# A Framework for Bluetooth-Based Real-Time Audio Data Acquisition in Mobile Robotics
## 3 Theoretical Framework and Novel Methods  
### Novel Audio Acquisition and Adaptive Compression Theory  
This section presents our novel theoretical framework for real-time audio acquisition and adaptive compression in mobile robotics, extending beyond existing digital signal processing principles to address the unique challenges of resource-constrained mobile platforms.  
The theoretical foundation of this audio acquisition system is rooted in digital signal processing principles, particularly as they apply to resource-constrained embedded systems. The INMP441 MEMS microphone utilized in this design converts acoustic pressure waves into digital signals through a sigma-delta modulator, producing a pulse-density-modulated (PDM) bitstream that is decimated to provide pulse code modulation (PCM) audio data [3; 39].  
The I2S protocol enables the transfer of this digital audio data with minimal computational overhead, operating as a synchronous serial interface with three essential lines: bit clock (SCK), word select (WS), and serial data (SD). This configuration allows for time-division multiplexed stereo channels, though this implementation utilizes only the left channel to reduce bandwidth requirements. This approach aligns with the methodologies described by [PERSON] and [PERSON] [40] in their development of autonomous noise-monitoring systems based on digital MEMS microphones.  
Novel Adaptive Compression Algorithm: We introduce a novel adaptive compression methodology that dynamically optimizes audio quality versus bandwidth utilization based on real-time system conditions. Unlike fixed compression schemes, our algorithm continuously adapts to environmental acoustics and system performance constraints.  
For a digital audio system with sampling rate \(f_{s}\) and bit depth \(b\), the theoretical data rate \(R\) can be expressed as  
\[R=f_{s}\times b\times c \tag{1}\]  
where \(c\) represents the number of channels. In this implementation with \(f_{s}=16\) kHz, \(b=24\) bits (native INMP441 resolution), and \(c=1\) (mono), the raw data rate is 384 kbps, exceeding the practical sustainable throughput of Bluetooth Classic for concurrent control and streaming applications.  
To address this bandwidth constraint, we develop a novel dynamic range compression algorithm that maps 24-bit samples to optimal 8-bit representation through our adaptive transform function \(T(x)\):  
\[T(x)=\frac{x\times S(t)}{D(t)}+128 \tag{2}\]  
where \(x\) is the original 24-bit sample value, \(S(t)\) is our time-adaptive sensitivity multiplier, \(D(t)\) is our novel adaptive dynamic range estimator, and 128 centers the output in the 8-bit range.  
Our novel dynamic range estimator \(D(t)\) employs a multi-scale temporal analysis:  
\[D(t)=\alpha_{fast}\times D_{fast}(t-1)+\alpha_{slow}\times D_{slow}(t-1)+(1- \alpha_{fast}-\alpha_{slow})\times\max(|x(t)|) \tag{3}\]This dual-time-constant approach enables rapid adaptation to transient events while maintaining stability during steady-state conditions, representing a significant advancement over traditional single-parameter approaches.