Study of the continuity of the phase of harmonics at the Nyquist frequency, search for stable features of digital voice recorders..
Ivanov I.L.
Orel
Study of the continuity of the harmonic phase at the Nyquist frequency, search for stable features of digital voice recorders.
Expert practice of studying phonograms presented on digital media (CD-ROM, etc.), obtained by rewriting from digital recording devices, has shown that when answering questions about editing or changes made during or after recording, the expert may encounter the absence of any diagnostic or identification features on the phonogram being examined. At the same time, the fact that the expert understands that the phonogram from the digital voice recorder directly gets to the computer hard drive as an audio file, which can then be manipulated in any way in standard audio editors, may lead to an uncertain state when answering questions, especially computer editing. This is due to the absence of traces of the recording channel and all stable features characteristic of analog recording on the phonogram.
A detailed study of the recording channels of high-end digital voice recorders showed that they also leave traces. It turned out that the built-in ADC in the recording channel leaves some traces in the form of Aliasing, as well as good traces at the Nyquist frequency, which is not audible, and not visible in most cases on standard audio editors. As an example, let's look at the average spectrum of a part of a phonogram using Sound Forge and analyze the Nyquist frequency of a phonogram originally recorded on a high-end digital voice recorder, then copied from a flash drive to a laser compact disc — a real examination.
The mathematics embedded in audio editors refuses to perceive the Nyquist frequency, since it is the limit. The pictures differ sharply when compared with the expert software both in time and frequency resolution: Fig. below.
The Nyquist frequency is perfectly visualized, measured, etc.
In the process of studying the average frequency response, it was revealed that a low-pass filter is used in the recording path, with a cutoff frequency starting from 6000 Hz, as well as the presence of the Nyquist frequency as a half sampling frequency of 16 kHz — i.e. 8000 Hz, which is clearly observed in the average frequency response at the level of -88.7 dB. From the theory: this frequency in the signal is represented by only two samples, i.e. we have the Nyquist limit. The phase characteristic must be represented by only two components shifted by exactly 180 degrees.
Let's look at the phase behavior of this frequency:
The study confirms our assumption that at this frequency, if there are breaks in phase, but only by 180 degrees. But let's also pay attention to the constancy of the amplitude of the presented harmonic. It does not depend on the recording channel and is constantly present on the phonogram. In the figure, we see its amplitude of about 1 count. An attempt to remove any time interval from this phonogram will lead to a break of 0 degrees or 180 degrees, which complicates the expert's actions on probability = 0.5 (if at the moment of removal the phase break = 0 degrees, then we do not see a phase break). When inserting a fragment, we will observe two phase transitions:
The joint between the soundtrack and the beginning of the insert.
The exit from the fragment and the continuation of the soundtrack.
But in the insert mode, the probability of detecting the moment of insertion increases to 1-(0.5*0.5)=0.75. The figure above. And at the same time, this does not affect the amplitude in any way (which is a very good sign of the editing location)
3. An attempt to superimpose a previously copied section in two adjacent places of the soundtrack is shown below:
In this case, as we see in the figure, in which two superpositions were made, the picture is clearly different from deletion or insertion. Since the amplitudes coincide, and the phase can take only two values: 0 or 180 degrees, then by the amplitude we can immediately estimate this: either it has increased or decreased. When adding (superpositioning) the signal by amplitude 1:1 — we observe either an increase in amplitude by two times or a decrease to zero — as can be seen in the figure (depending on how the phases of 0 or 180 degrees coincide for this frequency).
When studying the phase and amplitude characteristics of the entire phonogram, it was shown that in places of overload, when the acoustic signal at the Nyquist frequency is comparable in amplitude, in these places we observe amplitude interference. At moments of zero amplitude, as we see in the figure, there is uncertainty in the phase measurement and the phase can change sign by 180 degrees. This is observed on very loud ringing sounds («ч, щ», etc.). But the phase gap is understandable to the expert, since it is usually within one word, editing on which is very difficult without the ability to control your actions, or on the other hand — this will be noticeable at the auditory-linguistic level.
At the moments of recording channel overload we can observe the aliasing effect, see below: Note in the center of the graph, from 6000 to 8000 kHz there is a spectral herringbone, although, starting from 6000 kHz, we have a fairly good filter with a large suppression slope.
Thus, we can summarize some of the results of the study and list the features found.
Constancy of the frequency response of the recording channel, due to the built-in filter before the ADC, i.e. the presence of a cutoff and its constancy of decline with increasing frequency.
The suppression level reaches -130 dB, which is unattainable if the phonogram is on a magnetic tape.
The amplitude tends to zero when studying frequencies around 0 Hz. At moments of overload, the aliasing effect is observed.
Constancy of the amplitude of the harmonic with the Nyquist frequency, independent of the recording channel.
Time intervals without channel overload clearly preserve the behavior of the phase and amplitude of the Nyquist frequency under study.
In moments associated with channel overload, a 180 degree break is allowed if the moment of break coincides with the moment of zero amplitude of the frequency under study.
Absence of a smooth change in the Nyquist frequency, since this frequency in modern recording devices has quartz stabilization.
Absence of jitter (secondary modulation), if the phonogram is in analog form on magnetic tape.