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Compute 2-D inverse discrete cosine transform (IDCT)
The 2-D IDCT block calculates the two-dimensional inverse discrete cosine transform of the input signal. The equation for the two-dimensional IDCT is
$$f(x,y)=\frac{2}{\sqrt{MN}}{\displaystyle \sum _{m=0}^{M-1}{\displaystyle \sum _{n=0}^{N-1}C(m)C(n)F(m,n)\mathrm{cos}\frac{(2x+1)m\pi}{2M}}}\mathrm{cos}\frac{(2y+1)n\pi}{2N}$$
where F(m,n) is the DCT of the signal f(x,y) and for $$m,n=0$$ and $$C(m),C(n)=1$$ otherwise.
The number of rows and columns of the input signal must be powers of two. The output of this block has dimensions the same dimensions as the input.
Port | Input/Output | Supported Data Types | Complex Values Supported |
---|---|---|---|
Input | Vector or matrix of intensity values |
| No |
Output | 2-D IDCT of the input | Same as Input port | No |
If the data type of the input signal is floating point, the output of the block is the same data type.
Use the Sine and cosine computation parameter to specify how the block computes the sine and cosine terms in the IDCT algorithm. If you select Trigonometric fcn, the block computes the sine and cosine values during the simulation. If you select Table lookup, the block computes and stores the trigonometric values before the simulation starts. In this case, the block requires extra memory.
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.
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, refer to Multiplication Data Types. You can set the sine table, product output, accumulator, and output data types in the block mask as discussed in the next section.
The Main pane of the 2-D IDCT dialog box appears as shown in the following figure.
Specify how the block computes the sine and cosine terms in the IDCT algorithm. If you select Trigonometric fcn, the block computes the sine and cosine values during the simulation. If you select Table lookup, the block computes and stores the trigonometric values before the simulation starts. In this case, the block requires extra memory.
The Data Types pane of the 2-D IDCT dialog box appears as shown in the following figure.
Select the Rounding Modes for fixed-point operations.
Select the Overflow mode for fixed-point operations. The sine table values do not obey this parameter; instead, they are always saturated.
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 Overflow mode parameters; instead, they are always saturated and rounded to Nearest.
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
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 for more information.
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
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 data type parameter.
See Specify Data Types Using Data Type Assistant for more information.
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:
$$W{L}_{idealoutput}=W{L}_{input}+floor({\mathrm{log}}_{2}(DCTlength-1))+1$$
$$F{L}_{idealoutput}=F{L}_{input}$$
Using these ideal results, the internal rule then selects word lengths and fraction lengths that are appropriate for your hardware. For more information, 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 data type parameter.
See Specify Data Types Using Data Type Assistant for more information.
Select this parameter to prevent any fixed-point scaling you specify in this block mask from being overridden by the autoscaling tool in the Fixed-Point Tool. For more information, see fxptdlg, a reference page on the Fixed-Point Tool in the Simulink^{®} documentation.
Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask. For more information, see fxptdlg, a reference page on the Fixed-Point Tool in the Simulink documentation.
[1] Chen, W.H, C.H. Smith, and S.C. Fralick, "A fast computational algorithm for the discrete cosine transform,"IEEE Trans. Commun., vol. COM-25, pp. 1004-1009. 1977.
[2] Wang, Z. "Fast algorithms for the discrete W transform and for the discrete Fourier transform," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 803-816, Aug. 1984.