LPC Wireless Simulator
Analyze (Encoder) $\rightarrow$ Bitstream (.lpc) $\rightarrow$ Synthesis (Decoder)
PCM Bitrate
705.6 kbps
LPC Bitrate
~4.2 kbps
Ratio
168:1
Status
Idle
📡 1. TRANSMITTER
⚙️ SETTINGS
Real-time Spectral Envelope
📻 2. RECEIVER (Decoder - upload payload.lpc file)
Binary Bitstream Preview
Mathematical Formulae
LPC Analysis (The Encoder)
Calculates coefficients $a_i$ using the Levinson-Durbin recursion:
$\hat{s}[n] = \sum_{i=1}^{P} a_i s[n-i]$
LPC Synthesis (The Decoder)
Reconstructs speech by exciting an all-pole filter:
$H(z) = \frac{G}{1 - \sum_{i=1}^{P} a_i z^{-i}}$
Bitrate Calculation Logic
1. Original Bitrate (PCM)
The original audio is processed as raw Pulse Code Modulation (PCM). It measures the actual air pressure $44,100$ times every second.
$$R_{orig} = f_s \times b \times c$$
- $f_s$ (Sample Rate): 44,100 Hz
- $b$ (Bit Depth): 16 bits
- $c$ (Channels): 1 (Mono)
- Total: 705,600 bps (705.6 kbps)
2. LPC Bitrate (Compressed)
LPC doesn't send samples; it sends "parameters" for a mathematical model of the voice, updated in frames.
$$R_{lpc} = (P \cdot b_{coeff} + b_{gain} + b_{pitch}) \times F$$
- $P$ (LPC Order): 12 coefficients
- $b_{coeff}$ (Quantization): 5 bits/coeff (60 bits total)
- $b_{gain} + b_{pitch}$: 14 bits/frame
- $F$ (Frame Rate): 50 frames per second (20ms frames)
- Total: ~4,200 bps (4.2 kbps)
By transmitting the "recipe" of the sound rather than the sound itself, we achieve a compression ratio of: $\frac{705.6}{4.2} \approx 168:1$