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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.
|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|