Pure Tone Combinations with Balanced Interference

Abstract

Apparatus for estimating motion of a target, comprises a speaker, to output a combination of three or more acoustic pure tones having frequencies and relative amplitudes symmetrically distributed abou

Description

Acoustic pure tones can be utilized on devices such as smartphones to enable contactless motion detection functionality for a myriad of useful applications, including 5 sleep tracking, breathing detection, gaming, musical instruments, and user interface control, as described in earlier patent by the Inventor (British patent 2609061), and the present invention is made in this context. Ultrasonic pure tones with frequencies above 18 kHz are of particular utility as they are io inaudible to most adults. Motion can be inferred via analysis of reflected signals received by a microphone, which contain information about fast moving reflective surfaces such as a hand moving towards the phone, through Doppler shifts, and about slower changes in the distance of reflective surfaces such as chest movements that cause spectral shifts over time, which is useful for estimating breathing during sleep tracking. 15 It is possible to increase the accuracy of ultrasonic motion detection systems by combining multiple pure tones of different frequencies. Information from multiple frequency ranges around the constituent tones can be combined, such as by averaging, to mitigate the impact of factors such as external noises and interference effects related 20 to the distance of the reflective surface with respect to the tone wavelength, to enable more accurate motion estimates. Although multi-tone systems provide greater information than single tone systems, deploying them does create complications that require consideration. This is because 25 when multiple tones are combined, interference patterns occur at the frequency interval between the tones (the beat frequency). Such interference patterns can cause fluctuations in acoustic pressure that can induce physiological effects such as brainwave entrainment for lower frequency beat intervals (e.g. less than 100Hz) and nerve and muscular responses at higher frequency beat intervals, such as tingling sensations in the 30 skin. Brainwave entrainment is a phenomenon whereby brain activity synchronizes with the frequency of external stimuli, such as acoustic patterns, which can lead to effects such as heightened alertness. The Inventor has previously explored methods for deploying such effects beneficially. However, in many instances, such stimulation effects are undesirable, for example, in a context such as sleep-tracking. Such effects do not 35 typically occur with single frequency systems, making them generally superior for applications such as sleep tracking where it is desirable for stimulation effects to be minimised. The current disclosure focuses on methods to construct signals that combine multiple 5 tone frequencies in such a way as to minimise fluctuations in the combined signal amplitude, and hence acoustic pressure, and reduce stimulation effects. This is achieved by configuring combinations of tones such that there is a characteristically flat signal envelope in the time domain 10 Specifically, tones are combined with relative amplitudes and phase such that there exist periodic instants in time at which a majority of the tones are in phase alignment with each other, whilst other tones are in antiphase alignment with the majority, creating an algebraic cancellation of beat effects. 15 In the present disclosure, ‘phase alignment’ describes two signals which have a phase offset of zero, or multiples of 2tt radians at an instant in time, which combine constructively at that instant. ‘Antiphase alignment’ describes two signals which have a phase offset of tt radians at an instant in time, and which combine destructively at that instant. 20 When tone combinations with such opposing interference patterns are combined, the points of constructive interference from one set of tones align with points of destructive interference from the other set of tones. This has the effect of suppressing constructive and destructive interference peaks in the combination and flattening the envelope of the 25 combined signal. The frequency offset and tone frequencies can be optimized for compatibility with other motion detection techniques from the Inventor, notably those disclosed in British patent 2609061 and international patent application WO 2024 / 175934. A short and precisely-defined period of alignment, referred to herein as a ‘loop cycle’, can be obtained if tone frequencies and frequency offset are a function of 30 the sampling rate, which is used to advantageous effect in combination with the Doppler motion systems described in British patent 2609061 and international patent application WO 2024 / 175934. Algebraic solutions are presented for configuring five and seven tone combinations so that amplitude fluctuations are minimised in their combination. These are set out in the series of clauses appended to this disclosure. 5 The algorithms have another useful property of compressing the maximal amplitude of the tone combination compared to the sum of the constituent tone amplitudes. For example, some 7-tone combinations (referred to herein as EQUINOX combinations) have maximal amplitude of less than 45% of the sum of the amplitudes of the constituent tones, whilst exhibiting a flat and consistent signal envelope within a recurrent loop io optimized for motion tracking. The optimised multitone signals enable precise and superior measurement of both Doppler shifts and breathing compared to single tone systems, and the flat output signals have the intended effect of substantially reducing stimulation effects compared to non-15 optimised combinations that exhibit greater amplitude variation. Despite these superior properties, however, these flattened tone combinations are not able to match single frequency systems in terms of stimulation effect minimisation. This is because when their precisely balanced output signals interfere with time delayed 20 reverberations (e.g. reflections from walls and ceilings), the delicate phase and amplitude structure becomes unbalanced, leading to increased pressure fluctuations. Consequently, these optimised multitone configurations are best suited for short term applications that benefit from increased precision such as gaming or short term breathing rate measurement (e.g. over a 20-minute meditation session), but are less well suited to 25 prolonged use over multiple hours for sleep tracking. Worked Example An example of a five-tone combination using this principle has the following characteristics, with respect to first (Ti), second (T2), third (T3), fourth (T4) and fifth (T5) 30 tones, having respective amplitudes Ai, A2, A3, A4, As distributed around the central frequency of the third tone, and with a constant frequency spacing fstep between adjacent tones in the combination: Relative amplitudes, A: 1:4:8:4:1; 35 Phase alignment condition, ¢: 0:0:0:tt:0. The magnitude of the interference effects between two tones is determined by the product of their respective amplitudes. Additionally, a scalar of 1 is applied when the two tones have the same phase alignment condition, whilst a scalar of -1 is applied when the 5 two tones have an opposite phase alignment condition. Four tone pairs have a frequency separation of a single unit of fstep. The products of their amplitudes are: io Ai x A2 = 1 x 4 = 4 A2 x A3 = 4x8 = 32 A3 x A4 = 8 x -4 = -32 T4 x T5 = -4 x 1 = -4 15 The sum of their interference patterns is 4 + 32 - 32 - 4 = 0, meaning that the interference at fstep is balanced. Three tone pairs have a frequency separation of a two offset units, 2fstep. The products of their amplitudes are: 20 Ai x A3 = 1 x 8 = 8 A2 x A4 = 4 x -4 = -16 A3XA5 = 8x1=8 25 The sum of their interference patterns is 8 -16 + 8 = 0, meaning that the interference pattern at 2fstep is balanced. Two tone pairs have a frequency separation of three offset units, 3fstep. The products of their amplitudes are: 30 Ai x A4 = 1 x -4 =-4 A2 x A5 = 4 x 1 = 4 The sum of their interference patterns is 4 - 4 = 0, meaning that the interference pattern 35 at 3fsteP is balanced. The interference between the outer pair of tones, Ti and Ts, cannot be cancelled in this way as there is no other pair with the same frequency spacing. In practice, in order to produce a flat signal, the outer pair of tones are configured to have a low amplitude 5 relative to other tones in the combination. The explanation set out above applies equivalently to a five-tone combination in which the phase offset of tt is applied to the second tone, rather than the fourth tone. 10 More generally, for the five-tone configuration set out above, the tone combination is the sum of the following products: (Ai x A2) + (A2 x A3) + (Ai x A3) + (A3 x As) + (A2 x As) + (Ai x As ) — (A3 x A4) — (A4 x As) — (A2x A4) - (A1X A4). 15 Disregarding the product of the outer tones, which do not cancel, and with T1 and Ts each having a weighting of 1, the summation becomes: A2 + (A2 x A3) + A3 + A3 + A2 — (A3 x A4) - A4 — (A2 X A4) - A4. 20 With a symmetrically distributed set of relative amplitudes, such that (i.e. Ai = As, and A2 = A4), the summation becomes: A3 - A22. 25 For complete interference cancellation of these terms, the expression sums to zero, such that A22 = 2A3. As such, if an amplitude weighting, x, is applied to A2 and A4, the required weighting of 30 T3 is (x2 / 2). This condition is satisfied in the example above, in which x is 4. The relative amplitudes of the combination are thus 1 : x : (x2 / 2): x : 1. A similar algebraic solution for cancelling inter-tone interference with seven tones has amplitudes 1 : x : (x2 / 2) : ((z2 - 2z) / 2x) : (x2 / 2) : x : 1, with z = (x2 / 2), and phase 35 conditions of either 0:0:0:0:77:0: 77, or 77:0:77:0:0:0:0. The resultant combinations (referred to previously as EQUINOX combinations) can exhibit a high level of amplitude compression, with peak amplitudes of less than 45% of the sum of the individual tone amplitudes. 5 In the case where x = 2, an interesting six-tone solution is yielded, with relative tone amplitudes of 1:2:2:0:2:2:1. In this combination, each non-zero tone is over 10% of the total amplitude, and four of the tones have equal amplitude, making the combination particularly suitable for averaging. This combination is used effectively in high-precision, low-latency motion tracking applications such as musical instrument io simulation or ‘air guitar’ application. Further examples are illustrated in the charts below, with tone frequencies distributed symmetrically around a central frequency of 18,750 Hz, and with a frequency offset unit of 234.375 Hz. Such frequencies and spacings enable seven tones to be used which all 15 have a frequency of more than 18 kHz, with an upper limit of less than 19,500 Hz, which is within the output capabilities of current-generation mobile phone speakers and microphone sensitivities. The precise frequencies and tone spacings are such that the tone combination loops precisely in 1024 frames of a 48 kHz sampling rate. Furthermore, the tone frequencies correspond precisely to bin frequencies of a Radix-2 FFT used in 20 embodiments of the present invention to estimate motion. Tone ampiituces A are normaiiseti by their sum J A; Max refers to the maximum value of the combined signal The invention can be characterized by the following series of clauses: Clause 1: An apparatus for estimating motion of a target, comprising: a speaker, configured to output a combination of three or more acoustic pure 5 tones having frequencies and relative amplitudes symmetrically distributed about a central pilot frequency, wherein the spacing between each tone frequency is an integer multiple of an offset frequency unit; a microphone for receiving and sampling reflections, by the target, of the three or more tones; and io a motion estimator for estimating motion of the target from frequency analysis of the reflected three or more tones. wherein periodically, the tones have a phase alignment such that a majority of the tones align in phase, while all other tones have a phase offset of tt radians from the majority of the tones, and 15 the relative amplitudes are such that all interference patterns between constituent tones in the combination are counterbalanced, with the exception of interference patterns between the two tones with greatest frequency spacing. Clause 2: An apparatus according to clause 1, wherein the speaker is configured to 20 output a first tone and a third tone having respective first and third frequencies which are offset respectively below and above a central second frequency of a second tone by one offset frequency unit, and the majority of the tones comprises either: the first tone and the second tone, or 25 the second tone and the third tone. Clause 3: An apparatus according to clause 2, wherein the first, second and third tones have relative amplitudes in the ratio of 1 : x : 1. 30 Clause 4: An apparatus according to clause 1, wherein the speaker is configured to output: a first tone and a fifth tone having respective first and fifth frequencies which are offset respectively below and above a third central frequency of a third tone by two offset frequency units, and a second tone and a fourth tone having respective second and fourth frequencies which are offset respectively below and above the third central frequency of the third tone by one offset frequency unit, and the majority of the tones comprises either: 5 the first tone, the second tone, the third tone and the fifth tone, or the first tone, the third tone, the fourth tone and the fifth tone. Clause 5: An apparatus according to clause 4, wherein the first, second, third, fourth and fifth tones have relative amplitudes in the ratio of 1 : x : (x2 / 2) : x : 1. io Clause 6: An apparatus according to clause 1, wherein the speaker is configured to output: a first tone and a seventh tone having respective first and seventh frequencies which are offset respectively below and above a fourth central frequency of a fourth tone 15 by three offset frequency units, and a second tone and a sixth tone having respective second and sixth frequencies which are offset respectively below and above the fourth central frequency of the fourth tone by two offset frequency units, and a third tone and a fifth tone having respective second and sixth frequencies which 20 are offset respectively below and above the fourth central frequency of the fourth tone by one offset frequency unit, and the majority of the tones comprises either: the first tone, the second tone, the third tone, the fourth tone, and the sixth tone, or 25 the second tone, the fourth tone, the fifth tone, the sixth tone and the seventh tone. Clause 7: An apparatus according to clause 6, wherein the first, second, third, fourth, fifth, sixth and seventh tones have relative amplitudes in the ratio of 1 : x : (x2 / 2) 30 : ((z2- 2z) / 2x) : (x2 / 2) : x : 1, with z= (x2 / 2). 19 09 25

Claims

1. An apparatus for estimating motion of a target, comprising:a speaker, configured to output a combination of three or more acoustic pure 5 tones having frequencies and relative amplitudes symmetrically distributed about a central pilot frequency, wherein the spacing between each tone frequency is an integer multiple of an offset frequency unit;a microphone for receiving and sampling reflections, by the target, of the three or more tones; andio a motion estimator for estimating motion of the target from frequency analysis ofthe reflected three or more tones;wherein periodically, the tones have a phase alignment such that a majority of the tones align in phase, while all other tones have a phase offset of tt radians from the majority of the tones, and15 the relative amplitudes are such that all interference patterns between constituenttones in the combination are counterbalanced, with the exception of interference patterns between the two tones with greatest frequency spacing.

2. An apparatus according to claim 1, wherein the speaker is configured to output a 20 first tone and a third tone having respective first and third frequencies which are offset respectively below and above a central second frequency of a second tone by one offset frequency unit, andthe majority of the tones comprises either:the first tone and the second tone, or25 the second tone and the third tone.

3. An apparatus according to claim 2, wherein the first, second and third tones have relative amplitudes in the ratio of 1 : x : 1.30 4. An apparatus according to claim 1, wherein the speaker is configured to output:a first tone and a fifth tone having respective first and fifth frequencies which are offset respectively below and above a third central frequency of a third tone by two offset frequency units, and19 09 25a second tone and a fourth tone having respective second and fourth frequencies which are offset respectively below and above the third central frequency of the third tone by one offset frequency unit, andthe majority of the tones comprises either:5 the first tone, the second tone, the third tone and the fifth tone, orthe first tone, the third tone, the fourth tone and the fifth tone.

5. An apparatus according to claim 4, wherein the first, second, third, fourth and fifth tones have relative amplitudes in the ratio of 1 : x : (x2 / 2) : x : 1.io6. An apparatus according to claim 1, wherein the speaker is configured to output: a first tone and a seventh tone having respective first and seventh frequencies which are offset respectively below and above a fourth central frequency of a fourth tone by three offset frequency units, and15 a second tone and a sixth tone having respective second and sixth frequencieswhich are offset respectively below and above the fourth central frequency of the fourth tone by two offset frequency units, anda third tone and a fifth tone having respective second and sixth frequencies which are offset respectively below and above the fourth central frequency of the fourth tone20 by one offset frequency unit, andthe majority of the tones comprises either:the first tone, the second tone, the third tone, the fourth tone, and the sixth tone, orthe second tone, the fourth tone, the fifth tone, the sixth tone and the 25 seventh tone.

7. An apparatus according to claim 6, wherein the first, second, third, fourth, fifth, sixth and seventh tones have relative amplitudes in the ratio of 1 : x : (x2 / 2) : ((z2- 2z) / 2x): (x2 / 2) : x : 1, with z = (x2 / 2).A

Images