https://github.com/stevengj/mdct.jl

fast modified discrete cosine transform (MDCT and IMDCT) for the Julia language
https://github.com/stevengj/mdct.jl

fft fourier-transform julia math mdct

Last synced: 3 months ago
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fast modified discrete cosine transform (MDCT and IMDCT) for the Julia language

• Host: GitHub
• URL: https://github.com/stevengj/mdct.jl
• Owner: stevengj
• License: mit
• Created: 2013-04-05T16:39:44.000Z (almost 12 years ago)
• Default Branch: master
• Last Pushed: 2021-11-02T22:52:59.000Z (about 3 years ago)
• Last Synced: 2024-08-11T13:56:27.843Z (5 months ago)
• Topics: fft, fourier-transform, julia, math, mdct
• Language: Julia
• Size: 23.4 KB
• Stars: 10
• Watchers: 4
• Forks: 5
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

        
# MDCT module for Julia

[![Build Status](https://github.com/stevengj/MDCT.jl/workflows/CI/badge.svg)](https://github.com/stevengj/MDCT.jl/actions)

This module computes the modified discrete cosine transform (MDCT) in

the Julia language and the inverse transform (IMDCT), using the fast

type-IV discrete cosine tranform (DCT-IV) functions in the

[FFTW.jl package](https://github.com/JuliaMath/FFTW.jl).

Definitions of the MDCT and IMDCT can be found, for example in the

[Wikipedia MDCT

article](http://en.wikipedia.org/wiki/Modified_discrete_cosine_transform).

The MDCT is a linear transformation that takes 2N inputs and produces

N outputs, which is designed to be applied to a sequence of

50%-overlapping blocks of a longer sequence (e.g. audio samples).

Because this is non-square (fewer outputs than inputs), the IMDCT is

not an "inverse" transformation in the usual sense; it only recovers

the original data when IMDCTs of overlapping blocks are added (by

"time-domain aliasing cancellation").

## Installation

Within Julia, just use the package manager to run

`Pkg.add("MDCT")` to install the files.

## Usage

To use the MDCT functions, simply do

    using MDCT

    Y = mdct(X)

    Z = imdct(Y)

where `X` is any numeric `AbstractVector` (1d array).  Currently, the

length of `X` must be a multiple of 4.

For example, suppose we make a random vector `X` of length 1000 and

consider 50%-overlapping blocks of length 100 (`X[1:100]`,

`X[51:150]`, `X[101:200]`, and so on).  If we perform the MDCT of two

such blocks, then the IMDCT, and then add the overlapping halves of

the IMDCT outputs, we recover that portion of the original data:

    X = rand(1000)

    Y1 = mdct(X[1:100])

    Y2 = mdct(X[51:150])

    Z1 = imdct(Y1)

    Z2 = imdct(Y2)

    norm(Z1[51:100] + Z2[1:50] - X[51:100])

where the last line computes the difference between the overlapped

IMDCT sum and the original data, and should be around

10−15 (floating-point roundoff error).

## Planning

To create a pre-planned transforms for a given size of input vector

do:

    using MDCT

    Mp = plan_mdct(X)

    Ip = plan_imdct(Y)

where `Ip` and `Mp` are pre-planned transforms optimized to allow much

quicker subsequent transformations. To use them simply:

    Xt = Mp*X

    Yt = Ip*Y

## Author

This module was written by [Steven G. Johnson](http://math.mit.edu/~stevenj/).