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 MbyN 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
Input 1 — Input signal
vector  matrix  ND array
Specify the input signal as a vector, matrix, or an ND array.
For all ND 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 poweroftwo length.
When the input to the DCT block is an MbyN matrix, the block treats each input column as an independent channel containing M consecutive samples.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
 bus
Complex Number Support: Yes
Output
Output 1 — DCT output
vector  matrix  ND array
The block outputs the DCT of the input signal as a vector, matrix, or an ND array.
When the block outputs an MbyN matrix, the l^{th} column of the matrix contains the lengthM DCT of the corresponding input column.
$$y(k,l)=w(k){\displaystyle \sum _{m=1}^{M}u(m,l)\mathrm{cos}\frac{\pi (2m1)(k1)}{2M}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}k=1,\mathrm{...},M$$
where
$$w(k)=\{\begin{array}{c}\frac{1}{\sqrt{M}},\\ \sqrt{\frac{2}{M}},\end{array}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\begin{array}{c}\begin{array}{l}k=1\\ \end{array}\\ 2\le k\le M\end{array}$$
When the input is fixedpoint (signed and unsigned), the output is signed fixedpoint.
Data Types: single
 double
 int8
 int16
 int32
 fixed point
 bus
Complex Number Support: Yes
Parameters
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 speedoptimized 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 speedoptimized 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 fixedpoint 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
fixedpoint operation. When you clear this parameter, the block wraps
the result of its fixedpoint operation. For details on
saturate
and wrap
, see overflow
mode for fixedpoint 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 fullprecision mode.
Sine table — Sine table
Inherit: Same word length as
input
(default)  fixd(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
 fixd(1,16,0)
Specify the product output data type. See FixedPoint 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
 fixd(1,16,0)
Specify the accumulator data type. See FixedPoint 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
 fixd(1,16,0)
Specify the output data type. See FixedPoint 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:$$W{L}_{idealoutput}=W{L}_{input}+floor({\mathrm{log}}_{2}(DCTlength1))+1$$
$$F{L}_{idealoutput}=F{L}_{input}$$
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 fixedpoint 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 fixedpoint data types
Lock data type settings against changes by the fixedpoint tools — Prevent fixedpoint tools from overriding data types
off
(default)  on
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify in the block dialog box.
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

More About
FixedPoint Data Types
The following diagrams show the data types used within the DCT block for fixedpoint 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 nonrecursive.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
Version History
Introduced before R2006a
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