Engineering Education and Research Using MATLAB
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Fig. 5. Shows adding Gaussian white noise to sine signal
4. Wavelets theory
Wavelets are used in a variety of fields including physics, medicine, biology and statistics.
Among the applications in the field of physics, there is the removal of noise from signals
containing information. There are different ways to reduce noise in audio. (Johnson et al.,
2007) demonstrated the application of the Bionic Wavelet Transform (BWT), an adaptive
wavelet transform derived from a non-linear auditory model of the cochlea, to enhance
speech signal. (Bahoura & Rouat, 2006) proposed a new speech enhancement method based
on time and scale adaptation of wavelet thresholds. (Ching-Ta & Hsiao-Chuan Wang, 2003
& 2007) proposed a method based on critical-band decomposition, which converts a noisy
signal into wavelet coefficients (WCs), and enhanced the WCs by subtracting a threshold
from noisy WCs in each subband. Additionally, they proposed a gain factor in each wavelet
subband subject to a perceptual constraint. (Visser et al., 2003) has presented a new speech
enhancement scheme by spatial integration and temporal signal processing methods for
robust speech recognition in noisy environments. It further de-noised by exploiting
differences in temporal speech and noise statistics in a wavelet filter bank. (Képesia &
Weruaga, 2006) proposed new method for time–frequency analysis of speech signals. The
analysis basis of the proposed Short-Time Fan-Chirp Transform (FChT) defined univocally
by the analysis window length and by the frequency variation rate, that parameter predicted
from the last computed spectral segments. (Li et al., 2008) proposed an audio de-noising
algorithm based on adaptive wavelet soft-threshold, based on the gain factor of linear filter
system in the wavelet domain and the wavelet coefficients teager energy operator in order
to progress the effect of the content-based songs retrieval system. (Dong et al., 2008) has
proposed a speech de-noising algorithm for white noise environment based on perceptual
weighting filter, which united the spectrum subtraction and adopted auditory perception
properties in the traditional Wiener filter. (Shankar & Duraiswamy, 2010) proposed an
audio de-noising technique based on biorthogonal wavelet transformation.
Wavelets are characterized by scale and position, and are useful in analyzing variations in
signals and images in terms of scale and position. Because of the fact that the wavelet size
can vary, it has advantage over the classical signal processing transformations to
simultaneously process time and frequency data. The general relationship between wavelet
scales and frequency is to roughly match the scale. At low scale, compressed wavelets are
used. They correspond to fast-changing details, that is, to a high frequency. At high scale,