Computes the Chirp-Z transform of the input sequence X. Wire data to the X input to determine the polymorphic instance to use or manually select the instance.

The Chirp-Z transform algorithm is also known as Bluestein's FFT algorithm.


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The Chirp Z Transform VI evaluates the z transform along a spiral in the z-plane at the following points:

zk = AW-k

for k = 0, 1, …, M–1

where M is the # of bins, A is the starting point, and W is the increment.

The following illustration shows samples in the z-plane.

Set A and W as follows:

A = 1 W =

where N is the length of X. Let M equal N. When M samples are evenly distributed on the unit circle, as shown in the following front panel, 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 A and W as follows:

A = W =

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 front panel.

You can use either the direct form method or the frequency domain method to calculate the Chirp-Z transform.

Direct Form Method

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

for k = 0, 1, …, M–1

where N is the length of X.

Frequency Domain Method

The direct form can be reformulated with the convolution between gi and W-i²/2 as follows:

where gi = xiA-iW-i²/2. You can perform the convolution operation using an FFT-based technique.

Examples

Refer to the following example files included with LabVIEW.

  • labview\examples\Signal Processing\Transforms\Spectrum using Chirp Z Transform.vi