Time-Frequency and Wavelet Analysis
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We have already noted some of the limitations of Fourier decomposition. The assumption of periodicity in the calculation of the DFT is one main limitation. Another more subtle limitation is the unavoidable compromise between time resolution and frequency resolution. This is due to the fact that the DFT is computed on a block of data. This fixes the time window or resolution as ΔT r=N/F s, where N is the block size and F S is the sampling rate. It also fixes the frequency resolution as ΔF r=F s/N. The product of the time resolution and frequency resolution, ΔT r•ΔF r is constant, which means that improvement in time resolution can be obtained only at the expense of frequency resolution and vice versa.
KeywordsWavelet Analysis Wavelet Coefficient Slow Component Finite Impulse Response Frequency Resolution
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