As discussed in the earlier section, wavelet transform of the signals is recommended due to the limitations offered by STFT. AWT (Analytic Wavelet Transform) provides suitable and adaptive time-scale and time-frequency domains. Zhu [15] found better results using AWT over STFT while analyzing the noise causing human hearing loss. AWT is a type of the Continuous Wavelet Transform that calculates the product of signals and complex Morlet wavelet due to which the resulting coefficients are complex numbers and analytic in nature therefore makes it a complex continuous wavelet transform [16]. The mother wavelet in AWT is given in Eq. 5. (5)
Where j is a complex number, is a real function and is the frequency parameter. The complex Morlet wavelet …show more content…
Considering it a relatively novel approach, there are two motives of using AWT, 1st; to validate the results of the earlier sections by employing a method without using any Fourier transform or filters, 2nd; AWT was found more straightforward application and a superior alternative of STFT providing satisfactory information of the T-F characteristics. Ref. [16] explained a comparison between STFT and AWT, shown in fig. 16. Instead of STFT with uniform T-F resolution, AWT does not compromise on either temporal or frequency resloution and provides fine …show more content…
Visual inspection of low pass filtered time traces is still the most fundamental technique of investigating corellation of temporal and spatial signals. However, filter range is the decisive aspect which may result a shift or lag on time scale and in some cases disturbance frequencies may also be filtered out. Therefore, a verification of results is mendetory. DSFS gives spatial coherence with respect to temporal resolution of the disturbance. Spatial features of the individual disturbance are merged into Fourier components however, rotating disturbance can be detected. Results improve only after the application of filters. A free from filtering T-F analysis for the varying spectral characteristics of pressure signals is recommended. In STFT, window size limits to either fine spectral or fine temporal resolutions. Although, compromizing on time resolution in our case, STSF identified rotating stall frequency on waterfall plot and spectrogram but left a question mark on temporal resolution and hence in detecting the rotating deisturbance. AWT features both Fourier transform and wavelet transform. Suitable for high sampled data withiout pre-requisition of filters, AWT spectrogram provides an excelent temporal and spectral resolution of pre-stall and stall process however, it costs longer computational time than all other techniques. A comparison
Where j is a complex number, is a real function and is the frequency parameter. The complex Morlet wavelet …show more content…
Considering it a relatively novel approach, there are two motives of using AWT, 1st; to validate the results of the earlier sections by employing a method without using any Fourier transform or filters, 2nd; AWT was found more straightforward application and a superior alternative of STFT providing satisfactory information of the T-F characteristics. Ref. [16] explained a comparison between STFT and AWT, shown in fig. 16. Instead of STFT with uniform T-F resolution, AWT does not compromise on either temporal or frequency resloution and provides fine …show more content…
Visual inspection of low pass filtered time traces is still the most fundamental technique of investigating corellation of temporal and spatial signals. However, filter range is the decisive aspect which may result a shift or lag on time scale and in some cases disturbance frequencies may also be filtered out. Therefore, a verification of results is mendetory. DSFS gives spatial coherence with respect to temporal resolution of the disturbance. Spatial features of the individual disturbance are merged into Fourier components however, rotating disturbance can be detected. Results improve only after the application of filters. A free from filtering T-F analysis for the varying spectral characteristics of pressure signals is recommended. In STFT, window size limits to either fine spectral or fine temporal resolutions. Although, compromizing on time resolution in our case, STSF identified rotating stall frequency on waterfall plot and spectrogram but left a question mark on temporal resolution and hence in detecting the rotating deisturbance. AWT features both Fourier transform and wavelet transform. Suitable for high sampled data withiout pre-requisition of filters, AWT spectrogram provides an excelent temporal and spectral resolution of pre-stall and stall process however, it costs longer computational time than all other techniques. A comparison