# Automatic Detection of Whistler Waves in the Top-Side Ionosphere: The WhISPER Technique
## 2 Data and Methods
### Detection Algorithm  
WhISPER directly utilizes PSD data provided by the satellite to enhance computational speed. Given the typical duration of whistler waves (see, e.g., [41]) their presence should manifest as an enhanced PSD across a broad frequency range within the temporal window (TW) employed for both EFD and SCM PSD calculation. Specifically, to explicitly illustrate the expected enhancement, the WhISPER technique leverages the Integrated PSD (IPSD), defined as follows:  
\[IPSD_{i}=\sum_{j_{MAX}}^{j_{MAX}}PSD_{i}\,f_{j} \tag{1}\]  
where \(i=x,y,z\) represents the electric or magnetic field component and \(f_{j}\) is the frequency corresponding to bin index \(j\). The inclusion of frequency \(f_{j}\) as a weighting factor emphasizes the initial, high-frequency portion of whistler waveforms. As detailed in Sections 2.1 and 2.2, the upper frequency bin index \(j_{MAX}\) is equal to 801 for SCM and to 1024 for EFD. Regarding the lower-frequency bin index \(j_{MIN}\), it was set to 1 for SCM and 30 for EFD. This distinction arises from the EFD-ELF data's inclusion of frequencies starting from DC, therefore including the long-term trend constituting the ionospheric background and peculiar low-frequncy ionospheric signals characterized by high PSD, such as Schumann resonances (SR, \(\sim\)6-30 Hz, [42]) and the first Power Line Harmonic Radiation (PLHR, 50-60 Hz, [43]). Consequently, the summation for EFD data starts from \(\sim\)73 Hz, equivalent to \(j_{MIN}=30\). The necessity of excluding low-frequency components from the summation is demonstrated in Figure 1, which compares the IPSD calculated using \(j_{MIN}=1\) (Panel 1a) and \(j_{MIN}=30\) (Panel 1b) for EFD-ELF data recorded on 18 August 2020. As shown in Figure 1a, a small peak emerges in the IPSD at approximately 05:50 UT, observable in both the X and Y components. The removal of the lowest frequency components, as shown in Figure 1b, greatly emphasizes this peak, showing how the long-term trend (due to the satellite's motion along its orbit) and low-frequency noise (primarily below \(\simeq\) 60 Hz, as discussed before) hinder the detection of this peak. The identification of peaks within the IPSD forms the foundational step of WhISPER. Figure 2 (top three panels) illustrates SCM-ELF PSD data from the diurnal semiorbit 226220 (1 March 2022), with the X, Y, and Z magnetic field components (from top to bottom) visualized as time-frequency spectrograms. The bottom panel presents the total Integrated Power Spectral Density (IPSD\({}_{\text{t}}\)), obtained by summing IPSD\({}_{\text{X}}\), IPSD\({}_{\text{y}}\) and IPSD\({}_{\text{z}}\), with local maxima (grey dots) identified using the MATLAB R2024a built-in function \"findpeaks\". Vertical dashed lines highlight the most prominent peak (blue),detected at \(t_{a}=12\):34:37.973 UT, and a representative minor peak (red), identified at \(t_{b}=12\):26:29.495 UT. As observed in the top three panels of Figure 2, no discernible whistler signature is evident within the spectrograms, apparently suggesting the absence of whistler waves at the identified IPSD peaks locations. However, this may be attributed to the limited temporal resolution inherent in the satellite's PSD data. To confirm the presence of whistler waves associated with detected IPSD peaks, we investigated the signal waveform and performed high-resolution time-frequency spectrograms within a \(\simeq 2\) s time window centered on each peak. Specifically, we calculated a STFT by sliding an analysis window of length \(N\) data points over the signal with no overlapping and performing a discrete Fourier transform (DFT) on each windowed segment. The window length \(N\) was set to 32 for EFD and 64 for SCM, resulting in frequency resolutions of 156.25 Hz and 160 Hz for electric and  
Figure 1: Effect of removing the lowest frequency components in EFD-ELF IPSD. (**a**) IPSD calculated using \(j_{MIN}=1\). (**b**) IPSD calculated using \(j_{MIN}=30\).