DCT
Discrete cosine transform (DCT) of input
Library
Transforms
dspxfrm3
Description
The DCT block computes the unitary discrete cosine transform (DCT) of each channel in the MbyN input matrix, u.
y = dct(u) % Equivalent MATLAB code
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. The block outputs an MbyN matrix whose lth column 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
$$w(k)=\{\begin{array}{c}\frac{1}{\sqrt{M}},\\ \sqrt{\frac{2}{M}},\end{array}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\begin{array}{c}\begin{array}{l}k=1\\ \end{array}\\ 2\le k\le M\end{array}$$
The Sine and cosine computation parameter determines how the block computes the necessary sine and cosine values. This parameter has two settings, each with its advantages and disadvantages, as described in the following table.
Sine and Cosine Computation Parameter Setting  Sine and Cosine Computation Method  Effect on Block Performance 

 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 usually runs much more quickly, but requires extra memory for storing the precomputed trigonometric values. 
 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 usually 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. 
This block supports Simulink^{®} virtual buses.
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 DCT block dialog as discussed in Parameters.
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.
Parameters
Main Tab
 Sine and cosine computation
Sets 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
). See the table in the Description section.
Data Types Tab
 Rounding mode
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
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
andwrap
, see overflow mode for fixedpoint operations.Note
The Rounding mode and Saturate on integer overflow parameters have no effect on numeric results when all 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
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; instead, they are always saturated and rounded to
Nearest
. Product output data type
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
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
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
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
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
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on the block mask.
Supported Data Types
Port  Supported Data Types 

Input 

Output 

Extended Capabilities
Version History
Introduced before R2006a