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

    Derive a copy

    If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.