Engee documentation

idct

Inverse discrete cosine transform.

Library

EngeeDSP

Syntax

Function call

  • x = idct(y) — returns the inverse discrete cosine transform of the input array y. Size of the output array x matches the size of y. If y it has several dimensions, the function idct performs an operation on the first dimension of an array, the size of which is larger 1.

  • x = idct(y,n) — adds zeros or truncates the corresponding dimension y up to length n before the conversion.

Arguments

Input arguments

# y is the input discrete cosine transform

+ vector | the matrix | An N-dimensional array

Details

The input discrete cosine transform, defined as a vector, matrix, or N-dimensional array with real or complex values.

Типы данных

Float32, Float64
Support for complex numbers

Yes

# n is the length of the inverse transformation

+ a positive integer scalar

Details

The length of the inverse transformation, specified as a positive integer scalar.

Типы данных

Float32, Float64

Output arguments

# x is the inverse discrete cosine transform

+ vector | the matrix | An N-dimensional array

Details

The inverse discrete cosine transform, returned as a real or complex vector, matrix, or N-dimensional array.

Examples

Signal recovery using the inverse discrete cosine transform

Details

We will generate a signal consisting of a sine wave with a frequency of 25 Hz, sampled with frequency 1000 Hz during 1 seconds. White Gaussian noise with variance is added to the sine wave 0.01.

import EngeeDSP.Functions: randn

using Random
Random.seed!(1234)

Fs = 1000
t = 0:1/Fs:1-1/Fs
x = sin.(2π * 25 * t) + randn(length(t), 1) / 10

Let’s calculate the discrete cosine transformation (DCT) of the sequence. Let’s determine how many of 1000 The PREP coefficients are significant. Let’s choose a threshold of significance 1.

import EngeeDSP.Functions: dct

y = dct(x)

sigcoeff = abs.(y) .>= 1

howmany = sum(sigcoeff)
17

Reconstruct the signal using only significant components.

import EngeeDSP.Functions: idct

y[.!sigcoeff] .= 0

z = idct(y)

Let’s plot the original and reconstructed signals.

p1 = plot(t, x, title = "Original")
yl = ylims(p1)

p2 = plot(t, z, title = "Reconstructed")
ylims!(p2, yl)

plot(p1, p2, layout = (2, 1), legend = false)

idct

Additional Info

Inverse discrete cosine transform

Details

The inverse discrete cosine transform reconstructs the sequence from its coefficients of the discrete cosine transform (DCT). Function idct is the inverse of the function dct.

PREP has four standard options. Only the DKP-2 type is implemented for this function. For the converted signal lengths and the Kronecker symbol The inverse transformations are defined as follows:

  • Reverse PREP-1:

  • Reverse PREP-2:

  • Reverse PREP-3:

  • Reverse PREP-4:

The rows are indexed from and instead of the usual ones and since the Engee vectors vary from before , not from before .

All PREP variants are unitar (or, equivalently, _orthogonal): to find direct transformations, swap and in every definition. DKP-1 and DKP-4 are the opposite of each other. DKP-2 and DKP-3 are the opposite of each other.

Literature

  1. Jain, A. K. Fundamentals of Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.

  2. Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. 2nd Ed. Upper Saddle River, NJ: Prentice Hall, 1999.

  3. Pennebaker, W. B., and J. L. Mitchell. JPEG Still Image Data Compression Standard. New York: Van Nostrand Reinhold, 1993.