Differences Among Wavelet- And Fourier-based Center Frequency Estimates With Distributional Changes In The Power Spectrum

Abstract

PURPOSE To compare wavelet- and Fourier-based center frequency estimates for stationary synthetic and real EMG signals with changes in the distributional shape of the power spectrum. METHODS Ten adults (mean ± SD age=22 ± 3 yrs) performed maximal isometric muscle actions of the dominant forearm flexors. The surface EMG signal was recorded with a bipolar surface electrode arrangement placed over the biceps brachii muscle. Twenty synthetic sinusoidal signals (10 without noise; 10 with random white noise) were generated to simulate a systematic increase in the bandwidth toward the higher frequencies, which sequentially increased the positive skewness of the power spectra. Discrete Fourier transforms (DFT) were used to generate the power spectra, calculate bandwidth, and provide the mean power frequency (MPF) and median frequency (MDF) estimates. Complex continuous wavelet transforms (CWT) were used to provide average instantaneous mean frequency (AIMF) estimates. All signal synthesis and processing was done with LabVIEW 7 programming software. RESULTS Bandwidths of the synthetic signals increased toward the higher frequencies from 53–132 Hz (noise-free) and 56–136 Hz (with noise), while the bandwidth ranged from 49–170 Hz for the EMG signals. Frequency at peak spectral power was held constant at 50 Hz for the synthetic signals, but ranged from 38–92 Hz for the EMG signals. For the noise-free synthetic and EMG signals, MPF, MDF, and AIMF increased (p ≤ 0.05) with increases in bandwidth. For the synthetic signals with noise, MDF and AIMF increased (p ≤ 0.05), while MPF decreased (p ≤ 0.05) with increases in bandwidth. There were no differences (p > 0.05) between the slope coefficients for increases in MPF and MDF with increases in bandwidth, however, the slope for increases in AIMF was always lower (p ≤ 0.05). MPF was consistently the highest center frequency estimate, while AIMF was consistently the lowest and closest to the frequency at peak spectral power. CONCLUSIONS These findings indicated differences among the patterns of response for MPF, MDF, and AIMF center frequency estimates with increases in bandwidth toward higher frequencies, despite signal stationarity. Comparatively, MDF and AIMF estimates responded consistently under the modulated synthetic and EMG signal conditions, while MPF estimates responded differently, especially when simulated noise was introduced. Though MDF and AIMF estimates consistently tracked the frequency shifts, AIMF estimates were always closest to the frequency at peak spectral power, which may reflect the densest regions of the power spectrum. Overall, normalization may be necessary when reporting center frequencies.