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Inverse DCT (G Dataflow)

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    Last Modified: January 9, 2017

    Computes the inverse Discrete Cosine Transform (DCT) of a sequence.

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    DCT{x}

    The real input sequence.

    This input can be a 1D or 2D array of double-precision, floating-point numbers.

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    error in

    Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

    Default: No error

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    x

    The inverse DCT of the real input sequence.

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    error out

    Error information. The node produces this output according to standard error behavior.

    Algorithm Definition for 1D Inverse DCT

    If y represents a 1D array as the input sequence DCT{x}, the one-dimensional inverse Discrete Cosine Transform of y is defined as:

    x n = 2 N ∑ k = 0 N − 1 α k y k cos ( 2 n + 1 ) k π 2 N

    and

    α k = { 1 2 ⁢                         k = 0 1 ⁢                         k = 1 ,   2 ,   ... ,   N − 1

    where

    • N is the length of DCT{x}
    • yk is the kth element of DCT{x}
    • xn is the nth element of x

    This node applies a fast inverse DCT algorithm instead of calculating the inverse Discrete Cosine Transform directly. This node implements the fast inverse DCT algorithm using an FFT-based technique.

    Algorithm Definition for 2D Inverse DCT

    If y represents a 2D array as the input sequence DCT{x}, the two-dimensional inverse Discrete Cosine Transform of y is defined as:

    x ( m , n ) = 2 M 2 N ∑ u = 0 M − 1 ∑ v = 0 N − 1 α u α v y ( u , v ) cos ( 2 m + 1 ) u π 2 M cos ( 2 n + 1 ) v π 2 N

    where

    • M is the number of rows of DCT{x}
    • N is the number of columns of DCT{x}
    • x(m, n) is the element of x with row number m and column number n
    • y(u, v) is the element of DCT{x} with row number u and column number v

    This node performs a two-dimensional inverse DCT using the following two steps:

    1. Perform a one-dimensional inverse DCT row-by-row on DCT{x}. The output is Y'.
    2. Perform a one-dimensional inverse DCT column-by-column on Y'. The output is x.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: Not supported

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