220.127.116.11(3). Definitions of time constant
When comparing the effects different compression systems, it is important to knowhow attack and release time are defined, since they describe the reaction of a compressor to changes in signal amplitude. Currently, several definitions of attack and release time are in use. The two standards that are most frequently used are an international/European (IEC 60118-2, 1983) and an American (ANSI S3.22, 1996) standard. Both the IEC 60118-2 (1983) and the previous (obsolete) ANSI S3.22 from 1987, define attack and release time according to a change in input level from 55 to 80 dB (and vice versa) of a sine wave with a frequency of 2 kHz. Both attack and release times are defined with respect to a level 2 dB off the steady state output level.
However, the new ANSI S3.22 (1996) defines attack and release time for a change in input level from 55 to 90 dB (and vice versa) for a sine wave of arbitrary frequency. Attack time is defined as the time it takes the output level to reach 3 dB above steady state output level, release time is the time it takes to reach 4 dB below steady state output level.
Both IEC and ANSI define time constant as the time it takes the output level to reach a certain distance from the final steady state level. This type of definition is ambiguous because the value of time constant is not only influenced by the speed of the peak detector (the RC constant), but also by the amount of overshoot. This implies that the behavior of two systems with the same IEC/ANSI time constant can be very different (Kates, 1993). For instance, one system with a low threshold and fast compression, and another system with a high threshold and slow compression, might have the same release time constant when measured over the entire input range. Of course, this is remedied by IEC and ANSI through the specification of fixed input levels for time constant measurements.
In contrast to IEC and ANSI, we define time constant mathematically as the time it takes for the output level to reach 1/e (± 37%) of the ultimate change in gain. Fig. 1 illustrates the difference between our and the IEC definition. From the figure it can be seen that the definitions are fundamentally different. Both the IEC and ANSI definitions are based on the tail of the response, while our definition is based on the initial part. Consequently, the ratio of time constants according to the IEC/ANSI definition and ours is not constant, but depends on the amount of overshoot (and therefore on the combination of input signal, compression ratio and threshold).
A change in input from 55 to 80 dB with CR=2 results in an overshoot of the output level of 12.5 dB. Using this overshoot and assuming logarithmic decay for an IEC system, the ratio between our (Texp) and the IEC definition (TIEC) is Texp/TIEC = 0.4 for both attack and release time. For an ANSI (1996) system the ratio for the same input rise is Texp/TANSI = 0.5 for attack time and Texp/TANSI = 0.6 for release time. Since these ratios depend on overshoot, they differ for different input signals and compression ratios.
An overshoot of 6.25 dB (25 dB input change with CR=4) and 16.7 dB (25 dB inputchange with CR=1.5) results in Texp/TIEC = 0.7, and Texp/TIEC = 0.3, respectively. In comparing our results to those specified in terms of TIEC or TANSI we suggest to use the factor of 0.4.
- Dillon, H. (1996), “Compression?: Yes, but for low or high frequencies, for low or high intensities, and with what response times?” Ear and Hearing 17, 287–307.
- Goedegebuure A. ‘Phoneme Compression Processing of the Speech Signal and Effects on Speech Intelligibility in Hearing-Impaired Listeners’. Proefschrift Erasmus Universiteit Rotterdam, 2005.
- Goldstein, JL. (1967), ‘Auditory nonlinearity’ Journal of the Acoustical Society of America 41, 676–689.
- Houben 2006. ‘The Effect of Amplitude Compression on the Perception of Speech in Noiseby the Hearing Impaired
- Killion, M. C., Staab,W. J., and Preves, D. (1990), ‘Classifying automatic signal processors. Hearing Instruments 41, 24–26.
- Lyzenga, J., Festen, J., and Houtgast, T. (2002), ‘A speech enhancement scheme incorporating spectral expansion evaluated with simulated loss of frequency selectivity’. Journal of the Acoustical Society of America 112, 1145–1157.
- Oxenham, A. J. and Bacon, S. P. (2003), “Cochlear compression: Perceptual measures and implications for normal and impaired hearing,” Ear and Hearing 24, 352–366.
15 augustus 2017