The analysis of filtration influence at primary pulsed-code conversion on distortion of input signals of coders with a compression of audio data

In psychoacoustic models of MPEG standards the mechanisms of time masking of signals, spatial dismasking the sources of a sound producing a stereo panorama on front, depth and feature of perception of reverberation components of the stereophonic signals are not considered. These mechanisms of spatial hearing play the most important role for stereo reproduction; they define perception of the basic features of quality of the stereophonic sounding, such as spatial perception, sounding transparency, naturalness and wealth of timbres of instruments and voices, perception of acoustic atmosphere of a primary room (a concert hall, studio), etc. Occurrence of this set of distortions leads to decrease in quality of sounding which is distinctly observing by listeners.

However it is necessary to consider, that digital audio signals arrive on an input of coder with a compression after pulsed-code (PSM) conversion. Thus quality of conversion is meant ideal. In a number of works, for example [1], an influence of the errors of quantization on sounding the audio signals written down or transferred with a compression of audio data is shown.

The selective analogue-digital and digit-analogue (ADC and DAC) PSM conversion provide an essential influence on producing the high quality indicators at using the digital methods of sound recording as well as at organizing the digital sound broadcasting.

The low-frequency filters (LPF), limiting a spectrum of input frequencies and eliminating high-frequency components of a output signal accordingly are located at theinputofADCandattheexitofDAC.

Signal suppression of LPF on the frequency equal to half of frequency of digitization, should be not less than 60 dB. In this case the steepness of slope of LPF should be very high (120 dB\octave). For achievement of such values of steepness the high order LPF should be created. Such filters have considerable disadvantages and the main essentially nonlinear phase characteristic that leads to distortions of audio signals appreciable by ear as loss of “transparency” of the sound. Besides, such filters becomes rather difficult in manufacturing and adjustment, and, hence, expensive. In audio equipment the greatest distribution was received by Butterworth and Chebyshev filters.

A dependences of an order of the filter ( N_b , N_c ) from demanded attenuation ( A _min) on boundary frequency of a leakless strip ( f _gtsll) at admissible non-uniformity in pass-band A _max = 0.5dB for typical ADC cases are calculated for Butterworth and Chebyshev LPFs and shown in figure 1:

• –    for signals of a sound broadcasting ( V) for the higher classofquality ( f_b =15,000Hz, f _gtsll=16,000Hz);

• –    for audio signals at a sound recording ( f_b = 20,000 Hz, f _gtsll=20,000Hz).

All calculations in the given work were carried out in software MathCAD.

The figures shows, that for the reception of the required attenuation 60 dB at the boundary frequency of a leakless band the filter order of approximately 124 in the first case, and more than 42 in the second case is required. Such filters in analogue circuitry cannot been realized.

Calculations shows that, for the case of sound recording with the aid of Chebyshev or Butterworth filters, the orders of such filters of 12 and 42 are required respectively. In analogue circuitry the filters with orders 6 or 8, but not above, can be realized. As a criterion of linearity of the phase characteristic a change of group delay time ( τ _gt) which is normalized the domestic State Standard (GOST) 11515–91 for the channels of sound broadcasting can be considered. It is obvious, that the requirements shown to the sound recording and sound reproducing equipment should be more rigid, than to the channels.

In figures 2 and 3 the received dependences of group delay time for Butterworth filters with order 42 and Chebyshev filter with order 12 are shown. The normalized frequency ( w ) is postponed along X axis, and w = l corresponds to the boundary frequency of a pass band.

Along with impossibility to realize analogue filters with considered orders, the non-uniformity of group delay time in a pass band is 40 ms for the Butterworth filter and 73 ms for the Chebyshev filter. Such non-uniformity of group delay time essentially deforms a primary audio signal (an input signal of the filter).

One of known methods for the solution of the given problem is the using of the PSM coders (decoders) in which

Amin

Fig. 1. Dependences of an order of Butterworth ( N_b ) and Chebyshev ( N_c ) filters

from Amin (— — for signals 3 V, for a sound recording case)

T(w)

idop(w)

w

Fig. 2. The dependence of group delay time of Butterworth filter from normalized frequencies ( τ ( w )) as well as standard ( τ _dop ( w )) admissible delay time

TO)

Tdop(w)

Fig. 3. The dependence of group delay time of Chebyshev filter from normalized frequencies ( τ ( w )) as well as standard ( τ _dop ( w )) admissible delay time

ADC (DAC) work at the raised frequency. It allows to make considerably lower the requirements to the slope steepness and to the order of analogue LPF, which provide a preliminary filtration of the primary signal. Then the basic attenuation at the boundary frequency of a leakless strip will be provided with a digital filter.

At the choice of structure of the digital filter the nonrecursive filters have preference in this case.

The decisive advantage of such filters is possibility to receipt the linear phase-frequency characteristics. In this case, the definition of the requirements to analogue LPF and the order of such LPF should be focused on preliminary filtration and providing the demanded non-uniformity of group delay time in a filter pass band.

In figure 4 the calculated dependences of group delay time from normalized frequencies (WBasignalitisequal1) are shown for Butterworth LPF. Such dependences for Chebyshev LPF (with 2nd, 4th, 6th and 8th orders) are shown uniformity in a pass band does not exceed 3.5 ms [2]. Working attenuation on the boundary frequency of leakless strip (Apmin) of 5 dB for the case of digital transmission of the signals of sound broadcasting described above, and of 13 dB for the case of digital sound recording is thus provided.

The Chebyshev filter seems acceptable with an order not above than 6. In this case the non-uniformity on group delay time in a pass band does not exceed 11 ms, that seems acceptable with taking into account the properties of hearing. Besides the requirements of State Standard 11515–91 are practically satisfied. Thus LPF provides A _pmin of28dB(for the sound recording conditions given above) and 10 dB (for the case of transferring the signals of sound broadcasting).

At the using PSM coders (and decoders) with redigitization in codec’s and compression of audio data for digital transmitting the signals of sound broadcasting and for digital sound recording the minimal distortion (appreciable on hearing) occur under the best linearity of phase

Fig. 4. The dependence of group delay time from normalized frequencies for Butterworth LPF 2nd (τ(w)), 4th (τ1(w)),

6th ( τ 2( w )) and 8th ( τ 3( w ) orders

Fig. 5. The dependence of group delay time from normalized frequencies for Chebyshev LPF ( τ 1( w )), 4th ( τ 2( w )), 6th ( τ 3( w )) and 8th ( τ 4( w )) orders

For the filters realized in analogue circuitry the preliminary filtration is preferable to carry out with the help of Chebyshev filters which provide acceptable non-uniformity of group delay time from the point of view of acoustical perception of admissible distortions and provide rather big attenuation on boundary frequency of a leakless strip.

For receiving the linear phase-frequency characteristics in ADC and DAC with redigitization it is necessary to use non-recursive digital filters.