Ada Audits the Voice Budget

Ada separates PCM baseline, the Nyquist limit, and model-coder savings in the voice budget

ADA · CALCULATION AUDIT

Ada Audits the Voice Budget

Voice coding starts as physics bookkeeping: sample the waveform, count the bits, then check how much a speech model can shrink the stream before packet headers and loss are added.

A battery-powered site intercom captures narrowband speech from a MEMS microphone and sends it over Wi-Fi or LTE-M backhaul, where raw 8 kHz, 16-bit, mono PCM costs 128 kbps before packet headers, while the classic 8-bit narrowband baseline is 64 kbps. The chapter says an LPC-style speech coder can instead spend roughly 0.5 to 1.5 bits per sample. This audit asks the question that budget invites: how much smaller than the 64 kbps PCM baseline can that LPC-style range actually make the stream, before packet headers and loss are added?

Companion to the chapter Voice and Audio Compression for IoT — every number here comes from that chapter.

1. Start from the chapter's PCM formula

For one channel, the bit rate is the sample rate multiplied by the bits in each sample.

bit rate = sample rate x bits per sample x channels

Budget check	Arithmetic	Audited result
Classic 8-bit narrowband PCM	8000 samples/s x 8 bits x 1 channel = 64,000 bits/s	64 kbps before packet headers.
16-bit narrowband PCM example	8000 samples/s x 16 bits x 1 channel = 128,000 bits/s	128 kbps before packet headers.
Why 16-bit doubles the stream	128,000 / 64,000 = 2	The sample rate stayed fixed; doubling bits per sample doubles the carried stream.

2. Check the sampling physics separately

The chapter's 8 kHz sampling rate sets a mathematical ceiling on the highest represented frequency.

Sampling check	Arithmetic	Audited result
Nyquist limit	8000 samples/s / 2 = 4000 cycles/s	Content up to about 4 kHz can be represented.
What compression cannot fix	Frequencies above the sampling limit were never represented in the samples.	A codec can shrink the stream, but it cannot restore missing high-frequency content.

3. Use the chapter's LPC-style range as a savings estimate

The later speech-model section says LPC-style coding can spend roughly 0.5 to 1.5 bits per sample instead of sending every PCM sample.

Model-coder check	Arithmetic	Audited result
Lower end of the range	8000 samples/s x 0.5 bits/sample = 4000 bits/s	About 4 kbps before packet headers.
Upper end of the range	8000 samples/s x 1.5 bits/sample = 12,000 bits/s	About 12 kbps before packet headers.
Compression versus 64 kbps PCM	64 / 4 = 16; 64 / 12 = 5.33	Roughly 5.3x to 16x smaller than the 8-bit PCM baseline, before overhead and losses.

What the mathematics buys you: the link budget separates three questions that are easy to blur: what the sampling rate can represent, how many raw bits the device produces, and how much a speech model can reduce the stream before the packet network adds delay, headers, and loss.

Every number above is taken from this chapter's own worked example and re-derived step by step.