Time-frequency scaling transformation of the phonocardiogram based of the matching pursuit method

Abstract

A time-frequency scaling transformation based on the matching pursuit (MP) method is developed for the phonocardiogram (PCG). The MP method decomposes a signal into a series of time-frequency atoms by using an iterative process. The modification of the time scale of the PCG can be performed without perceptible change in its spectral characteristics. It is also possible to modify the frequency scale without changing the temporal properties. The technique has been tested on 11 PCG's containing heart sounds and different murmurs. A scaling/inverse-scaling procedure was used for quantitative evaluation of the scaling performance. Both the spectrogram and a MP-based Wigner distribution were used for visual comparison in the time-frequency domain. The results showed that the technique is suitable and effective for the time-frequency scale transformation of both the transient property of the heart sounds and the more complex random property of the murmurs. It is also shown that the effectiveness of the method is strongly related to the optimization of the parameters used for the decomposition of the signals.

Fig. 1

Intensity of heart sounds and murmurs in correspondence with the threshold of audibility and speech (from [4]). An important part of the intensity and frequency distribution of the heart sounds and murmurs is out of the human hearing range.

Fig. 2

The evaluation procedure for time-frequency scaling of PCG signals. A scaling/inverse scaling procedure was used to evaluate the performance of the MP method for the time-frequency scaling of the PCG.

Fig. 3

Average errors of the time-scaling transformation as a function of the number of atoms M and the maximum octave value J = 6, 7, and 8. (a) The reconstruction error (E_mp1 + E_mp2). (b) The time scaling error (E_s). (c) The total error E_t. The best value of J which is seven is relatively independent of the value of M.

Fig. 4

(a) The original PCG of aortic regurgitation. (b) The time scaled signal of (a) by factor γ = 2. (c) The frequency scaled signal of (a) by factor ξ = 2. (d) The time-frequency scaled signal of (a) by factors of γ = 2 and ξ = 2. This figure clearly shows the effectiveness of the method for time-frequency scaling of the PCG.

Fig. 5

(a) The original PCG of aortic regurgitation. (b) The inverse time scaled signal of Fig. 4(b) by factor γ = 0.5. (c) The inverse frequency scaled signal of Fig. 4(c) by factor ξ = 0.5. (d) The inverse time-frequency scaled signal of (a) by factors of γ = 0.5 and ξ = 0.5. The inverse-scaled PCG signals appear to be very similar to the original PCG signal.

Fig. 6

The MP-based Wigner-distributions (left panels) and spectrograms (right panels) of (a1), (b1) the original signal of the pathological PCG of Fig. 5, (a2), (b2) the time scaled signal by factor of γ = 2, (a3), (b3) the frequency scaled signal by factor of ξ = 2., and (a4), (b4) the time-frequency scaled signal by factors of γ = 2 and ξ = 2. This figure qualitatively shows that the structure of the original PCG signal is preserved after time, frequency, and both time and frequency scaling of the PCG signal.

Fig. 7

Average errors of the joint time-frequency scaling transformation as a function of the number of atoms M and the maximum octave value J = 6, 7, and 8. (a) The reconstruction error (E_mp1 + E_mp2). (b) The time-frequency scaling error (E_s). (c) The total error E_t. The best value of J, which is eight, is relatively independent of the value of M.