Measurements of Correlation, Amplitude, and Statistical Properties of Breath Sounds

Specific features of breath sounds, not otherwise visible in the graphic records, can be identified by correlation methods. Autocorrelation — the comparison of a wave with itself (delayed by a finite time interval) — is useful for identifying periodic events within an otherwise noisy signal. ¹ Cross-correlation is useful for detection of similarities between two coherent signals and the time difference between them. Breath sounds or transmitted sounds detected simultaneously at two sites over the chest wall may be cross-correlated to evaluate the delay between them in order to measure the rate of acoustic wave propagation in the thorax (see Chapter 13). Consider two signals, x(t) and y(t), sampled simultaneously at intervals Δt = 1/f_samp to produce the time series of samples x_i and y_i . If the signals are the outcome of a single process or source, it is likely they will be similar. However, when acoustic phenomena are involved, wave propagation can be subject to delays that may differ for the two signals. One method of measuring the relative delay between the signals is by calculating the cross-correlation of the two signals. Examples of related signals are breath sounds detected with a pair of sensors, one placed on the trachea and the other on the chest wall, or with the sensors on two sites on the chest. ² If the path distance between the sensors is known, and a delay, measured by the cross-correlation method, is known, the wave propagation rate can be calculated. ^3,4 The wave propagation rate is potentially useful for characterizing the mechanical properties of the lung and thorax. ^5,6