Computes the Chirp-Z transform of a sequence. The Chirp-Z transform algorithm is also known as Bluestein's FFT algorithm.
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.
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
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
The increment between each point to evaluate for the Chirp-Z transform.
increment cannot be 0.
Default: 1 + 0i
Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
Default: No error
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:
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 g _{ i } and ${W}^{-{i}^{2}/2}$ as follows:
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
The Chirp-Z transform of the input sequence.
Error information.
The node produces this output according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
This node evaluates the z transform along a spiral in the z-plane at the following points:
for k = 0, 1, ..., M-1
where
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:
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:
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
Web Server: Not supported in VIs that run in a web application