Chirp Z Transform VI

Owning Palette: Transforms VIs

Requires: Full Development System

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.

Details  Example

Use the pull-down menu to select an instance of this VI.

Select an instance Chirp Z Transform (DBL)Chirp Z Transform (CDB)

Add to the block diagram

Find on the palette

Chirp Z Transform (DBL)

	X is a real vector.
	# of bins determines the length of Chirp-Z {X}. If # of bins is less than or equal to 0, this VI sets # of bins to the length of X.
	starting point is the point at which to begin evaluating the Chirp-Z transform and is best described by the equation in the details section. If starting point is 0, the VI returns an error.
	increment is the increment between each point to evaluate for the Chirp-Z transform. increment cannot be 0.
	algorithm specifies the transform method to use. When algorithm is direct, this VI computes the Chirp-Z transform using the direct form method. When algorithm is frequency domain, this VI computes the Chirp-Z transform using an FFT-based technique. If the size of X or the # of bins is small, the direct method is faster. If the size of X or the # of bins is large, the frequency domain method is faster.
	Chirp-Z {X} is the Chirp-Z transform of the input sequence X. # of bins determines the length of Chirp-Z {X}. If # of bins is less than or equal to 0, Chirp-Z {X} has the same length as X.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Chirp Z Transform (CDB)

	X is the complex valued input sequence.
	# of bins determines the length of Chirp-Z {X}. If # of bins is less than or equal to 0, this VI sets # of bins to the length of X.
	starting point is the point at which to begin evaluating the Chirp-Z transform and is best described by the equation in the details section. If starting point is 0, the VI returns an error.
	increment is the increment between each point to evaluate for the Chirp-Z transform. increment cannot be 0.
	algorithm specifies the transform method to use. When algorithm is direct, this VI computes the Chirp-Z transform using the direct form method. When algorithm is frequency domain, this VI computes the Chirp-Z transform using an FFT-based technique. If the size of X or the # of bins is small, the direct method is faster. If the size of X or the # of bins is large, the frequency domain method is faster.
	Chirp-Z {X} is the Chirp-Z transform of the input sequence X. # of bins determines the length of Chirp-Z {X}. If # of bins is less than or equal to 0, Chirp-Z {X} has the same length as X.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Chirp Z Transform Details

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

z_k = 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 g_i and W^-i2/2 as follows:

where g_i = x_iA^-iW^-i2/2. You can perform the convolution operation using an FFT-based technique.

Example

Refer to the Spectrum using Chirp Z Transform VI in the labview\examples\Signal Processing\Transforms directory for an example of using the Chirp Z Transform VI.

 Open example  Find related examples