04 PrProc.oc. of the 7 thth Int. Confer Conferenceence on Digital A Audioudio Ef Effectsfects (D (DAFx’04),AFx'04), Naples, Italy,Italy, October 5-8, 2004 DAFx DIGITAL EMULATION OF ANALOG COMPANDING ALGORITHMS FOR FM RADIO TRANSMISSION Jurgen¨ Peissig Jan Remmer ter Haseborg Sennheiser Electronic, Wedemark, Germany Technical University Hamburg-Harburg, Germany [email protected] [email protected] Florian Keiler, Udo Zolzer¨ Helmut-Schmidt-University, Hamburg, Germany [email protected] ABSTRACT expander control path inputs. Most of these artifacts cannot be Analog compander systems have been used to suppress the per- perceived because of being psychoacoustically masked by the pre- ception of noise in low dynamic range analog signal storage (tape ceding sounds (below masking threshold). recording) and signal transmission (FM radio). Commercial com- Several commercial analog compander systems were on the pander systems have been analyzed with respect to their signal pro- market. Each system was optimized for its main application. Op- cessing requirements. The general structures of single- and multi- timization could be done by choosing appropriate frequency pro- band compander systems have been implemented on a high per- cessing structures (broadband, sliding band or multi-band) as well formance audio PC workstation. Audio tests and measurements as optimizing the time dependent parameters like attack and de- with the optimized compander algorithms and parameters show cay times of the envelope (level) estimator and the compression very good performance. Even for transmission channels with very factors. Well known compander systems for professional applica- low signal-to-noise ratio (SNR of only 40 dB) an optimized dig- tions like studio tape recorders and movie sound recording are the ital multi-band compander emulation removes the channel noise Dolby A and SR type and the TELEFUNKEN Telcom C4 compan- perceptively from the output signal of the transmission system. der as well as the dbx compander. Principles of those companders have be simplified for usage in consumer variants like Dolby B and C, the TELEFUNKEN HighCOM system and the Burwen Noise 1. INTRODUCTION Eliminator for the use in cassette tape decks. Studio tape recorders and tape decks are not produced any Analog tape recorders as well as analog FM radio transmission more and their usage is very limited nowadays to those locations systems show an audio dynamic range of only 50 to 70 dB de- where a considerable amount of tape material is available (e.g. pending on tape material or RF reception. This reduced dynamic the archives of radio stations). Nevertheless analog compander range results in a clearly audible noise floor which is very distract- systems can still be found in wireless microphone systems. All ing. In order to reduce the noise perception audio compressors large brands use analog broadband or multi-band companders in have been used prior to the recording or transmitting process. The their wireless transmitters and complementary expanders in the re- compressor reduces the dynamic range of the input signal (e.g. 100 ceivers (e.g. the Sennheiser HiDyn Plus compander or the dbx-like dB to 50 dB at a compression ratio of 2) and as a result all signal compander circuitry in the Shure wireless FM systems). amplitudes are above the noise threshold of the tape or the FM As digital signal processing circuitry becomes cheaper but more transmission. During play-back or in the FM receiver an appropri- powerful, smaller, and less power consumptive, many analog cir- ate expander restores the original dynamic range of the signal by cuits are emulated on digital systems. This holds also for compan- applying an attenuation depending on the signal amplitude. This der systems. Most of the above mentioned compander systems are results in an expansion (e.g. from 50 dB to the original 100 dB) of emulated digitally and are used where the original equipment is the dynamic range which on the other hand reduces the noise level not available any more (e.g. in the radio-station to restore old ana- by 50 dB. With a compression ratio of 2 for example the perceived log tape material onto digital media.) The combination of analog signal-to-noise ratio (SNR) can be increased by a factor of 2 (e.g. FM transmission and digital companding algorithms is also used from 50 dB to 100 dB). in the field of wireless microphones. A digital emulation of the This processing is called companding (compression and ex- analog compander principles yields several advantages: pansion). Companding is a time-variable processing and thus can cause audible alterations of the processed signal. By using com- a) more complex compander algorithms can be realized on a plementary compressor and expander circuitry the original signal smaller circuit board size indeed can be restored at the output without any alteration if no b) compander parameters can be programmed via presets noise is added in the compressed path. In real companded signals with noise added we find signal alterations and disturbance like c) more complex / adaptive signal processing can be used. noise pumping and breathing as well as distortion caused by dy- All signal processing techniques aim at the reduction of compand- namic mistracking of the level of the respective compressor and ing artifacts, at the optimal adaptation of the compander settings DAFX-1 285 — DAFx'04 Proceedings — 285 PrProc.oc. of the 7 thth Int. Confer Conferenceence on Digital A Audioudio Ef Effectsfects (D (DAFx’04),AFx'04), Naples, Italy,Italy, October 5-8, 2004 a) to the FM transmission characteristics and at increased reliability Compressor Expander x(t) y(t) y’(t) x’(t) and convenience of the wireless FM link. Channel sC(t) Level detection Level detection sE(t) and and Compressor Expander control control b) Compressor Expander FC(x(t)) FE(y’(t)) x(t) y(t) y’(t) x’(t) x(t) y(t) y’(t) x’(t) Channel HC(z,t) Channel HE(z,t) Level detection sC(t) sE(t) Level detection and and control control Figure 1: Compander system. c) Compressor y(t) y’(t) Expander x(t) x’(t) Channel 2. THEORY OF OPERATION sC(t) Level detection Level detection sE(t) and and control control Compander systems are based on a compressor system before the d) transmission and expander system at the receiver (see Figure 1). Compressor y(t) y’(t) Expander x(t) x’(t) Existing compander systems are built complementary and have Channel time-variant transfer functions HC (z, t) and HE (z, t), where the expander transfer function HE (z, t) is the inverse of the compres- s (t) s (t) Level detection C E Level detection sor transfer function HC (z, t) according to and and control control 1 HE (z, t) = . (1) HC (z, t) Figure 2: Feed-back and feed-forward control structures of sylla- ble and formant companders. Single-band multiplicative structure The notation H(z, t) denotes a time-variant Z-transfer function, with control signal derived a) from the compressed signal and b) because we are aiming at discrete-time realizations for the com- from the original signal. Multi-band additive structure with con- pressor and the expander. If the compander processing does not trol signal derived from c) the compressed signal and d) from the meet equation (1), the original signal can not be restored and the original signal. compander processing becomes audible. For compander systems the compression factor k is calculated from the signal input level The compressed signal y(t) can thus be calculated by the envelope Px(t) in dB and the signal output level Py(t) in dB according to Envx(t) of the uncompressed signal or the envelope Envy(t) of the P (t) compressed signal according to k = x . (2) Py(t) F (Env (t)) y(t) = C x · x(t) (7) Envx(t) For the noiseless transmission case the compander relation can be Env (t) written as y(t) = y · x(t). (8) FE (Envy(t)) y(t) = FC (x(t)) (3) During reconstruction the expanded signal x0(t) is calculated 0 FE (y(t)) = x(t), (4) accordingly from the received compressed signal y (t) with the envelope of the input or the output of the expander given by where FE (x(t)) and FC (x(t)) denote the expander and compres- F (Env 0 (t)) sor law (gain functions) that depend on the input signal −1 ≤ x0(t) = E y · y0(t) (9) x(t) ≤ 1. For the compressor law the following relations hold Envy0 (t) Env 0 (t) x0(t) = x · y0(t). (10) FC (−x(t)) = −FC (x(t)) FC (Envx0 (t)) FC (±1) = ±1 These different approaches result in different possible processing |FC (x(t))| ≥ |x(t)|. structures for syllable and formant companders which are shown in Figure 2. The control signals sC (t) and sE (t) are the so-called Broadband (syllable) companders as well as multi-band (for- gain factors derived from the signal envelopes by nonlinear map- mant) companders use the signal envelope Envx(t) instead of the pings based on the compression factor k. actual signal x(t) to calculate the gain factors [1]. The compressor Those structures that derive the control signal from the com- law of a syllable or formant compander working with the envelope pressed signal are favoured in real applications because the enve- or an appropriate estimate is then defined by lope detector operates on a signal with reduced dynamic range, especially when the level detector contains true RMS (root mean Envy(t) = FC (Envx(t)) (5) square) processing. Working on signals with reduced dynamic range imposes less demands on the dynamic range of the analog and for the expander law respectively circuitry or the digital word length [2].