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Frequency domain analyses in electromyographic (EMG) signals are frequently applied to assess muscle fatigue and similar variables. Moreover, Fourier-based approaches are typically used for investigating these procedures. Nonetheless, Fourier analysis assumes the signal as stationary which is unlikely during dynamic contractions. As an alternative method, wavelet-based treatments do not assume this pattern and may be considered as more appropriate for joint time-frequency domain analysis. Based on the previous statements, the purpose of the present study was to compare the application of Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) to assess muscle fatigue in dynamic exercise of a 1-km of cycling (time-trial condition). The results of this study indicated that CWT and STFT analyses have provided similar fatigue estimates (slope) (p> 0.05). However, CWT application represents lesser dispersion p< 0.05) for vastus medialis (189.9 ± 82.1 for STFT vs 148.6 ± 60.2 for CWT) and vastus lateralis (151.6 ± 49.6 for STFT vs 103.5 ± 27.9 for CWT). In conclusion, despite the EMG signal did not change (p> 0.05) according to different methods, it is important to note that these responses seem to show greater values for CWT compared to STFT for 2 superficial muscles. Thereby, we are capable of considering CWT as a reliable and useful method to take into consideration when non-stationary or oscillating exercise models are evaluated.>

The use of surface electromyography (EMG) has been applied as a valuable and non-invasive method to study the human movement and its neurophysiological mechanisms of fatigue. The tool works through the electric activity in the excitable membranes of myofibrils, which comprise the motor units of the muscular system determining the output of muscle activation [

Fatigue can be defined as a decrease on the capacity of muscle to produce force [

When the signal is presented in the frequency domain, a variety of problems might appear, the spectral decomposition of muscle generally uses mathematical algorithms such as the Fast Fourier Transform (FFT) [

The suitable application of short-time Fourier Transform is much less restrictive than Fourier transform since the former only needs local stationarity, i.e., stationarity within its running window. Hence the spectral analysis over dynamic exercises signals will be more effective using the Short-Time Fourier Transform (STFT) than FFT if a representative number of samples (this number defines the granularity of frequencies scale in frequency domain) could be obtained into each running time-domain windows such as the signal samples in each running window results approximately stationary.

Some studies showed that STFT and CWT may yield comparable results regarding muscle fatigue in highly standardized protocols, both in static or dynamic exercise [

Thus, the purpose of this study was to compare STFT and CWT analysis in assessing muscle fatigue in dynamic exercise, in 1-km cycling time-trial (approximately 8 min of analysis).

Ten male cyclists (27 ± 8 years, 71 ± 10 kg, 173 ± 6 cm) participated in this study. All participants have practiced cycling for 7 ± 4 years with an average of 5.0 ± 1.0 training sessions per week, and also declared to have an average weekly training volume of 345 ± 92 km. This study was approved by the Research and Ethics Com- mittee of the State University of Londrina.

The 1-km time-trial was performed in a cyclesimulator (Velotron CS 2008™, RacerMate^{®}, USA). The subjects were required to complete the test as fast as they could. During the time-trial, the volunteers received strong verbal encouragement to motivate and ensure that they reached their maximum peak performance.

The EMG signals were recorded according to the guidelines of the International Society of Electrophysiology

and Kinesiology, using a 8-channel electromyography (TeleMyo 2400 TG2, NORAXON Inc. USA) with sampling rate of 2000 Hz. The raw EMG signals were filtered using a band-pass filter of 20 Hz and 500 Hz. The bipolar electrodes (TeleMyo 2400, NORAXON Inc. USA), were placed in the quadriceps muscles (QD): vastus lateralis (VL), vastus medialis (VM) and rectus femoris (RF) according to the SENIAM orientations [

For the spectral analysis, the values of MDF were obtained applying the STFT and CWT (Daubechies: db4) techniques. Short term Fourier transform is obtained applying recursively (over 1.0 sec time-windowed signal) a 1024-point fft (Fast Fourier Transform) with rectangular processing window algorithm, available at MatLab^{®} v.7.7. While the continuous wavelet transform is performed applying the CWT algorithm (overall the EMG signal, but analyzing the same 1.0 sec windows), available at Wavelet Toolbox™ of MatLab^{®} v.7.7.

Using these techniques, the following parameters were obtained: MDF, Variance

The MDF is the value of frequency that divides the EMG signal spectrum into two parts with equal energy, as demonstrated by Equation (1).

where

where

As an example, both techniques were applied to a 10 sec EMG signal (

For the whole 10 sec signal, the STFT analysis results in nine MDF values (^{2}, and slope of 0.51 Hz/sec.

For the CWT analysis, the whole 10 sec signal is used to obtain the wavelet coefficients using 128 scales,

The contour of this portion of the CWT coefficients is used to estimate the envelope of the power spectrum of the signal as shown in

Example 10 sec EMG signal used for illustration of both methods: STFT and CWT analysis

First 1 sec window of the example signal used in the STFT analysis

Fourier Transform of the first 1 sec window of the example signal

MDF values of the nine time-windowed signals of the 10 sec example EMG signal using the STFT technique

CWT coefficients of the 10 sec EMG example signal

Portion of the CWT coefficients used in the first windowing

Envelope of the power spectrum of the signal using the previous portion of the CWT coefficients

pling period). This figure also shows the MDF: the straight line at 89.29 Hz. The MDF values of the nine windows of the 10 sec signal is presented in ^{2}, and slope of 0.32 Hz/sec. We present the slope results only as an illustration of the techniques, because for a proper value, more samples should be used for the estimation.

The data were processed in the software package SPSS^{®} for Windows version 17.0. The distribution of the data was verified by the Shapiro-Wilk’s test and comparison of data regarding the STFT and CWT techniques by Student’s

The subjects showed a maximal workload of 390 ± 65 W. The mean workload during the 1-km time-trial was 376 ± 59 W, the mean speed was 43 ± 3 km∙h^{−1} and total time was 84 ± 6 sec.

The MDF from STFT and CWT means for quadriceps muscles are shown in

MDF values of the nine windowed signals of the 10 sec example EMG signal using the CWT technique

Variations of mean outcome between STFT and CWT during 1-km cycling time-trial analysed in quadriceps integrated

. Values of variance (hz2), and slope of mdf for the vastus lateralis (VL), vastus medialis (VM) and rectus femoris (RF) muscles

Parameters | STFT | CWT |
---|---|---|

VL Variance | 151.6 ± 49.6 | 103.5 ± 27.9^{*} |

Slope | −0.09 ± 0.07 | −0.09 ± 0.06 |

VM Variance | 189.9 ± 82.1 | 148.6 ± 60.2^{*} |

Slope | −0.12 ± 0.08 | −0.12 ± 0.09 |

RF Variance | 260.8 ± 265.3 | 238.7 ± 225.1 |

Slope | −0.1 ± 0.1 | −0.1 ± 0.1 |

*: Statistically significant differences for p < 0.05.

Typical time-domain EMG signal from VL muscle for a random subject and typical VL median frequency via STFT and CWT techniques respectively

Some studies compared the use of CWT and STFT in different exercises protocols [

Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates. The findings of this study corroborate the findings of Da Silva et al. (2008) [

Considering these findings some authors have suggested the CWT as an alternative method to decompose the EMG signal in dynamic contraction, since it presents more accurate and precise measurements [