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AI-Driven Sound Direction and Focus

1. Digital Beamforming with AI

Beamforming is a technique used to focus sound waves in a specific direction by adjusting the phase and amplitude of the sound emitted by an array of speakers. AI can optimize this process, making real-time adjustments based on environmental feedback.

The sound pressure at a given point \( \mathbf{r} \) at time \( t \) due to an array of \( N \) speakers can be expressed as:

\[ P(\mathbf{r}, t) = \sum_{n=1}^{N} A_n \cos(\omega t - \mathbf{k} \cdot \mathbf{r}_n + \phi_n) \]

where:

• \( P(\mathbf{r}, t) \) is the sound pressure at point \( \mathbf{r} \) and time \( t \)
• \( A_n \) is the amplitude of the \( n \)-th speaker
• \( \omega \) is the angular frequency of the sound wave
• \( \mathbf{k} \) is the wave vector
• \( \mathbf{r}_n \) is the position of the \( n \)-th speaker
• \( \phi_n \) is the phase shift applied to the \( n \)-th speaker

An AI model can be trained to optimize the values of \( A_n \) and \( \phi_n \) to maximize the sound intensity at a desired location while minimizing it elsewhere. This approach is adaptive and can be modified in real-time based on sensor feedback.

2. Parametric Audio Synthesis with AI

Parametric speakers use ultrasonic waves to carry audible sound, which is then demodulated by the nonlinearities in the air. This creates a highly directional sound beam that can be focused on a specific listener. AI can be used to modulate the ultrasonic carrier wave to achieve this effect.

The equation for the modulated ultrasonic wave \( S(t) \) is:

\[ S(t) = \cos(\omega_c t) \left[ 1 + m \cos(\omega_m t) \right] \]

where:

• \( \omega_c \) is the carrier frequency (ultrasonic)
• \( \omega_m \) is the modulating frequency (audible sound)
• \( m \) is the modulation index

AI can dynamically adjust the modulation index \( m \) and the carrier frequency \( \omega_c \) based on real-time data, ensuring the sound is focused exactly where needed.

3. Environment-Adaptive Sound Projection

Sound projection can be significantly affected by the environment, including factors such as reflections, absorption, and obstacles. AI can be used to analyze these factors in real-time and adjust the sound projection accordingly.

The intensity of sound \( I(r) \) at a distance \( r \) from the source, considering environmental absorption, is given by:

\[ I(r) = \frac{P_0}{4 \pi r^2} \cdot e^{-\alpha r} \]

where:

• \( P_0 \) is the power of the sound source
• \( \alpha \) is the absorption coefficient of the medium

An AI system can continuously monitor the environment using sensors (e.g., microphones, cameras) and adjust the parameters of the sound projection to maintain the desired intensity and focus at the target location.

4. AI-Driven Spatial Audio for Dynamic Focus

Spatial audio techniques allow the creation of 3D soundscapes where the listener perceives sound coming from specific directions or locations. AI can enhance this by dynamically focusing the sound on a moving target, such as a listener, while minimizing it in other areas.

The perceived direction \( \theta \) of a sound source can be calculated using the time difference of arrival (TDOA) between the left and right ears:

\[ \theta = \arcsin\left(\frac{c \cdot \Delta t}{d}\right) \]

where:

• \( c \) is the speed of sound
• \( \Delta t \) is the time difference of arrival
• \( d \) is the distance between the ears

AI can track the listener's position using computer vision or wearable sensors and adjust the spatial audio parameters in real-time to maintain a focused audio experience.

5. Custom Speaker Design with AI Integration

For even greater precision, custom speakers with multiple transducers can be designed. AI can control each transducer individually, creating highly focused sound beams that converge at a specific point.

The total sound pressure at a target location \( \mathbf{r}_t \) from an array of transducers can be expressed as:

\[ P(\mathbf{r}_t) = \sum_{n=1}^{N} P_n(\mathbf{r}_t) \]

where \( P_n(\mathbf{r}_t) \) is the contribution from the \( n \)-th transducer.

AI can dynamically adjust the phase and amplitude of each transducer to ensure that the sound waves constructively interfere at the target location, maximizing the sound intensity.

6. Digital Parametric Speaker Simulation

AI can also be used to simulate the effects of parametric speakers using digital signal processing (DSP) techniques. This involves digitally generating ultrasonic waves and modulating them to carry audible sound, which can be emitted from standard speakers.

The digitally generated ultrasonic wave \( S_d(t) \) can be expressed as:

\[ S_d(t) = A_d \cos(\omega_c t + \phi_d(t)) \]

where:

• \( A_d \) is the amplitude of the digitally generated wave
• \( \phi_d(t) \) is the phase modulation applied to encode the audible sound

AI can optimize the DSP algorithms to ensure that the simulated parametric speaker behaves as closely as possible to a physical one, providing focused sound projection from any standard speaker.

7. AI-Based Sound Masking and Steering

In environments where privacy or noise control is essential, AI can be used to steer sound towards specific listeners while masking it from others. This involves generating sound waves that cancel each other out in unwanted directions.

The sound pressure \( P(\mathbf{r}, t) \) at a point \( \mathbf{r} \) can be controlled using destructive interference:

\[ P(\mathbf{r}, t) = P_1(\mathbf{r}, t) + P_2(\mathbf{r}, t) \]

where \( P_1(\mathbf{r}, t) \) and \( P_2(\mathbf{r}, t) \) are the pressures from two sound sources, and are adjusted so that \( P_1(\mathbf{r}, t) + P_2(\mathbf{r}, t) \approx 0 \) in unwanted areas.

AI can monitor the environment and dynamically adjust the phases and amplitudes of the sound sources to achieve this effect.