**5. Real-Life Acoustic Recording Analysis**

In this section, we show the effects of a multi-path static channel on real-life acoustic recorded signals. We, first, underline how the impulse response of a multi-path channel may be estimated by means of an acoustic signal, as if it was a PN sequence. Then, we also show how the frequency selective transfer function of a channel may distort the frequency response of an acoustic signal. Finally, we also show some examples of how the spectral and time distribution of acoustic signals may be changed because of facing different types of multi-path channels.

## *5.1. Propagation on Real-Life Acoustic Recordings*

Among all the sample files of recorded ANEs, we have chosen some examples of those with good auto-correlation properties, in order to test whether they are able to estimate the channel response and its impairments, such as delay spread and the resultant distortion in the frequency domain. We also seek ANEs with different spectrum characteristics, in case they have different effects on the multi-path channels.

For instance, Figure 12 shows the channel impulse response, computed as in Equation (2), for the three channel models studied in this paper; however, no PN sequence was used in this case. Instead, the same ANE was used to detect the paths of the channel and, therefore, it was able to compute the rms delay spread. In Figure 12, we can see the impulse response of the three channel models computed with an ANE of a truck, with a bandwidth similar to the one shown in the spectrogram of Figure 6d. Due to the wide bandwidth of this ANE and, consequently, the high delay resolution, it was possible to detect the majority of the paths of the three models. This point can be checked if we compare the impulse response in Figure 12 with the channel impulse response computed with the PN sequence (see Figure 10). However, if the bandwidth of the ANE becomes narrow, the delay resolution dismisses and the probability of path detection reduces as well. For instance, Figure 13 depicts the impulse response computed by means of the acoustic signal of a brake, which had a narrow and discontinuous bandwidth, as shown in Figure 6c. Due to the narrow bandwidth and, hence, the poor delay resolution, it was not possible to detect all the paths of channel.

Regarding the frequency response of the three models, we found that they differed even if they were computed using the same ANE. For instance, Figure 14 plots a portion of the frequency response of the three models computed with an acoustic signal of a siren. It was a signal composed of a number of harmonics, as the spectrogram of Figure 6b shows. In Figure 14, we show three of its harmonics in the range between 800–1600 Hz and we can see that there was a maximum amplitude difference between channel frequency responses of 10 dB. This behavior is not consistent throughout the frequency axis and implies that a model does not always attenuate a frequency component with the same factor, since it computes the frequency response as a linear combination of attenuated paths with a phase that depends on the distance travelled and the frequency (see Equations (9)–(10)).

In addition to the different attenuation of frequency components in each model, we also observed a distortion phenomena which differed between models. For example, Figure 15 depicts the frequency component of an acoustic signal of a brake, for each of the three models, centered at 8 kHz. We can see that, while those models with similar delay spread (i.e., models A and C; see Table 2) had comparable frequency responses, model B had a higher delay spread, which distorted the frequency response. As explained above (see Section 4.3), the higher the delay spread, the narrower the coherence bandwidth of the channel and the higher the probability of signal distortion. The audio signal of a brake, as depicted in Figure 15, had a frequency bandwidth which happened to be flat for models A and C (wide coherence bandwidth), but not flat for model B (narrow coherence bandwidth). Therefore, the brake signal saw models A and C as non-frequency-selective channels, but model B as a frequency-selective channel.

**Figure 12.** Channel impulse response of models A, B, and C, computed by means of an audio signal of a truck from sensor hb137.

**Figure 13.** Channel impulse response of models A, B, and C, computed by means of an audio signal of a brake from sensor hb137.

**Figure 14.** Frequency response of models A, B, and C, computed by means of an audio signal of a siren obtained from sensor hb145.

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**Figure 15.** Frequency response of models A, B, and C, computed by means of an audio signal of a brake from sensor hb137.
