# Dual Window Express VI

LabVIEW 2014 Advanced Signal Processing Toolkit Help

Edition Date: June 2014

Part Number: 372656C-01

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Owning Palette: Time Frequency Transform VIs

Computes the dual windows for the Gabor transform and the Gabor expansion.

## Dialog Box Options

ParameterDescription
Dual WindowDisplays the analysis window and the synthesis window. You can use the analysis window and the synthesis window for the Gabor transform and the Gabor expansion, respectively. To characterize the local time and frequency properties of a signal in the joint time-frequency domain accurately, adjust the Synthesis Window Info and the Transform Info so that the analysis window and the synthesis window match as closely as possible.
Synthesis Window InfoContains the following options:
• Window type—Specifies the type of envelope window of the Gabor elementary functions. Options include:
• Gaussian (default)
• Low Sidelobe
• 7 Term B-Harris
• 4 Term B-Harris
• Flat Top
• Blackman
• Exact Blackman
• Blackman-Harris
• Hamming
• Hanning
• Optimal variance—Specifies to compute the variance of the Gaussian window automatically. When Optimal variance is TRUE, this VI sets the variance as the optimal value, which is equal to N (frequency bins)×dM (time steps)/(2 ). This control is available only when Window type is Gaussian.
• Window length—Specifies the window length, in samples, of the Gabor elementary functions. This VI sets Window length to a power of 2 automatically.
• Variance—Specifies the variance, in square samples, of the Gaussian window. This control is available only when Window type is Gaussian and you remove the checkmark from the Optimal variance checkbox.
Transform InfoContains the following options:
• dM (time steps)—Specifies the time shift, in samples, between elementary functions. The time sampling interval of the signal in the time-frequency domain is dM (time steps)/fs, where fs is the sampling rate of the signal. This VI sets dM (time steps) to a power of 2 and less than or equal to N (frequency bins) automatically. You also can consider dM (time steps) as the sampling period along the time axis in the joint time-frequency domain.
• N (frequency bins)—Specifies the number of carrier frequencies of the Gabor elementary functions. The frequency sampling interval of the signal in the time-frequency plane is fs/N (frequency bins), where fs is the sampling rate of the signal. This VI sets N (frequency bins) to a power of 2 and greater than or equal to dM (time steps). The ratio between N (frequency bins) and dM (time steps) is called the oversampling rate. You also can consider N (frequency bins) as the number of bins to sample the signal along the frequency axis in the joint time-frequency domain.
Data length equals window lengthSpecifies if the lengths of the window function and the signal are equal. When the window length is equal to the signal length, the chance of obtaining the corresponding dual function is higher.
Sampling GridDisplays the Gabor sampling lattice in the joint time-frequency domain.
• Zoom out—Zooms out the sampling plot grid.
• Zoom in—Zooms in the sampling plot grid.

## Block Diagram Inputs

ParameterDescription
error in (no error)Describes error conditions that occur before this node runs.

## Block Diagram Outputs

ParameterDescription
error outContains error information. This output provides standard error out functionality.
synthesis infoReturns the Gabor elementary functions for the Gabor expansion.
• synthesis window—Contains the window of the Gabor elementary functions. The size of synthesis window must be divided evenly by dM (time steps) and N (frequency bins).
• dM (time steps)—Contains the time shift, in samples, between elementary functions. The time sampling interval of the signal in the time-frequency domain is dM (time steps)/fs, where fs is the sampling rate of the signal.
• N (frequency bins)—Contains the number of carrier frequencies of the Gabor elementary functions. The frequency sampling interval of the signal in the time-frequency plane is fs/N (frequency bins), where fs is the sampling rate of the signal. N (frequency bins) must be a power of 2. For stable reconstruction, N (frequency bins) must be greater than or equal to dM (time steps). The ratio between N (frequency bins) and dM (time steps) is called the oversampling rate.
analysis infoReturns the analysis window for the Gabor transform.
• analysis window—Contains the window this VI used to compute the Gabor coefficients. analysis window is the dual window of the synthesis window, which is the envelope of the Gabor elementary functions. The size of analysis window must be divided evenly by dM (time steps) and N (frequency bins).
• dM (time steps)—Contains the time shift, in samples, between elementary functions. The time sampling interval of the signal in the time-frequency domain is dM (time steps)/fs, where fs is the sampling rate of the signal.
• N (frequency bins)—Contains the number of carrier frequencies of the Gabor elementary functions. The frequency sampling interval of the signal in the time-frequency plane is fs/N (frequency bins), where fs is the sampling rate of the signal. N (frequency bins) must be a power of 2. For stable reconstruction, N (frequency bins) must be greater than or equal to dM (time steps). The ratio between N (frequency bins) and dM (time steps) is called the oversampling rate.

## Dual Window Details

The synthesis window is the envelope window of the Gabor elementary functions. The dual window of the synthesis window is called the analysis window, which this VI uses in the Gabor transform to compute the complex weight of the Gabor elementary functions. You can use the resulting analysis info and synthesis info for the Gabor transform and the Gabor expansion, respectively.

This Express VI operates similarly to the following VIs and functions:

## Examples

Refer to the following VIs for examples of using the Dual Window Express VI:

• Online Noise Reduction VI: labview\examples\Time Frequency Analysis\TFAApplications
• Dual Function VI: labview\examples\Time Frequency Analysis\TFAGettingStarted
• Gabor Transform and Expansion VI: labview\examples\Time Frequency Analysis\TFAFunctions