2-D IDCT

Compute 2-D inverse discrete cosine transform (IDCT)

Libraries:
Computer Vision Toolbox / Transforms

Description

The 2-D IDCT block calculates the two-dimensional inverse discrete cosine transform of the input signal. The equation for the two-dimensional IDCT of an input signal is:

$f (x, y) = \frac{2}{\sqrt{M N}} \sum_{m = 0}^{M - 1} \sum_{n = 0}^{N - 1} C (m) C (n) F (m, n) \cos \frac{(2 x + 1) m π}{2 M} \cos \frac{(2 y + 1) n π}{2 N},$

where F(m,n) is the discrete cosine transform (DCT) of the signal f(x,y). If $m = n = 0$ , then $C (m) = C (n) = 1 / \sqrt{2}$ . Otherwise $C (m) = C (n) = 1$ .

Examples

Compress Image Using 2-D DCT

Compress an image using a 2-D discrete cosine transform (DCT). The example computes the 2-D DCT of 8-by-8 nonoverlapping blocks of the input image, discards (sets to zero) all but 10 of the 64 DCT coefficients in each block, and then reconstructs the image using the 2-D inverse discrete cosine transform (IDCT) of each block.

Open Script

Ports

Input

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Port_1 — Input data
matrix | vector

Specify input data as a vector or matrix of intensity values. The number of elements in the input data must be a power of two.

Output

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Port_1 — Output data
matrix | vector

Output data containing the 2-D IDCT of the input, returned as a matrix or vector. The size and data type of the output are the same as those of the input.

Parameters

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Main

Sine and cosine computation — How the block computes sine and cosine terms
`Table lookup` (default) | `Trigonometric fcn`

Specify how the block computes the sine and cosine terms to find the 2-D IDCT.

Table lookup — The block computes and stores the trigonometric values before the simulation starts. This option requires more memory than the Trigonometric fcn option.
Trigonometric fcn — The block computes the sine and cosine values during the simulation.

Data Types

For details on the fixed-point block parameters, see Specify Fixed-Point Attributes for Blocks (DSP System Toolbox).

Lock data type settings against change by the fixed-point tools — Data type override
`off` (default) | `on`

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in this block. For more information, see Lock the Output Data Type Setting (Fixed-Point Designer).

Block Characteristics

Data Types	`double` \| `fixed point` \| `integer` \| `single`
Multidimensional Signals	`no`
Variable-Size Signals	`no`

More About

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Fixed-Point Data Types

The following diagram shows the data types used in the 2-D IDCT block for fixed-point signals. Inputs are first cast to the output data type and stored in the output buffer. Each butterfly stage processes signals in the accumulator data type, with the final output of the butterfly being cast back into the output data type.

When at least one of the inputs to the multiplier is real, the output of the multiplier is in the product output data type. When both of the inputs to the multiplier are complex, the multiplication result is in the accumulator data type. For more information on the multiplication of real and complex numbers, see Multiplication Data Types.

References

[1] Wen-Hsiung Chen, C. Smith, and S. Fralick. “A Fast Computational Algorithm for the Discrete Cosine Transform.” IEEE Transactions on Communications 25, no. 9 (September 1977): 1004–9. https://doi.org/10.1109/TCOM.1977.1093941.

[2] Zhongde Wang. “Fast Algorithms for the Discrete W Transform and for the Discrete Fourier Transform.” IEEE Transactions on Acoustics, Speech, and Signal Processing 32, no. 4 (August 1984): 803–16. https://doi.org/10.1109/TASSP.1984.1164399.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a

2-D IDCT

Description