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Understanding Linear Time Frequency Analysis Methods (Advanced Signal Processing Toolkit)

LabVIEW 2013 Advanced Signal Processing Toolkit Help

Edition Date: June 2013

Part Number: 372656B-01

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In traditional spectral analysis, the discrete Fourier transform and the inverse discrete Fourier transform are complementary operations. The discrete Fourier transform computes a frequency-domain representation of time-domain signals. The inverse discrete Fourier transform converts the frequency-domain representation back to the time-domain representation.

Similarly, the discrete Gabor transform is a linear time-frequency analysis method that computes a linear time-frequency representation of time-domain signals. The discrete Gabor expansion is the inverse operation and converts the linear time-frequency representation back to the time-domain representation.

A linear time-frequency representation of a signal reveals not only the spectral content of the signal but also how the spectral content evolves over time. In many real-world applications, the signature of a signal and associated noise might not be obvious in the time domain or in the frequency domain alone but might be identified easily in the time-frequency domain. Also, because linear time-frequency domain representations are invertible, you can separate signal components or reduce noise in the time-frequency domain and then reconstruct the time-domain signal with the modified time-frequency representation. The reconstructed signal contains the signal components you want or the signal with the noise reduced.

The linear time-frequency analysis method you select depends on the requirements of the application. Consider the resolution and if the method is invertible when you select a linear time-frequency analysis method. The following table compares these properties of the linear time-frequency analysis methods in the LabVIEW Time Frequency Analysis Tools.

Method Resolution Invertible?
Short-time Fourier Transform (STFT) Affected by window type, window length No
Gabor transform Affected by window type, window length Yes, using Gabor expansion
Adaptive transform Adaptable to signal Yes, using Adaptive expansion

 

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