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WA Continuous Wavelet Transform VI

Owning Palette: Continuous Wavelet VIs

Installed With: Advanced Signal Processing Toolkit

Computes the continuous wavelet transform (CWT) of the 1D input signal with real-valued wavelets. Wire data to the signal input to determine the polymorphic instance to use or manually select the instance.

Details  Example

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

WA Continuous Wavelet Transform (waveform)

time steps specifies the number of samples to translate, or shift, the wavelet in the continuous 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.
wavelet specifies the wavelet type to use to compute the continuous wavelet coefficients. The default is db02. wavelet must be the same type as the wavelet type you selected in the WA Arbitrary Path Decomposition VI to compute path coef and residual info. If you used the analysis filters input of the WA Arbitrary Path Decomposition VI to specify wavelet, ignore this input and use the synthesis filters input of this VI to specify the synthesis filters of the wavelet. Use the user defined wavelet input to specify a customized wavelet.
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 CWT 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 scales input.
user defined wavelet specifies the mother wavelet function to use to compute the continuous wavelet transform. If you specify a value for user defined wavelet, the VI ignores the settings in the wavelet input. You can use the Wavelet Design Express VI to design the wavelet.
t0 specifies the initial time of the mother wavelet function.
dt specifies the time interval of the mother wavelet function in samples.
mother wavelet specifies the mother wavelet function.
CWT coef contains the results of the continuous wavelet transform. The element in the ith column and the jth row is the result of the continuous wavelet transform, where scale (a)=i+1, and shift ()=j×time steps. When you use user defined scales to define the scales of the continuous wavelet transform, the element in the ith column and the jth row is the result of the continuous wavelet transform, where scale (a) equals the ith element of user defined scales and shift () equals j×time steps. The squared magnitude of CWT 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. You also can consider the scalogram as the time-frequency representation of the signal. 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 Continuous Wavelet Transform (array)

time steps specifies the number of samples to translate, or shift, the wavelet in the continuous 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.
wavelet specifies the wavelet type to use to compute the continuous wavelet coefficients. The default is db02. wavelet must be the same type as the wavelet type you selected in the WA Arbitrary Path Decomposition VI to compute path coef and residual info. If you used the analysis filters input of the WA Arbitrary Path Decomposition VI to specify wavelet, ignore this input and use the synthesis filters input of this VI to specify the synthesis filters of the wavelet. Use the user defined wavelet input to specify a customized wavelet.
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 CWT 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 scales input.
user defined wavelet specifies the mother wavelet function to use to compute the continuous wavelet transform. If you specify a value for user defined wavelet, the VI ignores the settings in the wavelet input. You can use the Wavelet Design Express VI to design the wavelet.
t0 specifies the initial time of the mother wavelet function.
dt specifies the time interval of the mother wavelet function in samples.
mother wavelet specifies the mother wavelet function.
CWT coef contains the results of the continuous wavelet transform. The element in the ith column and the jth row is the result of the continuous wavelet transform, where scale (a)=i+1, and shift ()=j×time steps. When you use user defined scales to define the scales of the continuous wavelet transform, the element in the ith column and the jth row is the result of the continuous wavelet transform, where scale (a) equals the ith element of user defined scales and shift () equals j×time steps. The squared magnitude of CWT 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. You also can consider the scalogram as the time-frequency representation of the signal. 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 Continuous Wavelet Transform Details

The following equation defines the continuous wavelet transform:

where s(t) is the signal, is the mother wavelet function, and a and are the scale and shift of the wavelet, respectively. a can be any positive real value. Use user defined scales to specify the scales. If you do not specify values for user defined scales, this VI selects the scale, a, as 1, 2, 3, …, scales. This VI selects the shift, , as 0, dt, 2dt, 3dt, …, Ndt, where dt is time steps, and N is approximately equal to the signal length divided by time steps. Refer to A Wavelet Tour of Signal Processing for more information about the continuous wavelet transform.

Example

Refer to the Breakdown Point Detection VI in the labview\examples\Wavelet Analysis\WAApplications.llb for an example of using the WA Continuous Wavelet Transform VI.


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