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Chirp-Z Transform (G Dataflow)

Version:
    Last Modified: January 9, 2017

    Computes the Chirp-Z transform of a sequence. The Chirp-Z transform algorithm is also known as Bluestein's FFT algorithm.

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    x

    A real vector.

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

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    number of bins

    The length of the sequence after the Chirp-Z transform.

    If number of bins is less than or equal to 0, this node sets number of bins to the length of 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.

    Default: 1 + 0i

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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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    algorithm

    Transform method to use.

    Name Value Description
    direct 0 Computes the Chirp-Z transform using the direct form method. Use this method if the size of x or the number of bins is small.
    frequency domain 1 Computes the Chirp-Z transform using an FFT-based technique. Use this method if the size of x or the number of bins is large.

    Computing the Chirp-Z Transform Using the Direct Form Method

    The direct form method computes the Chirp-Z transform as follows:

    Y k = i = 0 N 1 x i ( A W k ) i

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

    where N is the length of X.

    Computing the Chirp-Z Transform Using the Frequency Domain Method

    The direct form can be reformulated with the convolution between gi and W i 2 / 2 as follows:

    Y k = W k 2 / 2 i = 0 N 1 g i W ( k i ) 2 / 2

    where g i = x i A i W i 2 / 2 . You can perform the convolution operation using an FFT-based technique.

    Default: frequency domain

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    chirp-z{x}

    The Chirp-Z transform of the input sequence.

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    error out

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

    Evaluating the Chirp-Z Transform Along a Spiral

    This node evaluates the z transform along a spiral in the z-plane at the following points:

    z k = A W k

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

    where

    • M is number of bins
    • A is starting point
    • W is increment

    The following illustration shows samples in the z-plane.

    You can use the Chirp-Z transform to calculate the FFT result. Set starting point and increment as follows:

    starting point = 1
    increment = e j 2 π N

    where N is the length of X. Let number of bins equal N. When the samples are evenly distributed on the unit circle, as shown in the following image, the Chirp-Z transform is the same as the fast Fourier transform (FFT).

    You also can use the Chirp-Z transform to calculate the partial FFT result. Set starting point and increment as follows:

    starting point = e j 2 π N s
    increment = e j 2 π N

    where s is the start bin and N is the length of X. This is useful when you are interested in only a small portion of a spectrum of a very long signal, as shown in the following image.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: Not supported


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