1 Acoustical Active Noise Control The basic concept of active noise control systems is introduced in this chapter. Different types of active noise control methods are explained and practical implementation in the analogue and digital domain is considered. As it has been explained in the introductory chapter, ANC is an electro-acoustic technique in which unwanted sound is canceled by introducing controllable secondary sources. Generally ANC-systems use the superposition property of sound waves. This property states that when combining two sound waves at a specific position, the resulting wave is found as the sum. Therefore it is possible to cancel out a sound if a sound wave with the opposite sign is emitted. (a) Amplitude Amplitude (b) (c) Amplitude Time Figure 1.1: Basic principle of ANC-systems. The principle is illustrated in figure 1.1. (a) is the noise, which is undesirable. If it is possible to emit a signal as shown in (b) in the spot where (a) is present the resulting signal is the one shown in (c). Hereby the noise has been reduced. Hence, the task of an ANC-system is to detect the noise and emit it with the opposite phase. The amplitude and phase of the primary and secondary noise must match precisely if we want to obtain a high noise reduction [Kuo and Morgan, 1996]. Group 863 April 5, 2005 21.54 1
Chapter 1. Acoustical Active Noise Control 1.1 Active Noise Control methods To find the antinoise signal it is necessary to detect the noise. Figure 1.2 shows a hearing protector equipped with two microphones for noise detection and a loudspeaker for sending out antinoise. The reference or external microphone detects the noise outside the hearing protector. The error or internal microphone detects the sound inside the cup. Hence the signal from the reference microphone is unaffected by the ANC-system. Conversely the error microphone is directly influenced of the output of the loudspeaker. Noise Reference microphone ANC System Loudspeaker Ear Error microphone Figure 1.2: Sketch of a ANC-system implemented in a set of hearing protectors The task of finding and emitting signals of same amplitude and opposite phase can be performed by two different approaches: 1. Feedforward ANC 2. Feedback ANC The difference between the two methods consists in the way the method estimates the noise inside the cup. The following describes the basic operation of the two methods. 1.1.1 Feedforward ANC In figure 1.3 a block diagram of the feedforward principle derived from figure 1.2 is illustrated. The feedforward approach uses the reference signal n(t) to estimate the signal inside the cup. The noise n(t) is filtered through the acoustic filter of the hearing protector H H and becomes the disturbance d(t) inside the cup. Furthermore the noise is picked up by the reference microphone with the transfer function H R and hereby transformed to the electric domain. This signal is filtered through the filters H A and E before it is converted back to the acoustic domain by the loudspeaker with transfer function H L. H A is a filter and H Eq is an 2 Group 863, April 5, 2005 21.54
1.1. Active Noise Control methods Acoustical domain n(t) H H d(t) + e(t) + H R H L H A H Eq Electrical domain Figure 1.3: Block diagram of a feedforward ANC-system. equalisation filter of the loudspeaker and microphone so that: H R H L H Eq = 1 (1.1) Now the transfer function of the feedforward system H F can be determined: H F = E N = H H+H R H A H L H E = H H +H A (1.2) If it is possible to design H A in such a way that H A = H H then H F = 0 and all noise is canceled. 1.1.2 Feedback ANC In figure 1.3 a block diagram of the feedback principle derived from figure 1.2 is depicted. The feedback approach uses the error signal e(t) to find the antinoise. n(t) Acoustical domain d(t) H H + + e(t) H L H E u(t) H A Electrical domain Figure 1.4: Block diagram of a feedback ANC-system. The noise n(t) is again filtered through the hearing protector and becomes the disturbance d(t). The error microphone with transfer function H E detects the error signal. This electrical signal is filtered through H A. The resulting signal is converted into the acoustical domain by the Group 863 April 5, 2005 21.54 3
Chapter 1. Acoustical Active Noise Control loudspeaker with transfer function H L. The system presents a feedback loop and hence the transfer function of the feedback ANC-system H B is given as: H B = E D = H H 1 H E H A H L (1.3) From this equation it is observed that the noise level is reduced by a factor of 1 H E H A H L. In order to achieve a large noise reduction this factor should be as large as possible. 1.2 Practical implementation The practical implementation of an ANC-system is a linear filter. Therefore both kind of ANC approaches can be realized in the analogue as well as in the digital domain. This section deals with the advantages and disadvantages in each domain. 1.2.1 Analogue ANC-systems An analogue ANC-system is an electrical filter which is supposed to be H A as depicted in figure 1.3 in the feedforward case or in figure 1.3 in the feedback case. The advantage of an analogue controller is, that it does provide a very short delay from the input to the output. The analogue approach is now discussed for the two ANC-methods. Analogue feedforward ANC To achieve an efficient noise cancellation H A needs to be equal to H H. Since this transfer function of the hearing protector is acoustical it is strongly dependent on the user. [Elliot, 2001, p. 361] states that the gain variation of an active headset is ±3 db and the phase varies ±20. This refers to the transfer function H L. Furthermore variations of H H will occur and the result is that the performance of the ANC-system will vary with the user and how the cup is placed on the head. Because of this variation it is impossible to implement an analogue filter that provides a high noise reduction for every user. Furthermore, the analogue filter has to be of a high order to estimate H H and the equalisation filter H Eq. Due to component tolerances higher order filters are difficult to implement precisely. Analogue feedback ANC Efficient noise cancellation using the feedback method is achieved by using an ANC-filter H A with a high gain, see equation 1.3. When using this principle the problematic part is to have a high gain and concurrently avoiding an unstable system. In order to have a stable system the open loop transfer function, as stated in 1.4, H O = H E H A H L, (1.4) needs to have a gain less than unity when the phase is 180. Due to the variation of the acoustical transfer functions it is difficult to design a filter H A such that H B is stable as well as providing a high noise reduction. 4 Group 863, April 5, 2005 21.54
1.2. Practical implementation 1.2.2 Digital ANC systems To use a digital filter the signals needs to be in the digital domain. Therefore an AD-converter and a DA-converter is necessary which will introduce a delay. This delay have the effect that the perfect ANC-filter H A becomes non-causal, which implies that it is necessary to know the future. On the other hand it is possible to change the filter coefficient with time. This makes it possible to adapt the system to the current noise figure and thereby reduce non-stationary deterministic disturbances. In the following two different digital approaches is discussed: Nonadaptive and adaptive. As described in section 1.2.1 the ANC problem can be solved using analogue filters. An approach similar to this can be implemented using digital filters and thereby bypassing the complications with component tolerances. Since the behaviour of a digital filter is completely predictable it is less problematic to use filters of higher orders. However the problem regarding delay is introduced and the problems regarding the acoustical variations are unsolved. An adaptive filter tries to adjust the filter coefficients in such a way that the minimum least square of an error signal is minimized. In this perspective the adaptive approach would be able to adapt H A and hereby deal with the acoustical variations. The following will discuss the use of adaptive filters for feedforward and feedback ANC-systems respectively. Adaptive feedforward ANC When using an adaptive filter the error signal needs to be present. Hence, an error microphone is needed. Figure 1.5 shows a block diagram of an adaptive feedforward ANC-system. Note the error microphone denoted by H E. Since H A (z) and H Eq (z) is now digital filters the microphone transfer functions include AD-converters and the loudspeaker transfer function includes a DA-converter. H Eq (z) is not strictly necessary anymore since the adaptive filter automatically performs this task. The arrow through H A (z) indicates, that this transfer function is adjusted with time in order to minimize the output of the error microphone. Acoustical domain n(t) H H d(t) + + e(t) H R H L H E H A (z) H Eq (z) Electrical domain Figure 1.5: Block diagram of an adaptive feedforward ANC-system. Because of the digital system the noise signal will propagate faster through the acoustical system H H (z) than the digital adaptive filter. Therefore the ideal ANC-filter is non-causal, therefore not realizable. For this reason the filter needs to adapt to the current noise profile. This leaves two main features of the filter: How well the filter is able to adapt to a stationary noise and how fast Group 863 April 5, 2005 21.54 5
Chapter 1. Acoustical Active Noise Control the filter is able to adapt to a new noise profile. Adaptive feedback ANC The adaptive feedback ANC uses the error signal for adjusting the filter coefficients as well as for the filter input. Figure 1.6 shows the way to use an adaptive filter in the feedback ANC-method. n(t) Acoustical domain d(t) H H + + e(t) H L H E u(t) H A (z) Electrical domain Figure 1.6: Block diagram of an adaptive feedback ANC-system. Again microphone and loudspeaker transfer functions include AD- and DA-converters. The delay of the digital system may result in instability of the system since the delay in the analogue domain can be seen as a phase lag. This is a problem that needs to be dealt with when using the adaptive feedback method. 1.3 Comparison This section sums up the properties of the two ANC-methods and the advantages and disadvantages in each domain. Table 1.1 displays the properties of the four different combinations of methods and domains. In the table only the adaptive solution is presented since the non-adaptive digital solution has the weaknesses of the analogue as well as the digital domain. Feedforward Feedback Pros Cons Pros Cons Digital Predictable Adapts to variations Non-causal model (delay) Needs DSP Predictable Only one microphone Delay cause stability problems Needs DSP Analogue Short delay Sensible to variations Component tolerances Short delay Realizable filter Variations may make the system unstable Table 1.1: Comparison of digital and analogue feedforward and feedback ANC. 6 Group 863, April 5, 2005 21.54
Appendix I Group 863 April 5, 2005 21.54 7
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Measuring reports A This appendix contains the measurements of insertion loss and impulse responses of the modified hearing protector. For each measurement the purpose, equipment, method/setup are stated and the results are presented and finally discussed. A.1 Insertion loss of hearing protector Date: 03-18-05 Location: VR Lab, B3-103 - Fredrik Bajers Vej 7 A.1.1 Purpose The purpose of this measurement is to find the insertion loss of the hearing protector. The loss is measured both for the original configuration of the cup and with the driver and microphone mounted in the cup. The insertion loss should be used to determine in what frequency band the active noise control should operate. A.1.2 Equipment Apparatus Name AAU-number Dual Channel Real-time Frequency Analyzer Brüel & Kjær Type 2133 08596 Sine/Noise Generator Brüel & Kjær Type 1049 08233 Stereo Amplifier Pioneer A-656 08698 Loudspeaker B & W DM1 S2 02144 Loudspeaker Home made, 2-way 07913 Microphone Amplifier N/A Miniature microphone Sennheiser KE4-211-2 Sn. 106 Hearing protector HP26-358 N/A A.1.3 Method/setup The insertion loss is defined as the mean algebraic difference in db between the one-third octave band sound pressure level, with the hearing protector absent, and the sound pressure level with the hearing protector on [DS/ISO/TR 4869-3, 1994]. The insertion loss was measured using a plane progressive wave using a pink noise sound source. The insertion loss was measured at all one-third octave bands from 63 Hz to 8000 Hz, the center frequencies are shown in table A.1. Five test persons were used for the measurement. The measuring microphone was placed at the entrance of the ear of the test person. The sound pressure levels at the microphone were Group 863 April 5, 2005 21.54 9
Appendix A. Measuring reports 63 80 125 1 200 250 315 400 500 630 800 0 1250 10 2000 2500 3150 4000 5000 6300 8000 Table A.1: Center frequencies (in Hz) used to derive the test signal from pink noise first measured without the hearing protector. The hearing protector was then placed on the test person and the sound pressure levels were measured again. Before each measurement the noise floor was measured to ensure that the test signal was significantly higher. It is assumed that any reflections caused by the room and the influence of the loudspeakers and microphone are the same for all measurements. Since the insertion loss is calculated as the difference between the sound pressure level with and without the hearing protector, these errors are negligible. The setup for this measurement is shown in figure A.1. Hearing protector Sennheiser KE4-211 Sn. 106 1 m Pioneer Stereo Amplifier A-656 Amplfier B & K Sine/noise Generaor Type 1049 Noise generator Microphone amplifier Frequency analyzer B & K Dual Channel Real-time Frequency Analyzer Type 2133 Figure A.1: Schematic diagram of the setup A.1.4 Results Figure A.2 presents the insertion loss for all one-third octave bands, measured both for the original configuration of the hearing protector and the modified hearing protector. The insertion loss is calculated as a mean of the five test persons. It is seen that the modified hearing protector has almost the same insertion loss as the original configuration. At 800 Hz there is a dip in the insertion loss for the modified hearing protector, it lies approximately 7 db below the original configuration. The insertion loss is almost constant for frequencies above 500 Hz and it is approximately 30 db. For frequencies below 500 Hz the insertion loss decreases as the frequencies get lower. A.1.5 Discussion The measured insertion loss deviates from the insertion loss supplied by the manufacture. This deviation is due to the fact that measurements are not performed in the same way. Furthermore the measurements are not A-weighted bla bla bla. The dip at 800 Hz for the modified hearing protector is due to vibrations in the plexiglass<. Below 500 Hz the insertion loss is less than 20 db, 10 Group 863, April 5, 2005 21.54
A.2. Impulse responses 40 30 db 20 10 0 10 62.5 125 250 500 0 2000 4000 8000 Frequency [Hz] Figure A.2: Plot of the mean insertion loss for the five test persons. The bold line shows the insertion loss measured for the original configuration of the hearing protector. The dashed line shows the insertion loss measured for the modified hearing protector. A.2 Impulse responses Date: 03-21-05 Location: VR Lab, B3-103 - Fredrik Bajers Vej 7 A.2.1 Purpose The purpose of these measurements is to obtain impulse responses measured from the speaker unit/far field source to the ear canal, the internal microphone, and the external microphone respectively. The impulse response from the speaker unit to the internal microphone and the ear canal are found in order to detect the differences between both responses. The impulse response from the speaker unit to the external microphone is found in order to detect if the signals from the speaker unit are fed back to this microphone and if they can be neglected. The same measurements are done using a far field source instead of the speaker unit mounted in the hearing protector. Again the purpose is to detect the differences of the impulse responses to the internal microphone and the ear canal. A secondary purpose is to ensure that the driver is able to reproduce the frequencies needed in a ANC system with reasonable attenuation. Group 863 April 5, 2005 21.54 11
Appendix A. Measuring reports A.2.2 Equipment Apparatus Name AAU-number Hearing protector HP26-358 N/A Power Supply Hameg HM 42 33914 MLSSA system 37493 Attenuator - 20 db N/A Microphone Amplifier N/A Miniature microphone Sennheiser KE4-211-2 Sn. 106 Stereo Amplifier Pioneer A-656 08698 Loudspeaker B&W DM1 S2 02144 Loudspeaker Home made, 2-way 07913 A.2.3 Method/setup The measurement setup is shown in figure A.3. All impulse responses were acquired with the Maximum Length Sequence System Analyzer (MLSSA). Hearing protector Sennheiser KE4-211 Sn. 106 1 m Pioneer Stereo Amplifier A-656 Amplifier Microphone Amplifier MLSSA System Microphone Amplifier Power supply Attenuator -20 db Speaker Amplifier The test person does the following: Figure A.3: Schematic diagram of the setup 1. Places ear plug with the miniature microphone mounted in it at the entrance of the ear canal. 2. Places the hearing protectors so that the cushion closes tightly to the head. In the speaker measurement case the output of the MLSSA system is fed to a 20 db attenuator 1 and on to the Speaker Amplifier, which feeds the speaker in the hearing protector. Three 1 The 20 db attenuation is needed since the gain of the speaker unit amplifier was too high. An adjustment of the speaker amplifier gain was performed after these measurements. 12 Group 863, April 5, 2005 21.54
A.2. Impulse responses measurements are done with the speaker for each person, and in between each measurement the correct microphone is input to the MLSSA system. The same applies for the far field case, here the far field source (i.e The Home Made loudspeaker) is fed by an amplifier. The test person follows the same procedure as before, but in this case the subject is placed one meter from the far field source. Again measurements are carried out with all three microphones. A.2.4 Setup of the MLSSA system The MLSSA system settings are summarized in the following: Acquisition: Mode: Cross Correlation Length: 4095 samples Sampling frequency: 4 khz Concurrent pre-averaging: 16 times 2 Auto range: Enabled Anti-aliasing filter: Type: Butterworth Bandwidth: 1 khz Amplification: 2 (± 2.5 volts range) A.2.5 Results The sensitivity has been measured for both the Sennheiser SN-106, and the internal and external microphone from Panasonic mounted on the hearing protectors. This gave the following sensitivities: Sennheiser: 2 mv re. 1 Pa @ 1 khz (1 Pa 94 db SPL) Panasonic: 65.8 mv re. 1 Pa @ 1 khz (1 Pa 94 db SPL) In all plots these sensitivities have been removed so the graphs can be compared directly. Furthermore the anti-aliasing filter of the MLSSA system has been removed from the plots. The plots have a resolution of about 1 Hz, nevertheless it has been chosen only to present the plots from 50 Hz to 1.5 khz. Below 50 Hz it was estimated that the results were found unreliable due to low attenuation at low frequencies. A 512 point FFT were performed on all impulse responses giving a frequency resolution of about 4 Hz. Figure A.4, and A.5 plot the frequency response measured from the speaker unit to the ear canal and to the internal microphone respectively. Figure A.6 plots the frequency response measured from the speaker unit to the external microphone. 2 Which according to [Rife and Vanderkoy, 1989] gives a 12 db increase of the SNR Group 863 April 5, 2005 21.54 13
Appendix A. Measuring reports Figure A.7, and A.8 plot the frequency response measured from the far field source to the ear canal and to the internal microphone respectively. Figure A.9 plots the frequency response measured from the far field source to the external microphone. A geometric mean was also calculated from these measurements. These can be seen in the following figures, which furthermore contain the geometrical mean of the phase: A.10, A.11, A.12, A.13, A.14, and A.15. speaker2earcanal 90 80 50 Figure A.4: Speaker to Miniature microphone mounted at the entrance at the ear canal speaker2mic SPL re. 20µPa 90 80 50 Figure A.5: Speaker to Microphone mounted inside the hearing protector A.2.6 Discussion Near field case: The measurements showed that the internally mounted microphone is a good approximation of the one in the ear canal. A gain difference of approximately 4-6 db is present, which may be caused by the small difference in distance between the ear canal and the internal microphone. Vibrations in the cup caused by e.g. the speaker unit may also cause deviances. Far field case: In the far field case the deviations are between 4 and 8 db. The large deviances in the higher frequencies are caused by the removal of the aliasing filter which amplifies noise, and can therefore be omitted. 14 Group 863, April 5, 2005 21.54
A.2. Impulse responses 50 40 30 20 10 speaker2extmic Figure A.6: Speaker to External Microphone mounted on hearing protector farfield2earcanal 90 80 50 Figure A.7: Farfield to Miniature microphone mounted at the entrance at the ear canal farfield2mic 90 80 50 Figure A.8: Farfield to Microphone mounted inside the hearing protector Group 863 April 5, 2005 21.54 15
Appendix A. Measuring reports farfield2extmic 90 80 Figure A.9: Farfield to External Microphone mounted on hearing protector Mean Speaker To Earcanal 90 80 400 Phase 300 Degrees 200 0 Figure A.10: Speaker to Miniature microphone mounted at the entrance at the ear canal 16 Group 863, April 5, 2005 21.54
A.2. Impulse responses Mean Speaker To Mic db re. 1 Pa/V 90 80 200 Phase Degrees 0 200 Figure A.11: Speaker to Microphone mounted inside the hearing protector 50 40 30 20 10 0 Mean Speaker To Ext. Mic Phase 200 Degrees 400 0 800 0 Figure A.12: Speaker to External Microphone mounted on hearing protector Group 863 April 5, 2005 21.54 17
Appendix A. Measuring reports Mean Farfield To Earcanal 90 80 50 0 Phase Degrees 0 2000 3000 Figure A.13: Farfield to Miniature microphone mounted at the entrance at the ear canal Mean Farfield To Mic 90 80 50 0 Phase 0 Degrees 2000 3000 4000 Figure A.14: Farfield to Microphone mounted inside the hearing protector 18 Group 863, April 5, 2005 21.54
A.2. Impulse responses Mean Farfield To Ext. Mic 90 80 0 Phase 0 Degrees 0 2000 3000 Figure A.15: Farfield to External Microphone mounted on hearing protector 12 10 8 6 4 2 0 Difference between ear canal and internal microphone from speaker Figure A.16: Difference between Speaker to internal Microphone and ear canal Group 863 April 5, 2005 21.54 19
Appendix A. Measuring reports 12 10 8 6 4 2 0 Difference between ear canal and internal microphone from far field Figure A.17: Difference between Farfield to internal Microphone and ear canal It is estimated that the deviances can be fitted to a straight line, according to an offset. Therefore the pressure at the ear canal can approximated by the internal microphone with a offset difference. 20 Group 863, April 5, 2005 21.54
Bibliography [DS/ISO/TR 4869-3, 1994] Dansk Standard. Acoustics - Hearing protectors - Part 3: Simplified method for the measurement of insertion loss of ear-muff type protectors for quality inspection purposes. DS-tryk, 1994, 1. udgave. [Elliot, 2001] Stephen Elliot. Signal Processing for Active Control. Academic Press, 2001. ISBN: 0-12-2385-6. [Kuo and Morgan, 1996] Sen M. Kuo og Dennis R. Morgan. Active Noise Control Systems, Algorithms and DSP Implementation. John Wiley and Sons, 1996. ISBN: 0-471-13424-4. [Rife and Vanderkoy, 1989] J. Audio Eng. Soc. Transfer-function measurement with maximum-length sequences. Douglas D. Rife og John Vanderkooy. nr. 6. June 1989. side 419 444.. Group 863 April 5, 2005 21.54 21