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Owning Palette: Continuous Wavelet VIs

Installed With: Advanced Signal Processing Toolkit

Uses the complex Morlet wavelet to compute the continuous wavelet transform of a 1D input signal. Wire data to the signal input to determine the polymorphic instance to use or manually select the instance.

The analytic wavelet transform also is known as the complex wavelet transform.

Details  Example

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

Select an instance WA Analytic Wavelet Transform (waveform)WA Analytic Wavelet Transform (array)

WA Analytic Wavelet Transform (waveform)

	normalization specifies how to scale the dilated wavelets. 0 energy (default)—Specifies that the wavelets have a unified energy in all scales. 1 amplitude—Specifies that wavelets at different scales have the same maximum amplitude of frequency response.
	time steps specifies the number of samples to translate, or shift, the wavelet in the analytic wavelet transform. The default is –1, which specifies that this VI adjusts time steps automatically so that no more than 512 coefficients exist at each scale. The number of rows in the output wavelet coefficients equals the signal length divided by time steps.National Instruments recommends that you set time steps such that the number of rows in the wavelet coefficients does not exceed 512. If you specify a small value for time steps, this VI might return a large number of wavelet coefficients, which requires a long computation time and more memory. If you need a small time step to observe more details and the signal length is large, divide the signal into smaller segments and compute the wavelet coefficients for each segment. If the signal is oversampled, you can downsample the signal. time steps must be greater than 0, or this VI sets time steps to the default value –1 automatically.
	signal specifies the input signal.
	scales specifies the number of scales of the dilated wavelet.
	scale sampling method specifies the method to use to select the scales of the wavelets. scale sampling method affects the mapping style of the y-axis of the scalogram. Use the user defined scales input to specify a customized scale. 0 even freq (default)—The center frequencies of the wavelets at the analyzed scales have evenly sampled the frequency range from 0 to fs/2. The central frequency of a wavelet is inversely proportional to the scale. The resulting scalogram is a kind of joint time-frequency representation with an adaptive time-frequency resolution. 1 even scale—The VI computes the continuous wavelet transform at positive integer scales 1, 2, 3, ..., scales.
	error in describes error conditions that occur before this VI or function runs. The default is no error. If an error occurred before this VI or function runs, the VI or function passes the error in value to error out. This VI or function runs normally only if no error occurred before this VI or function runs. If an error occurs while this VI or function runs, it runs normally and sets its own error status in error out. Use the Simple Error Handler or General Error Handler VIs to display the description of the error code. Use error in and error out to check errors and to specify execution order by wiring error out from one node to error in of the next node. status is TRUE (X) if an error occurred before this VI or function ran or FALSE (checkmark) to indicate a warning or that no error occurred before this VI or function ran. The default is FALSE. code is the error or warning code. The default is 0. If status is TRUE, code is a nonzero error code. If status is FALSE, code is 0 or a warning code. source specifies the origin of the error or warning and is, in most cases, the name of the VI or function that produced the error or warning. The default is an empty string.
	user defined scales specifies the scales to use to compute AWT coef. The scale must be positive and no greater than the length of signal. If you specify a value for user defined scales, the VI ignores the settings in the scale sampling method input and the scales input.
	AWT coef returns the results of the analytic wavelet transform. The element in the ith column and the jth row is the result of the analytic wavelet transform at the (i+1)th scale with a translation of j×time steps. When you use user defined scales to define the scales of the analytic wavelet transform, the element in the ith column and the jth row is the result of the analytic wavelet transform, where scale (a) equals the ith element of user defined scales and shift () equals j×time steps. The squared magnitude of AWT coef is the scalogram, which jointly represents a signal in terms of time and scale. Large scales correspond to low frequencies, and small scales correspond to high frequencies. Use the WA Scalogram Indicator to display the scalogram on an intensity graph.
	scale info returns the time information and the scale (frequency) information, which the VI uses in the scalogram plot.
	error out contains error information. If error in indicates that an error occurred before this VI or function ran, error out contains the same error information. Otherwise, it describes the error status that this VI or function produces. Right-click the error out front panel indicator and select Explain Error from the shortcut menu for more information about the error. status is TRUE (X) if an error occurred or FALSE (checkmark) to indicate a warning or that no error occurred. code is the error or warning code. If status is TRUE, code is a nonzero error code. If status is FALSE, code is 0 or a warning code. source describes the origin of the error or warning and is, in most cases, the name of the VI or function that produced the error or warning.

WA Analytic Wavelet Transform (array)

	normalization specifies how to scale the dilated wavelets. 0 energy (default)—Specifies that the wavelets have a unified energy in all scales. 1 amplitude—Specifies that wavelets at different scales have the same maximum amplitude of frequency response.
	time steps specifies the number of samples to translate, or shift, the wavelet in the analytic wavelet transform. The default is –1, which specifies that this VI adjusts time steps automatically so that no more than 512 coefficients exist at each scale. The number of rows in the output wavelet coefficients equals the signal length divided by time steps. National Instruments recommends that you set time steps such that the number of rows in the wavelet coefficients does not exceed 512. If you specify a small value for time steps, this VI might return a large number of wavelet coefficients, which requires a long computation time and more memory. If you need a small time step to observe more details and the signal length is large, divide the signal into smaller segments and compute the wavelet coefficients for each segment. If the signal is oversampled, you can downsample the signal. time steps must be greater than 0, or this VI sets time steps to the default value –1 automatically.
	signal specifies the input signal.
	scales specifies the number of scales of the dilated wavelet.
	scale sampling method specifies the method to use to select the scales of the wavelets. scale sampling method affects the mapping style of the y-axis of the scalogram. Use the user defined scales input to specify a customized scale. 0 even freq (default)—The center frequencies of the wavelets at the analyzed scales have evenly sampled the frequency range from 0 to fs/2. The central frequency of a wavelet is inversely proportional to the scale. The resulting scalogram is a kind of joint time-frequency representation with an adaptive time-frequency resolution. 1 even scale—The VI computes the continuous wavelet transform at positive integer scales 1, 2, 3, ..., scales.
	error in describes error conditions that occur before this VI or function runs. The default is no error. If an error occurred before this VI or function runs, the VI or function passes the error in value to error out. This VI or function runs normally only if no error occurred before this VI or function runs. If an error occurs while this VI or function runs, it runs normally and sets its own error status in error out. Use the Simple Error Handler or General Error Handler VIs to display the description of the error code. Use error in and error out to check errors and to specify execution order by wiring error out from one node to error in of the next node. status is TRUE (X) if an error occurred before this VI or function ran or FALSE (checkmark) to indicate a warning or that no error occurred before this VI or function ran. The default is FALSE. code is the error or warning code. The default is 0. If status is TRUE, code is a nonzero error code. If status is FALSE, code is 0 or a warning code. source specifies the origin of the error or warning and is, in most cases, the name of the VI or function that produced the error or warning. The default is an empty string.
	user defined scales specifies the scales to use to compute AWT coef. The scale must be positive and no greater than the length of signal. If you specify a value for user defined scales, the VI ignores the settings in the scale sampling method input and the scales input.
	sampling rate specifies the sampling rate of signal in hertz. sampling rate must be greater than 0, or the VI sets sampling rate to 1 automatically.
	AWT coef returns the results of the analytic wavelet transform. The element in the ith column and the jth row is the result of the analytic wavelet transform at the (i+1)th scale with a translation of j×time steps. When you use user defined scales to define the scales of the analytic wavelet transform, the element in the ith column and the jth row is the result of the analytic wavelet transform, where scale (a) equals the ith element of user defined scales and shift () equals j×time steps. The squared magnitude of AWT coef is the scalogram, which jointly represents a signal in terms of time and scale. Large scales correspond to low frequencies, and small scales correspond to high frequencies. Use the WA Scalogram Indicator to display the scalogram on an intensity graph.
	scale info returns the time information and the scale (frequency) information, which the VI uses in the scalogram plot.
	error out contains error information. If error in indicates that an error occurred before this VI or function ran, error out contains the same error information. Otherwise, it describes the error status that this VI or function produces. Right-click the error out front panel indicator and select Explain Error from the shortcut menu for more information about the error. status is TRUE (X) if an error occurred or FALSE (checkmark) to indicate a warning or that no error occurred. code is the error or warning code. If status is TRUE, code is a nonzero error code. If status is FALSE, code is 0 or a warning code. source describes the origin of the error or warning and is, in most cases, the name of the VI or function that produced the error or warning.

WA Analytic Wavelet Transform Details

The analytic wavelet transform is a special case of the continuous wavelet transform with the complex Morlet wavelet, also called the Gabor wavelet. The following equation defines the complex Morlet wavelet:

where is the standard deviation of the Gaussian envelope of the mother wavelet, and is the central frequency of the mother wavelet, which is in this VI.

Scale and Frequency

The following illustration shows the real parts of the complex Morlet wavelet. The scales and shifts, (a, ), are (16, 100), (32, 200), and (64, 300) respectively.

The following illustration shows the Fourier transforms of the previous complex Morlet wavelet:

From the above illustrations, you can see that the center frequency of the scaled wavelet is inversely proportional to the scale a.

The Fourier transform of is , where is the Fourier transform of the mother wavelet. Therefore, the center frequency of the scaled wavelet is . You can use the analytic wavelet transform to analyze the frequency content of a signal by selecting a set of scales.

Example

Refer to the Scalogram with Analytic Wavelet Transform VI in the labview\examples\Wavelet Analysis\WAGettingStarted.llb for an example of using the WA Analytic Wavelet Transform VI.