# An Audio Distortion Dynamic Range Index for Evaluating the Performance of Audio Systems
## 1 Introduction  
Objective performance measurement is of great significance to the design and evaluation of audio systems. Commonly used indexes are signal-to-noise ratio (SNR), total harmonic distortion (THD), and signal-to-noise and distortion ratio (SINAD), and dynamic range (DR). They are interrelated and can be derived from each other [1; 2]. For dynamic range performance evaluation, DR is an important index. However, the DR index in the existing literature does not show strictly consistent definitions and measurement conditions, which makes it difficult to achieve fair and effective performance comparisons between devices under test (DUTs). The DUT can be hardwares or algorithms. To the best of the authors' knowledge, there is no official or formal definition of the term DR. The \"Standard method for digital audio engineering measurement of digital audio equipment\" of Audio Engineering Society (AES) first defined its measurement as _\"a comparison between the peak instantaneous sound levels occurring during a music performance and the just audible threshold for white noise when added to the program source\"_[3]. Its latest version described DR as _\"the ratio of the full-scale level at the output of the EUT to the weighted noise and distortion level in the presence of a low-level signal. It includes all harmonic, inharmonic, and noise components.\"_[4]. Audio Precision stated that _\"Dynamic range is the difference, usually expressed in decibels, between the highest amplitude signal which a device can output atits rated distortion, and the noise level of the device_\" [5]. Other similar definitions of DR were given in [6; 7; 8; 9; 10]. Moreover, it is stated that DR can be replaced by SNR if SNR's measurement condition is 0 dBPS input [3; 8], which means the implication of DR and SNR are consistent under this condition [5]. However, the definition of SNR is still ambiguous for whether it includes harmonics and spurious. A direct description of \"S/(N+D)\" or \"S/N\" is clear but not convenient [11]. Currently, the DR index is normally defined by a ratio; however, some details of the numerator and denominator have not been explicitly specified. They are listed as follows. * The noise floor, which has been discussed in detail in [12]. The dominant view of noise floor calculation is to use the root-mean-square (RMS) amplitude of noise [3; 4; 6; 7]. The harmonic, spurious and DC components are included in the noise calculation in [4], and not included in [12; 13]. This determines whether DR equals to SINAD or SNR under 0 dBPS input. * The maximal output. An instantaneous peak was used in [3; 14], and an implied RMS peak was used in [4; 6; 7]. The inconsistency of definitions and the ambiguity of details lead to differences between critical measurement conditions and schemes. Except for the different measurement conditions listed in [6], other critical differences are as follows. * The amplitude of the testing signal. AES, IEC and EIAJ standards all use a \(-\)60 dBFS signal [3; 4; 15; 16], and they are commonly used in [17; 18]. But the amplitude is replaced by \(-\)40 dBFS in [19]. * The distortion degree. For example, _\"rated distortion\"_ was used in [8], and _\"often 1%\"_ was expressed in [5], and _\"without distortion\"_ was adopted in [9; 10]. Then there are the measurement schemes. AES standard directly measures the ratio of the maximum of DUT output to the noise and distortion by a notch filter [4; 19; 20]. IEC, EIAJ and Kester obtain DR by inverting the measured THD+N [15; 16; 21]. Subtracting THD+N from THD to make the measurement results meaningful in the presence of a signal is used in [19], because the noise floor is different when an input signal is absent or not. In summary, the definition and measurement methods of DR are ambiguous in many respects. However, there are two main reasons why the results vary greatly. First, the degree of distortion is not clearly specified during the measurement. Generally, it is smaller for a lower amplitude of the testing signal.