Biomedical Engineering Reference
In-Depth Information
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Discrete Time
FIGURE 11.28
MATLAB results showing noise removal by averaging a noisy sinusoid signal. Shown for
1, 10, and 100 averages.
11.8 THE WAVELET TRANSFORM AND THE SHORT-TIME
FOURIER TRANSFORM
The Fourier transform (Eq. (11.6)) is a well-known signal processing tool for breaking a
signal into constituent sinusoidal waveforms of different frequencies. For many applica-
tions, particularly those that change little over time, knowledge of the overall frequency
content may be all that is desired. The Fourier transform, however, does not delineate
how a signal changes over time.
The short-time Fourier transform (STFT) and the wavelet transform (WT) have been
designed to help preserve the time-domain information. The STFT approach is to perform
a Fourier transform on only a small section (window) of data at a time, thus mapping
