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Inverse Chirp-Z Transform (G Dataflow)

Version:
    Last Modified: January 9, 2017

    Computes the inverse Chirp-Z transform of a sequence.

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    chirp-z{x}

    The complex valued input sequence.

    The length of chirp-z{x} must be greater than or equal to number of samples.

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    number of samples

    Length of the sequence after the inverse Chirp-Z transform.

    number of samples must be less than or equal to the length of chirp-z{x}. If number of samples is less than or equal to 0, the node sets number of samples to the length of chirp-z{x}.

    Default: -1

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    starting point

    The point at which this node begins evaluating the Chirp-Z transform.

    If starting point is 0, the node returns an error.

    Default: 1 + 0i

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    increment

    The increment between each point to evaluate for the Chirp-Z transform.

    increment cannot be 0.

    Avoiding Singular Cases of the Inverse Chirp-Z Transform

    To avoid singular cases of the inverse Chirp-Z transform, increment must be different from where and N is number of samples.

    Default: 1 + 0.1i

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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 Chirp-Z transform of the complex valued input sequence.

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    error out

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

    Algorithm for Computing the Inverse Chirp-Z Transform

    If Y represents the input sequence chirp-z{x}, the following equation shows how this node performs the Chirp-Z transform to obtain the output sequence x:

    y k = n = 0 N 1 x n ( A W k ) n

    for k=0, 1, ..., M-1

    where

    • N is the length of x (number of samples)
    • M is the length of chirp-z{x}
    • A is the starting point
    • W is the increment
    • Xn is the nth element of x
    • Yk is the kth element of chirp-z{x}

    Implementing the Inverse Chirp-Z Transform Using a Convolution-Based Method

    This node employs a convolution-based method to implement the inverse Chirp-Z transform according to the following equations.

    x n = h n × m n

    with

    h n = { k = 0 N 1 C k y k z k n n 0 0 n < 0

    where

    C 0 = p = 1 N 1 1 / ( 1 W P )
    C k / C k 1 = ( 1 W k W N ) / ( 1 W k )
    k = 1 , 2 , ... , N 1
    z k = 0 , 1 , ... , N 1

    mn can be obtained from its z-transform M(z):

    M ( z ) = p = 0 N 1 ( 1 z p z 1 )

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: Not supported


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