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Created on 19.12.2008 17:44.

Updated 09.16.

Author: Alekseev Igor.

Electronics is the science of contacts.

Electroacoustics is the science of transducers.

The use of cascades in analog audio engineering, correcting the frequency response / phase response of the transmission path in accordance with the accepted standards for predistortion, used when recording phonograms on audio carriers, is mainly based on the use of chains containing reactive elements (C or L) in the correcting (amplifying) RCL stages. having a frequency-dependent impedance.

The use of correcting chains of the 1st order (RL or RC) does not introduce additional transient (oscillatory) processes in the reproduced audio signal, which cannot be said about correctors of higher orders. Nevertheless, frequency correction by circuits of the 2nd (and higher) orders in analog paths is used everywhere because caused by:

- the presence of electromechanical (100% non-resonant) or electromagnetic transducers in analog sound sources with anomalies in the operating frequency range (magnetoresistive, piezo-, photo-, thermal and “nano” transducers are not considered for obvious reasons);
- the need to use multi-stage amplifying circuits, the active elements of which have parasitic distributed capacitances (and the connecting wires have inductances) and which are built using feedback;
- the presence of electrodynamic (electrostatic) converters, for example, under the name “loudspeaker head” (also 100% non-resonant, including even in the middle part of the operating frequency range).

It should be noted that the most common methods for calculating corrective circuits that are used in practice by the creators of audio equipment are based on a mathematical apparatus based on the description of effects arising under the influence of periodic arguments (which may be a certain measuring signal of a pure tone or, for example, a signal of quasi-stationary interference).

These methods cannot be applied in their pure form for frequency equalization of a non-deterministic pre-determined musical audio signal, except for equalization that is completely complementary (carried out by the same methods) to that used to create pre-emphasis in the recording.

In addition, the applied mathematical apparatus can contain (and contains) particular solutions located in the negative quadrant of the plane of real / imaginary roots, which are always discarded in practice as unrealizable, having no practical value (resistance, capacitance, inductance, frequency, time, etc.). cannot be negative), which, by and large, is a methodological error.

So, for example, a digital processor based on FFT (Fast Fourier Transform – FFT) functions cannot be the final link in a real audio signal processing device and must be supplemented with an analog output adder performing digital processing error correction based on the data of the original (analog) signal.

For example, in the case of building digital band-pass filters for acoustic systems, only digital filters cannot be used, it is necessary to alternate digital band-pass filters with analog ones, obtained by subtracting the output signal of digital filters from the original signal and further analog (before) correction outside their bandwidth.

Otherwise, an uncontrollable digital processing error accumulates in the path, which leads to degradation of the result – “music reduction”.

Another methodological mistake, which is widespread among developers, is the analysis / modeling of losses and the synthesis of the necessary corrective circuits, based on the assumption of the equivalence of mechanoacoustic systems to their electrical counterparts. The error lies in the fact that the rate of energy transfer in electrical (equivalent) systems is close to the speed of light, while in mechanoacoustic systems (prototypes) the rate of energy transfer is determined by the speed of sound propagation in construction materials and air, which, in fact, is almost a million times less …

In other words, this means that developers lose sight of the order of the processes taking place in terms of their flow in time. The error also lies in the fact that any mechanoacoustic system consists of real elements that must withstand a certain mechanical load – to have a constructive margin of safety.

The safety factor can be realized only by increasing the mass of these elements. In relation to an electrical equivalent circuit, this should mean that any electrical element must have the properties of inductance / capacitance (a mechanical analogue of mass, depending on the situation, what we are considering: current or voltage), which must be taken into account when constructing equivalent circuits, and this means imperfection used for the analysis of equivalent models^{[11]}…

Thus, in order to ensure the “preservation of music” in the audio signal, it is necessary to clarify the permissible methods and their limitations for the calculation and application in classical (analog and “new” – digital) correction methods in audio equipment.

## Correction in a narrow frequency range (notches)

Active amplifying stages, in which one or another frequency correction is applied, are not absolutely ideal (linear) and introduce their own noise and distortion into the amplified signal. As a rule, regardless of the correction method: passive or included in the OS of the stage, noises and intrinsic distortions at the output of the correcting stage are correlated with the useful signal.

For example, reducing the level of the network background (subcarrier residues) with a high-quality classical notch filter (correcting cascade) made using minimum-phase mechanisms introduces a transient (oscillatory) process into the output signal and, at the same time, distorts according to the law of the same transfer function (which is designed to combat harmonic background noise) the desired audio signal passing through this stage. The higher the Q-factor of the filter, the higher the degree of distortion of the useful signal, which, in the general case, is not an interference.

In terms of auditory perception, this means a decrease in the amount of useful audio signal. Nevertheless, the interference (in this case, the network background / subcarrier), as a rule, is a rather stable subharmonic signal of approximately constant amplitude in time, while there is no need to talk about the constancy of the amplitude of the musical signal (any composition begins at some point and ends).

In this case, the dynamics of frequency components are distorted (and this is determined only by a real musical signal), the rate of change of the amplitude of which (or the derivative of this rate) falls into the frequency domain of the rejection correction. The same background / subcarrier interference present in a phonogram could be significantly attenuated by being mixed in antiphase with a matched amplitude …

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