DRC-动态范围控制

Basics

The dynamic range of a signal is defined as the logarithmic ratio of maximum to minimum signal amplitude and is given in decibels. The dynamic range of an audio signal lies between 40 and 120 dB. The combination of level measurement and adaptive signal level adjustment is called dynamic range control. Dynamic range control of audio signals is used in many applications to match the dynamic behavior of the audio signal to different requirements.

Figure 7.1 shows a block diagram of a sysstem for dynamic range control.After measuring the input level $X_{dB}(n)$,the output level $Y_{dB}(n)$ is affected by multiplying the delayed input signal $x(n)$ by a factor $g(n)$ according to

$$y(n)=g(n)\ast x(n-D)$$

The delay of the signal $x(n)$ compared with the control signal $g(n)$ allows predictive control of the output signal level.This multiplicative weighting is carried out with corresponding attack and release time.Multiplication leads,in terms of a logarithmic level representation of the corresponding signals,to the addition of the weighting level $G_{dB}(n)$ to the input level $X_{dB}(n)$,giving the output level

$$Y_{dB}(n)=X_{dB}(n)+G_{dB}(n)$$

Static Curve

The relationship between input level and weighting level is defined bu static level curve $ G_{dB}(n) = f(X_{dB}(n)) $.An example of such a static curve is given in Fig.7.2.Here,the output level and the weughtng level are given as functions of the input level.

With the help of a limiter, the output level is limited when the input level exceeds the limiter threshold LT. All input levels above this threshold lead to a constant output level. The compressor maps a change of input level to a certain smaller change of output
level. In contrast to a limiter, the compressor increases the loudness of the audio signal.The expander increases changes in the input level to larger changes in the output level.With this, an increase in the dynamics for low levels is achieved. The noise gate is used to suppress low-level signals, for noise reduction and also for sound effects like truncating the decay of room reverberation. Every threshold used in particular parts of the static curve is defined as the lower limit for limiter and compressor and upper limit for expander and noise gate.

In the logarithmic representation of the static curve the compression factor $R$ (ratio) is defined as the ratio of the input level change $\Delta P_1$ to the output level change $\Delta P_0$:

$$R=\frac{\Delta P_1}{\Delta P_0}$$

With the help of Fig.7.3 the straight line equation $Y_{dB}(n)=CT+R^{-1}(X_{dB}(n)-CT)$ and the compression factor

$$R=\frac{X_{dB}(n)-CT}{Y_{dB}(n)-CT}=tan{\beta }_C$$

are obtained,where the angle $\beta$ is defined as shown in Fig.7.2.The relationship between the ratio $R$ and slop $S$ can also be derived from Fig.7.3 and is expressed as

$$S=1-\frac{1}{R}$$

$$R=\frac{1}{1-S}$$

Typical compression factors are

$$\begin{gathered} R=\infty ,limiter, \\ R>1,compressor(CR:compressorratio), \\ 0<R<1,expander(ER:expanderratio), \\ R=0,noisegate. \end{gathered}$$

The transition from logarithmic to linear representation leads,from $R=\frac{X_{dB}(n)-CT}{Y_{dB}(n)-CT}=tan{\beta }_C$,to

$$R=\frac{{\log }_{10}\frac{\hat{x}(n)}{CT}}{{\log }_{10}\frac{\hat{y}(n)}{CT}}$$

where $ \hat{x}(n) $ and $ \hat{y}(n) $ are the linear levels and $CT$ denotes the linear compressor threshold.Rewriting previewing formula gives the linear output level

$$\begin{gathered} \frac{\hat{y}(n)}{CT}=10^{1/R{\log }_{10}(\hat{x}(n)/CT)}=(\frac{\hat{x}(n)}{CT}{)}^{1/R} \\ \hat{y}(n)={CT}^{1-1/R}\ast {\hat{x}}^{1/R}(n) \end{gathered}$$

as a function of input level.The control factor $g(n)$ can be calculated by the quotient

$$g(n)=\frac{\hat{y}(n)}{\hat{x}(n)}=(\frac{\hat{x}(n)}{CT}{)}^{1/R-1}$$

With the help of tables and interpolation methods, it is possible to determine the control factor without taking logarithms and antilogarithms. The implementation described as follows, however, makes use of the logarithm of the input level and calculates the control level $G_{dB}(n)$ with the help of the straight line equation. The antilogarithm leads to the value $f(n)$ which gives the control factor $g(n)$ with corresponding attack and release time (see Fig.7.1).