Method for electronically enlarging the distance between two acoustical/electrical transducers and hearing aid apparatus

The present invention is generically directed on a technique according to which acoustical signals are received by at least two acoustical/electrical transducers as e.g. by multidirectional microphones, respective output signals of such transducers are electronically computed so as to generate a result signal which represents said acoustical signals weighted by a spatial characteristic of amplification as a function of spatial angle under which the acoustical signal impinges on the two transducers provided. Thus, the result signal represents the received acoustical signal weighted by a spatial amplification characteristic as if reception of the acoustical signals had been done by means of e.g. an antenna with an according reception lobe or beam.

Figure 1 most generically shows such known technique for such "beam forming" on acoustical signals. Thereby, at least two multidirectional acoustical/electrical transducers 2_a and 2_b are provided, which both convert acoustical signal irrespective of their impinging direction θ and thus substantially unweighted with respect to impinging direction θ into electrical output signals A₁ and A₂. The output signals A₁ and A₂ are fed to an electronic signal processor unit 3 which generates from the input signals A₁, A₂ a result signal A_r. As shown within the block of unit 3 in that unit 3 the signals A₁,₂ are treated to result in the result signal A_r which represents either of A₁ or A₂, but additionally weighted by the spatial amplification function F(θ). Thus, acoustic signals may selectively be amplified dependent from the fact under which spatial angle θ they impinge, i.e. under which spatial angle the transducer arrangement 2a, 2b "sees" an acoustical source.

One approach to perform signal processing within processor unit 3 shall be exemplified with the help of Fig. 2. Thereby, all such approaches are based on the fact that due to a predetermined mutual distance p_P of the two transducers 2_a and 2_b, there occurs a time-lag dt between reception of an acoustical signal at the transducers 2_a, 2_b.

Considering a single frequency - ω - acoustical signal, received by the transducer 2_a, this transducer will generate an output signal<maths id="math0001" num="(1)"><math display="block"><mrow><msub><mrow><mtext> A</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext> = A · sinωt,</mtext></mrow></math><img file="EP0802699A2_D0001.tif" /></maths> whereas the second transducer 2_b will generate an output signal according to<maths id="math0002" num="(2)"><math display="block"><mrow><msub><mrow><mtext> A</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext> = A · sinω(t+dt),</mtext></mrow></math><img file="EP0802699A2_D0002.tif" /></maths> whereat dt is given by<maths id="math0003" num="(3)"><math display="block"><mrow><mtext> dt = </mtext><mfrac><mrow><msub><mrow><mtext mathvariant="italic">p</mtext></mrow><mrow><mtext mathvariant="italic">p</mtext></mrow></msub><mtext>sinθ</mtext></mrow><mrow><mtext mathvariant="italic">c</mtext></mrow></mfrac></mrow></math><img file="EP0802699A2_D0003.tif" /></maths> therein, c is the sound velocity.

By time-delaying A₁ by an amount<maths id="math0004" num="(4)"><math display="block"><mrow><msub><mrow><mtext> τ = p</mtext></mrow><mrow><mtext>P</mtext></mrow></msub><mtext>/c</mtext></mrow></math><img file="EP0802699A2_D0004.tif" /></maths> and forming the result signal A_r from the difference of time-delayed signal A₁', namely from<maths id="math0005" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><mtable><mlabeledtr><mtext>(5)</mtext><mtd><mrow><msub><mrow><mtext> A</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext>' = A · sinω(t+τ), and</mtext></mrow></mtd></mlabeledtr></mtable></mrow></mtd></mtr><mtr><mtd><mrow><mtable><mlabeledtr><mtext>(2)</mtext><mtd><mrow><msub><mrow><mtext> A</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext> = A · sinω(t+dt),</mtext></mrow></mtd></mlabeledtr></mtable></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0802699A2_D0005.tif" /></maths> there results, considered at the frequency ω, a spatially cardoid weighted signal A_r as shown in the block of processing unit 3:<maths id="math0006" num="(6)"><math display="block"><mrow><msub><mrow><mtext> |A</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><msub><mrow><mtext>| = |A</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext>' - A</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext>| = 2A sin(ω(τ-dt)/2)</mtext><mspace linebreak="newline" /><msub><mrow><mtext> = 2A sin(ω(τ-p</mtext></mrow><mrow><mtext>P</mtext></mrow></msub><mtext>*sinθ/c)/2).</mtext></mrow></math><img file="EP0802699A2_D0006.tif" /></maths>

At θ = 90° A_r becomes zero and at θ = -90° A_r becomes<maths id="math0007" num="(7)"><math display="block"><mrow><msub><mrow><mtext> A</mtext></mrow><mrow><mtext>rmax</mtext></mrow></msub><msub><mrow><mtext> = 2A sin ω p</mtext></mrow><mrow><mtext>P</mtext></mrow></msub><mtext>/c.</mtext></mrow></math><img file="EP0802699A2_D0007.tif" /></maths>

Such processing of the output signals of two omnidirectional order transducers leads to a first order cardoid weighing function F₁(θ) as shown in Fig. 3. By respectively selecting transducers with higher order acoustical to electrical conversion characteristic and/or by using more than two transducers, higher order - m - weighing functions F_m(θ) may be realised.

In Fig. 4 there is shown the amplitude A_rmax-characteristic, resulting from first order cardoid weighing as a function of frequency <maths id="math0008" num=""><math display="inline"><mrow><mtext>f = ω/2π</mtext></mrow></math><img file="EP0802699A2_D0008.tif" /></maths>. Additionally, the respective function for a second order cardoid weighing function F₂(θ) is shown. Thereby, there is selected a distance p_P of the two transducers 2_a and 2_b of fig. 1 to be 12 mm.

As may clearly be seen at a frequency f_r which is<maths id="math0009" num="(8)"><math display="block"><mrow><msub><mrow><mtext> f</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><mtext> = c/(4p)</mtext></mrow></math><img file="EP0802699A2_D0009.tif" /></maths> maximum amplification occurs of +6 dB at the first order cardoid and of +12 dB at a second order cardoid. For p_P = 12 mm, f_r is about 7 kHz.

From fig. 4 a significant roll-off for low and high frequencies with respect to f_r is recognised, i.e. a significant decrease of amplification.

Techniques for such or similar type of beam forming are e.g. known from the US 4 333 170 - acoustical source detection -, from the European patent application 0 381 498 directional microphone - or from Norio Koike et al., "Verification of the Possibility of Separation of Sound Source Direction via a Pair of Pressure Microphones", Electronics and Communications in Japan, Part 3, Vol. 77, No. 5, 1994, page 68 to 75.

Irrespective of the prior art techniques used for such beam forming with at least two transducers, the distance p_P is an important entity as may be seen e.g. from formula (8).

Formula (8) may be of no special handicap if such technique is used for narrow band signal detection or if no serious limits are encountered for geometrically providing the at least two transducers at a large mutual distance p_P.

Nevertheless, and especially for hearing aid applications, the fact that f_r is inversely proportional to the distance p_P of the transducers is a serious drawback, due to the fact that for hearing aid applications the audio frequency band up to about 4 kHz for speech recognition should be detectable by the at least two transducers which further should be mounted with the shortest possible mutual distance p_P.

It is thus a first object of the present invention to remedy the drawbacks encountered with respect to p_P dependency of acoustical "beam forming".

The first object of the present invention is reached by providing a method for electronically changing the distance between a first and a second acoustical/electrical transducer, generating, respectively, first and second electrical output signals which represent substantially simultaneously impinging acoustical signals, whereby the first and second electrical output signals are electronically treated so as to generate a result signal which result signal is a function of acoustical signals at least substantially simultaneously received at the two transducers and amplified by a spatial reception characteristic of amplification as a function of spatial angle under which the acoustical signals impinge on the two transducers, which method further comprises the steps of generating a third signal from at least one of the first and second output signals by shifting the phase of at least one of said output signals by an amount according to phase difference of the first and second output signals - being dependent from the physical distance p_P of said two transducers - multiplied by a constant factor not equal to unity or by a factor which is a function of frequency, and generating the result signal from at least one of the first and second output signals and the third signal, which latter represents an acoustical signal as it would be received if a transducer was placed at a distance from one of the provided transducers, which is given by the predetermined factor.

Thereby, there is introduced a virtual distance p_V of transducers which becomes clearly preferable, as for hearing aid applications,<maths id="math0010" num="(9)"><math display="block"><mrow><msub><mrow><mtext> p</mtext></mrow><mrow><mtext>V</mtext></mrow></msub><msub><mrow><mtext> &gt; p</mtext></mrow><mrow><mtext>P</mtext></mrow></msub><mtext>.</mtext></mrow></math><img file="EP0802699A2_D0010.tif" /></maths>

Thereby, according to formula (8), f_r is shifted to lower frequencies.

Thereby, it becomes possible to realise f_r values well in the audio-frequency band for speech recognition (&lt; 4 kHz) with physical distances of microphones, which are considerably smaller than this was possible up to now.

Multiplying the phase difference by a constant factor does nevertheless not affect the roll-off according to fig. 4. This roll-off is significantly improved, leading to an enlarged frequency band B_r according to fig. 4 if the predetermined function of frequency is selected as a function which is at least in a first approximation inversely proportional to the frequency of the acoustic signal.

For instance for the first order cardoid according to fig. 3 and fig. 4, there may be reached a flat frequency characteristic between 0,5 and 4 kHz and thus a significantly enlarged frequency band B_r with well-defined roll-offs of amplification at lower and higher frequencies by accordingly selecting the frequency dependent function to be multiplied with the phase difference.

To fulfil the above mentioned object there is further provided a hearing aid apparatus which comprises at least two acoustical/electrical transducers spaced from each other by a predetermined distance, whereby the at least two transducers generate, respectively, first and second electrical output signals and wherein the outputs of the acoustical/electrical transducers are operationally connected to a signal processing unit which generates a result output signal from the first and second output signals of the transducers, which result output signal being a function of acoustical signals received at least substantially simultaneously at the two transducers and amplified by a spatial reception characteristic of amplification as a function of spatial angle under which the acoustical signals impinge on the two transducers and which further comprises <ul id="ul0001" list-style="dash"><li>a phase difference detection unit operationally connected to the outputs of the two transducers and generating a phase difference indicative signal; and wherein</li><li>the output of the phase difference detecting unit is operationally connected to the first input of a multiplier unit, the second input thereof being connected to the output of a function or constant generator unit, the output of the multiplication unit being operationally connected to the control input of a phase shifter unit with a signal input operationally connected to the output of one of the transducers, the output of the phase shifter unit and at least one of the outputs of the at least two transducers being operationally connected to the processing unit.</li></ul>

Other objects of this invention will become apparent as the description proceeds in connection with the accompanying drawings, of which show: <dl id="dl0001"><dt>Fig. 1:</dt><dd>A functional block diagram of a two-transducer acoustic receiver with directional beam forming according to prior art;</dd><dt>Fig. 2:</dt><dd>one of prior art beam forming techniques as may be incorporated in the apparatus of fig. 1, shown in block diagram form;</dd><dt>Fig. 3:</dt><dd>a two-dimensional representation of a three-dimensional cardoid beam, i.e. amplification characteristic as a function of incident angle of acoustical signals;</dd><dt>Fig. 4:</dt><dd>the frequency dependency of the maximum amplification value according to fig. 3 for first and second order cardoid functions;</dd><dt>Fig. 5:</dt><dd>a pointer diagram resulting from the technique according to fig. 2, still prior art;</dd><dt>Fig. 6:</dt><dd>a pointer diagram based on fig. 5 (prior art), but according to the inventive method, which is performed by an inventive apparatus;</dd><dt>Fig. 7:</dt><dd>a simplified block diagram of an inventive apparatus, especially of an inventive hearing aid apparatus, wherein the inventive method is implemented.</dd></dl>

As was mentioned above, in the figs. 1 to 4 known beam forming techniques based on at least two acoustical/electrical transducers spaced from each other by a predetermined distance p_P have been explained.

In fig. 5 there is shown a pointer diagram according to (6).

The basic idea of the present invention shall be explained now with the help of the stil simplified one - ω - frequency example. The inventively realised pointer diagram is shown in fig. 6. The phase difference ω · dt between signal A₂ and A₁ according to fig. 6 is<maths id="math0011" num="(10)"><math display="block"><mrow><mtext> ω · dt = ω · </mtext><mfrac><mrow><msub><mrow><mtext mathvariant="italic">p</mtext></mrow><mrow><mtext mathvariant="italic">p</mtext></mrow></msub><mtext>sinθ</mtext></mrow><mrow><mtext mathvariant="italic">c</mtext></mrow></mfrac><mtext> = Δϕ.</mtext></mrow></math><img file="EP0802699A2_D0011.tif" /></maths>

This phase difference is determined and is multiplied by a value dependent from frequency, thus with the respective value of a function M(ω), which may be also a constant M_o # 1.

By phase shifting one of the two signals A₁, A₂ according to the respective pointers in fig. 6, e.g. of A₂ by<maths id="math0012" num=""><math display="block"><mrow><msub><mrow><mtext>M(ω) · Δϕ or by M</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><mtext> · Δϕ,</mtext></mrow></math><img file="EP0802699A2_D0012.tif" /></maths> there results the phase shifted pointer A_2V. This pointer would have also occurred if dt had been larger by an amount according to M(ω) or M₀, thus if a "virtual transducer" had been placed distant from transducer 1_a by the virtual distance p_V, for which:<maths id="math0013" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><mtable><mlabeledtr><mtext>(11)</mtext><mtd><mrow><msub><mrow><mtext> p</mtext></mrow><mrow><mtext>V</mtext></mrow></msub><msub><mrow><mtext> = M(ω) · p</mtext></mrow><mrow><mtext>P</mtext></mrow></msub><mtext> or</mtext></mrow></mtd></mlabeledtr></mtable></mrow></mtd></mtr><mtr><mtd><mrow><mtable><mlabeledtr><mtext>(12)</mtext><mtd><mrow><msub><mrow><mtext> p</mtext></mrow><mrow><mtext>V</mtext></mrow></msub><msub><mrow><mtext> = M</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> · p</mtext></mrow><mrow><mtext>P.</mtext></mrow></msub></mrow></mtd></mlabeledtr></mtable></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0802699A2_D0013.tif" /></maths>

As we consider one single frequency for simplicity we may write <maths id="math0014" num=""><math display="inline"><mrow><msub><mrow><mtext>M</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> = M</mtext></mrow><mrow><mtext>ω</mtext></mrow></msub></mrow></math><img file="EP0802699A2_D0014.tif" /></maths>.

With virtual τ_V<maths id="math0015" num="(13)"><math display="block"><mrow><msub><mrow><mtext> τ</mtext></mrow><mrow><mtext>V</mtext></mrow></msub><msub><mrow><mtext> = M</mtext></mrow><mrow><mtext>ω</mtext></mrow></msub><mtext> · τ and</mtext></mrow></math><img file="EP0802699A2_D0015.tif" /></maths><maths id="math0016" num=""><img file="EP0802699A2_D0016.tif" /></maths> we get according to the present invention:<maths id="math0017" num=""><img file="EP0802699A2_D0017.tif" /></maths>

With (8) we further get:<maths id="math0018" num=""><math display="block"><mrow><msub><mrow><mtext>f</mtext></mrow><mrow><mtext>rV</mtext></mrow></msub><mtext> = </mtext><mfrac><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext>4</mtext><msub><mrow><mtext mathvariant="italic">M</mtext></mrow><mrow><mtext>ω</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic">P</mtext></mrow><mrow><mtext mathvariant="italic">p</mtext></mrow></msub></mrow></mfrac><mtext> = </mtext><mfrac><mrow><mtext>1</mtext></mrow><mrow><msub><mrow><mtext mathvariant="italic">M</mtext></mrow><mrow><mtext>ω</mtext></mrow></msub></mrow></mfrac><msub><mrow><mtext> · f</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><mtext>.</mtext></mrow></math><img file="EP0802699A2_D0018.tif" /></maths>

Therefrom, we may see that for a given p_P, which would lead to a too high f_r, f_rV is reduced by the factor <maths id="math0019" num=""><math display="inline"><mrow><mfrac><mrow><mtext>1</mtext></mrow><mrow><mtext>Mω</mtext></mrow></mfrac></mrow></math><img file="EP0802699A2_D0019.tif" /></maths>, taken M_ω &gt; 1. In fig. 7 there is schematically shown a preferred realisation form of an inventive apparatus in a simplified manner, especially for implementing the inventive method into an inventive hearing aid apparatus. Thereby, the output signals of the acoustical/electrical transducer 2_a and 2_b are fed to respective analogue to digital converters 20a, 20b, the outputs thereof being input to time domain to frequency domain - TFC - converter units as to Fast-Fourier Transform units 22a and 22b. A spectral phase difference detecting unit 27 spectrally detects phase difference Δϕ_n for all n spectral frequency components which are then multiplied by a set of constants c_n. If M(ω) is valid, then the c_n can be different for different frequencies, and represent a frequency dependent function or factor. If on the other hand the phase differences Δϕ_n are multiplied by the same <maths id="math0020" num=""><math display="inline"><mrow><msub><mrow><mtext>c</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> = c</mtext></mrow><mrow><mtext>n</mtext></mrow></msub><mtext> # 1</mtext></mrow></math><img file="EP0802699A2_D0020.tif" /></maths> this accords with using a constant M₀.

This multiplication according to (3_V) is done at a spectral multiplication unit 28. Signal A₁ in its spectral representation is then spectrally phase shifted at a spectral phase shifter unit 29 by the multiplied spectral phase difference signals output by multiplier unit 28.

According to fig 7 the signal A₁ in its spectral representation and inventively, spectrally phase shifted is computed in a spectral computing unit 23 together with A₂ in its spectral representation, as if transducer 2a was distant from transducer 2b by a distance <maths id="math0021" num=""><math display="inline"><mrow><msub><mrow><mtext>p</mtext></mrow><mrow><mtext>V</mtext></mrow></msub><msub><mrow><mtext> = M(ω)p</mtext></mrow><mrow><mtext>P</mtext></mrow></msub></mrow></math><img file="EP0802699A2_D0021.tif" /></maths>_. The resulting spectrum is transformed back by a frequency to time domain converter - FTC - as by an Inverse-Fast-Fourier-Transform unit 24 to result in A_r#.

Thereby, other beam forming techniques than that described with the help of figs 1 to 4, i.e. using the time delaying technique - transformed in the frequency domain - may be used in unit 23.

Nevertheless the time delaying technique is preferred.

With an eye on fig. 4 it has been explained that by inventively introducing a "virtual" transducer with a virtually enlarged distance from one of the two physically provided transducers, it becomes possible to shift the high gain frequency f_r towards lower frequencies, which is highly advantageous especially for hearing aid applications. This is already reached if instead of a frequency dependent function M(ω), a constant M₀ is multiplied with the phase difference as explained.

In a preferred mode of the invention the frequency dependent function M(ω) is selected to be, at least in a first approximation,<maths id="math0022" num="(14)"><math display="block"><mrow><mtext> M(ω) ∼ </mtext><mfrac><mrow><mtext>1</mtext></mrow><mrow><mtext>ω</mtext></mrow></mfrac></mrow></math><img file="EP0802699A2_D0022.tif" /></maths>

Thereby, it is reached that different from fig. 4 there will be no roll-off and the gain in target direction will be constant over the desired frequency range. By appropriately selecting the function M(ω) it is e.g. possible to reach a flat characteristic within a predetermined frequency range, e.g. between 0.5 and 4 kHz with defined roll-offs at lower and higher frequencies. With appropriately selecting the function M(ω) practically any kind of beam forming can be made.

For generating higher order cardoid weighing functions it is absolutely possible to additionally use the not phase-shifted output signal A₁ - as shown in fig. 7 by dotted line - as computing input signal to unit 23 too, thus "simulating" three transducers.

It is evident for the skilled artisan that <ul id="ul0002" list-style="bullet"><li>more than two real transducers may be used and/or</li><li>more than one M(ω) function may be used to produce more than one virtual transducer signal from one or from more than one real transducer signals respectively.</li></ul>

With selecting the number of physical and virtual transducers the spatial weighing function may be selectively tailored, thereby e.g. to completely suppress signals from unwanted directions, e.g. only to pass signals from within a narrow range of target direction and suppress all others. On the other hand, it is also possible to just suppress unwanted sources, thus realising an in fact omnidirectional behaviour, thereby just suppressing one or more distinct noise sources at predetermined spatial angles.

The present invention under its principal object makes it possible to realise beam forming with at least two transducers separated by only a predetermined small distance, due to the fact that electronically there is provided a virtual transducer distance from one of the two physically provided transducers.

Thereby, roll-off may be significantly reduced by such virtual transducer, which is established with a distance dependent from frequency. For a hearing aid apparatus the real distance between the at least two transducers, i.e. microphones, is selected to be 20 mm at most.