*5.2. Spectral Distributions over Propagation Channels*

In this section, we evaluate the changes suffered in the frequency and time domain when the recorded ANEs were propagated through the three different multi-path channels (models A, B, and C, as explained in Section 4.2). Figures 16–18 show the outcomes related to different ANEs (i.e., the noise of an aeroplane, a brake, and a truck). For the sake of brevity we only show these three examples, as they are representative of the phenomena we want to outline. For each of them, we show the spectrogram of the emitted signal in the upper plot and then we divide the remaining plot into three rows, one for each model. In the first column, from row two to four, we show the spectrogram of the received signal through models A, B, and C, respectively.

**Figure 16.** Accumulated energy along time and frequency, through channels A, B, and C, of an audio signal of an aeroplane at sensor hb137.

In the second column, from row two to four, we show the accumulated energy throughout the whole bandwidth for each time point, for each propagating model. Finally, in the third column, from row two to four, we show the accumulated energy throughout the whole time duration of the ANE for each frequency, for each propagating model. The spectrogram divides the signal into 40 ms-length segments, which were windowed with a Hanning window to reduce leakage and transformed into the frequency domain by means of a 2048-points Fast Fourier Transform (FFT), diplayed in logarithmic scale. Consecutive segments were overlapped by a factor of 87.5% to maximise the probability of detection. The plots of accumulated energy, in time and frequency, were normalised to the maximum energy and displayed in logarithmic scale. In these plots, we show the accumulated energy of the ANEs prior to being transmitted in black and the accumulated energy after being transmitted through models A, B, and C in blue, red, and green, respectively.

In all three figures, we can observe that the accumulated energy throughout the whole frequency band (middle column) at the emitter was more similar to the accumulated energy at the receiver when

propagating through a low delay spread channel (i.e., models A and C), rather than through a higher delay spread channel (i.e., model B). The important factor that enables the spreading of energy over time is not the number of paths but the time distance between them, as well as the weight of each of them.

In all three figures, we can also underline the fact that the accumulated energy throughout the whole time span of the recorded ANEs (right column) approached the original level (i.e., prior to being propagated through the channel) when propagating through a high delay spread channel. In other words, it appears that channels with narrow coherence bandwidths managed to confine the energy into a similar range of values as the original signal. In a different manner, when facing wider coherence bandwidth channels (e.g., models A and C) the accumulated energy in the time domain tended to differ from the original one.

**Figure 17.** Accumulated energy along time and frequency, through channels A, B, and C, of an audio signal of an brake at sensor hb137.

The following step of this analysis will be to systematically analyse all ANEs from both sensors when transmitted through different types of channels (e.g., narrow streets, streets with tall buildings, wide streets with high background noise, and so on). The goal will be to find a systematic repetition of received signal characteristics related to environment factors. Another interesting point will be to study time-variant channels to check whether the time variation factor affects the received signal characteristics.

**Figure 18.** Accumulated energy along time and frequency, through channels A, B, and C, of an audio signal of an truck at sensor hb145.
