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Inverse DST (G Dataflow)

Version:
    Last Modified: January 9, 2017

    Computes the inverse Discrete Sine Transform (DST) of a sequence.

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    DST{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 DST 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 DST

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

    x n = 2 N + 1 k = 0 N 1 y k sin π ( k + 1 ) ( n + 1 ) N + 1

    where

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

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

    Algorithm Definition for 2D Inverse DST

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

    x ( m , n ) = 2 M + 1 2 N + 1 u = 0 M 1 v = 0 N 1 y ( u , v ) sin π ( u + 1 ) ( u + 1 ) N + 1 sin π ( v + 1 ) ( v + 1 ) M + 1

    where

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

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

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

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: Not supported


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