I don't believe the second statement given in the copied text and repeated below is accurate, which gives me less confidence that the developer of the new algorithm had a complete understanding of signal processing:
Simple decimation is not good enough since the frequency band of
interest may lie above the frequency range allowed by the sampling
frequency.
And then the article further suggests that a special new technique that didn't otherwise exist is needed in order to reduce the sampling frequency while retaining the spectral information in a band of interest that lies at frequencies higher than half the new sampling frequency.
No such special new technique is needed. Simple decimation is the combination of a frequency selective filter and down-sampling (selecting every Dth sample for a decimate by D and throwing away the rest). This does not preclude the use of bandpass filters as the filtering solution which for a real signal would retain all spectral information in any band extending over half the sampling rate. To preserve all spectral information in any band extending over the full sampling rate, a complex signal is needed.
The article describes using complex demodulation, meaning shifting a passband of interest to baseband where a low pass filter could be used prior to decimation. This process is referred to as homodyning the signal by multiplying it by a complex tone at the center frequency of the signal such as to move the signal in frequency to baseband. Instead, the filter coefficients themselves in the low pass filter can be homodyned with the same process, resulting in transforming the low pass filter to a band pass filter (moving the filter to the signal instead of moving the signal to the filter). The decimation process itself will then directly create the spectrum at baseband at the lower sampling rate.
Also to note regarding the unique spectrum that can be preserved when a complex signal is used. Complex demodulation preserves the entire frequency range from DC to the sampling rate, or equivalently from $-F_s/2$ to $+F_s/2$ (Where $F_s$ is the sampling rate). Any real signal will be complex conjugate symmetric in frequency, and thus the negative half spectrum ($-F_s/2$ to $0$) is equivalent to the positive half spectrum ($0$ to $+F_s/2$) with a conjugation of the phase for that case, so provides no further information; therefore the unique spectrum for any real signal can only exist in a frequency band that extends over half the sampling rate. We have no such restriction when we work with a complex signal, and therefore the entire frequency range from $-F_s/2$ to $+F_s/2$ (or any band over $F_s$) would be unique. By multiplying the real passband signal with a complex Local Oscillator (done with a sine and cosine and two multipliers), we get the complex output representing the complex down-converted spectrum. This process too can be transformed to quadrature bandpass filters which would provide the Hilbert transform to the real passband signal, converting it to a complex passband signal (when the interest is preserving the full band over the decimated sampling rate).
This is explained in more detail at this post.
So if there was interest in preserving a unique spectrum that extends over a frequency span equal to the new decimated sampling rate, the common techniques are to use complex demodulation followed by two low pass filters (on the I and Q datapaths for the complex output signal) and then down-sampling by selecting every Dth sample, or quadrature bandpass filters followed by the same down-sampling.
