Abstract: In this study, a spatial wavelet-based crack localization technique for a thick beam is presented. Wavelet scale in spatial wavelet transformation is optimized to enhance crack detection sensitivity. A windowing function is also employed to erase the edge effect of the wavelet transformation, which enables the method to detect and localize cracks near the beam/measurement boundaries. Theoretical model and vibration analysis considering the crack effect are first proposed and performed in MATLAB based on the Timoshenko beam model. Gabor wavelet family is applied to the beam vibration mode shapes derived from the theoretical beam model to magnify the crack effect so as to locate the crack. Relative wavelet coefficient is obtained for sensitivity analysis by comparing the coefficient values at different positions of the beam with the lowest value in the intact area of the beam. Afterward, the optimal wavelet scale corresponding to the highest relative wavelet coefficient at the crack position is obtained for each vibration mode, through numerical simulations. The same procedure is performed for cracks with different sizes and positions in order to find the optimal scale range for the Gabor wavelet family. Finally, Hanning window is applied to different vibration mode shapes in order to overcome the edge effect problem of wavelet transformation and its effect on the localization of crack close to the measurement boundaries. Comparison of the wavelet coefficients distribution of windowed and initial mode shapes demonstrates that window function eases the identification of the cracks close to the boundaries.
Abstract: Mostly the real life signals are time varying in nature. For proper characterization of such signals, time-frequency representation is required. The STFT (short-time Fourier transform) is a classical tool used for this purpose. The limitation of the STFT is its fixed time-frequency resolution. Thus, an enhanced version of the STFT, which is based on the cross-level sampling, is devised. It can adapt the sampling frequency and the window function length by following the input signal local variations. Therefore, it provides an adaptive resolution time-frequency representation of the input. The computational complexity of the proposed STFT is deduced and compared to the classical one. The results show a significant gain of the computational efficiency and hence of the processing power. The processing error of the proposed technique is also discussed.
Abstract: Fractional Fourier Transform is a generalization of the
classical Fourier Transform. The Fractional Fourier span in general
depends on the amplitude and phase functions of the signal and varies
with the transform order. However, with the development of the
Fractional Fourier filter banks, it is advantageous in some cases to
have different transform orders for different filter banks to achieve
better decorrelation of the windowed and overlapped time signal. We
present an expression that is useful for finding the perturbation in the
Fractional Fourier span due to the erroneous transform order and the
possible variation in the window shape and length. The expression is
based on the dependency of the time-Fractional Fourier span
Uncertainty on the amplitude and phase function of the signal. We
also show with the help of the developed expression that the
perturbation of span has a varying degree of sensitivity for varying
degree of transform order and the window coefficients.
Abstract: The frequency contents of the non-stationary
signals vary with time. For proper characterization of such
signals, a smart time-frequency representation is necessary.
Classically, the STFT (short-time Fourier transform) is
employed for this purpose. Its limitation is the fixed timefrequency
resolution. To overcome this drawback an enhanced
STFT version is devised. It is based on the signal driven
sampling scheme, which is named as the cross-level sampling.
It can adapt the sampling frequency and the window function
(length plus shape) by following the input signal local
variations. This adaptation results into the proposed technique
appealing features, which are the adaptive time-frequency
resolution and the computational efficiency.
Abstract: Smoothing or filtering of data is first preprocessing step
for noise suppression in many applications involving data analysis.
Moving average is the most popular method of smoothing the data,
generalization of this led to the development of Savitzky-Golay filter.
Many window smoothing methods were developed by convolving
the data with different window functions for different applications;
most widely used window functions are Gaussian or Kaiser. Function
approximation of the data by polynomial regression or Fourier
expansion or wavelet expansion also gives a smoothed data. Wavelets
also smooth the data to great extent by thresholding the wavelet
coefficients. Almost all smoothing methods destroys the peaks and
flatten them when the support of the window is increased. In certain
applications it is desirable to retain peaks while smoothing the data
as much as possible. In this paper we present a methodology called
as peak-wise smoothing that will smooth the data to any desired level
without losing the major peak features.
Abstract: This paper proposes an efficient method for the design
of two channel quadrature mirror filter (QMF) bank. To achieve
minimum value of reconstruction error near to perfect reconstruction,
a linear optimization process has been proposed. Prototype low pass
filter has been designed using Kaiser window function. The modified
algorithm has been developed to optimize the reconstruction error
using linear objective function through iteration method. The result
obtained, show that the performance of the proposed algorithm is
better than that of the already exists methods.
Abstract: The tree structured approach of non-uniform filterbank
(NUFB) is normally used in perfect reconstruction (PR). The PR is
not always feasible due to certain limitations, i.e, constraints in
selecting design parameters, design complexity and some times
output is severely affected by aliasing error if necessary and
sufficient conditions of PR is not satisfied perfectly. Therefore, there
has been generalized interest of researchers to go for near perfect
reconstruction (NPR). In this proposed work, an optimized tree
structure technique is used for the design of NPR non-uniform
filterbank. Window functions of Blackman family are used to design
the prototype FIR filter. A single variable linear optimization is used
to minimize the amplitude distortion. The main feature of the
proposed design is its simplicity with linear phase property.
Abstract: In this paper newly reported Cosh window function is
used in the design of prototype filter for M-channel Near Perfect
Reconstruction (NPR) Cosine Modulated Filter Bank (CMFB). Local
search optimization algorithm is used for minimization of distortion
parameters by optimizing the filter coefficients of prototype filter.
Design examples are presented and comparison has been made with
Kaiser window based filterbank design of recently reported work.
The result shows that the proposed design approach provides lower
distortion parameters and improved far-end suppression than the
Kaiser window based design of recent reported work.