Analysis Of Short Time Fourier Transform And Wavelet Transform

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In order to clearly understand the signal, it is found that frequency content of the signal is well understood. For the analysis and processing of breathing sound which is recorded by the sensory audio reader (sensor), the Short Time Fourier Transform and wavelet transform is applied to it. And the programs were developed in MATLAB. Short time Fourier transform (STFT) is a Fourier related transform which is used to determine the sinusoidal frequency and phase content of the signal which changes over time. The STFT method is used to analyze the non-stationary signal i.e., it has the property that changes with time. Through a moving window process the longer length signal is divided in to shorter segment of equal length and Fourier transform is computed for each shorter segment signal …show more content…

It divides continuous time function in to wavelet. The CWT is defined as follows, X(a,b;x(t),φ(t)=1/√a ∫_(-∞)^∞▒〖x(t) φ^* 〗 ((t-b)/a)dt Where, * denote the complex conjugate Ѱ(t) continuous function in both time and frequency domain called as mother wavelet The wavelet type may also affect the value of the coefficients. By continuously varying the values of the scale parameter a, and the position parameter b, the CWT coefficients X (a, b) can be obtained. By multiplying each coefficient with the scale and shifted wavelet yields the constituents wavelet of the original signal. Normally the output X(a, b) is a real valued function when the mother wavelet is complex, the complex mother wavelet convert the CWT to a complex valued function. Comparing the signal to the wavelet at various positions and scales a function with two variable is obtained. The 2-D representation of the 1-D signal create redundancy i.e. ., the signal which is no longer useful for the analysis. The mother wavelet is the small wave, which is the prototype for generating other window function. The main two difference between STFT and CWT

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