Ultrasonic Doppler signals are widely used in the detection of cardiovascular pathologies or the evaluation of the degree of stenosis in the femoral arteries. The presence of stenosis can be indicated by disturbing the blood flow in the...
moreUltrasonic Doppler signals are widely used in the detection of cardiovascular pathologies or the evaluation of the degree of stenosis in the femoral arteries. The presence of stenosis can be indicated by disturbing the blood flow in the femoral arteries, causing spectral broadening of the Doppler signal. To analyze these types of signals and determine stenosis index, a number of time-frequency methods have been developed, such as the short-time Fourier transform, the continuous wavelets transform, the wavelet packet transform, and the S-transform Keyword: Continuous wavelet transform Doppler ultrasound SBI Stenosis S-transform The wavelet packet transform 1. INTRODUCTION Fourier analysis is a basic tool in signal processing. It is indispensable in many areas of research; unfortunately it has limitations when implemented beyond the strict framework of its definition: the area of stationary finite energy signals. In Fourier analysis, all the temporal aspects become illegible in the spectrum. The study of non-stationary signals therefore requires either an extension of the Fourier Transform (or stationary methods), introducing a temporal aspect, or the development of specific methods. A first solution, implemented intuitively in the mid-century, corresponds to Fourier analysis sliding window or short time Fourier transform (STFT), which was introduced in 1945 by D. Gabor with the idea of a time-frequency plan where time becomes an additional parameter of frequency [1]. This method shows that a joint exact location in time and frequency is impossible, and introduces the idea of a discrete basis, minimum, resulting in a few coefficients of the signal energy distribution in time-frequency plan. Other methods are used in this work, namely the continuous wavelet transform and wavelet packets. these two variances of the wavelet transform have existed in a latent state in both mathematics and signal processing, but the real expansion began in the early 1980s. The last method used in this work (based on the wavelet transform) is the S-trasform proposed by Stokwellet al.; it is similar to STFT with an exception that the amplitude and width of the analysis window are a function of frequency, as in the wavelet transform [2].