DCT

Discrete cosine transform (DCT) of input

Libraries:
DSP System Toolbox / Transforms

Description

The DCT block computes the unitary discrete cosine transform (DCT) of the input signal u. When the input is an M-by-N matrix, the block computes the DCT of each channel in the matrix.

Here is the equivalent MATLAB^® code.

y = dct(u)

This block supports Simulink^® virtual buses.

Ports

Input

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Input 1 — Input signal
vector | matrix | N-D array

Specify the input signal as a vector, matrix, or an N-D array.

For all N-D input arrays, the block computes the DCT across the first dimension. The size of the first dimension (frame size) must be a power of two. To work with other frame sizes, use the Pad block to pad or truncate the frame size to a power-of-two length.

When the input to the DCT block is an M-by-N matrix, the block treats each input column as an independent channel containing M consecutive samples.

Output

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Output 1 — DCT output
vector | matrix | N-D array

The block outputs the DCT of the input signal as a vector, matrix, or an N-D array.

When the block outputs an M-by-N matrix, the l^th column of the matrix contains the length-M DCT of the corresponding input column.

$y (k, l) = w (k) \sum_{m = 1}^{M} u (m, l) \cos \frac{π (2 m - 1) (k - 1)}{2 M}, k = 1, ..., M$

where

$w (k) = {\begin{matrix} \frac{1}{\sqrt{M}}, \\ \sqrt{\frac{2}{M}}, \end{matrix} \begin{matrix} \begin{array}{l} k = 1 \end{array} \\ 2 \leq k \leq M \end{matrix}$

When the input is fixed-point (signed and unsigned), the output is signed fixed-point.

Data Types: single | double | int8 | int16 | int32 | fixed point | bus
Complex Number Support: Yes

Parameters

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Main Tab

Sine and cosine computation — Sine and cosine computation
`Table lookup` (default) | `Trigonometric fcn`

Set the block to compute sines and cosines by either looking up sine and cosine values in a speed-optimized table (Table lookup), or by making sine and cosine function calls (Trigonometric fcn).

To compute sines and cosines, set the parameter to one of these values:

Table lookup –– The block computes and stores the trigonometric values before the simulation starts, and retrieves them during the simulation. When you generate code from the block, the processor running the generated code stores the trigonometric values computed by the block in a speed-optimized table, and retrieves the values during code execution.
The block runs much more quickly, but requires extra memory for storing the precomputed trigonometric values.
Trigonometric fcn –– The block computes sine and cosine values during the simulation. When you generate code from the block, the processor running the generated code computes the sine and cosine values while the code runs.
The block runs more slowly, but does not need extra data memory. For code generation, the block requires a support library to emulate the trigonometric functions, increasing the size of the generated code.

Data Types Tab

Rounding mode — Rounding mode
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

Select the rounding mode for fixed-point operations. The sine table values do not obey this parameter; they always round to Nearest.

Saturate on integer overflow — Saturate on integer overflow
`off` (default) | `on`

When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details on saturate and wrap, see overflow mode for fixed-point operations.

Note

The Rounding mode and Saturate on integer overflow parameters have no effect on numeric results when these conditions are met:

Product output data type is Inherit: Inherit via internal rule.
Accumulator data type is Inherit: Inherit via internal rule.

With these data type settings, the block operates in full-precision mode.

Sine table — Sine table
`Inherit: Same word length as input` (default) | `fixdt(1,16)`

Choose how you specify the word length of the values of the sine table. The fraction length of the sine table values always equals the word length minus one. You can set this parameter to:

A rule that inherits a data type, for example, Inherit: Same word length as input
An expression that evaluates to a valid data type, for example, fixdt(1,16)

The sine table values do not obey the Rounding mode and Saturate on integer overflow parameters. The block always saturates and rounds off the sine table values to Nearest.

Product output — Product output
`Inherit: Inherit via internal rule` (default) | `Inherit: Same as input` | `fixdt(1,16,0)`

Specify the product output data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set this parameter to:

A rule that inherits a data type, for example, Inherit: Inherit via internal rule. For more information on this rule, see Inherit via Internal Rule.
An expression that evaluates to a valid data type, for example, fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output data type parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Accumulator — Accumulator
`Inherit: Inherit via internal rule` (default) | `Inherit: Same as input` | `Inherit: Same as product output` | `fixdt(1,16,0)`

Specify the accumulator data type. See Fixed-Point Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

A rule that inherits a data type, for example, Inherit: Inherit via internal rule. For more information on this rule, see Inherit via Internal Rule.
An expression that evaluates to a valid data type, for example, fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Output — Data type of output
`Inherit: Inherit via internal rule` (default) | `Inherit: Same as input` | `fixdt(1,16,0)`

Specify the output data type. See Fixed-Point Data Types for illustrations depicting the use of the output data type in this block. You can set this parameter to:

A rule that inherits a data type, for example, Inherit: Inherit via internal rule.
When you select Inherit: Inherit via internal rule, the block calculates the output word length and fraction length automatically. The internal rule first calculates an ideal output word length and fraction length using the following equations:
$W L_{i d e a l o u t p u t} = W L_{i n p u t} + f l o o r (\log_{2} (D C T l e n g t h - 1)) + 1$
$F L_{i d e a l o u t p u t} = F L_{i n p u t}$
Using these ideal results, the internal rule then selects word lengths and fraction lengths that are appropriate for your hardware. For more information on this rule, see Inherit via Internal Rule.
An expression that evaluates to a valid data type, for example, fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.

See Control Data Types of Signals (Simulink) for more information.

Output Minimum — Output minimum
`[]` (default) | scalar

Specify the minimum value that the block should output. The default value is [] (unspecified). Simulink software uses this value to perform:

Simulation range checking (see Specify Signal Ranges (Simulink))
Automatic scaling of fixed-point data types

Output Maximum — Output maximum
`[]` (default) | scalar

Specify the maximum value that the block should output. The default value is [] (unspecified). Simulink software uses this value to perform:

Simulation range checking (see Specify Signal Ranges (Simulink))
Automatic scaling of fixed-point data types

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in the block dialog box.

Block Characteristics

Data Types	`bus` \| `double` \| `fixed point` \| `integer` \| `single`
Direct Feedthrough	`no`
Multidimensional Signals	`yes`
Variable-Size Signals	`no`
Zero-Crossing Detection	`no`

More About

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Fixed-Point Data Types

The following diagrams show the data types used within the DCT block for fixed-point signals. You can set the sine table, accumulator, product output, and output data types displayed in the diagrams in the block parameters dialog box of the DCT block.

Inputs to the DCT block 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.

The output of the multiplier is in the product output data type when at least one of the inputs to the multiplier is real. When both of the inputs to the multiplier are complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed, see Multiplication Data Types.

Note

When the block input is fixed point, all internal data types are signed fixed point.

Extended Capabilities

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

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

To comply with the embedded systems coding standards, generated code is non-recursive.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced before R2006a

DCT

Description