Voice Budget Calculation Audit
Voice Budget Calculation Audit
Ada separates PCM baseline, the Nyquist limit, and model-coder savings in the voice budget
ADA · CALCULATION AUDIT
Voice Budget Calculation Audit
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.
See the relationship before changing it
The figure reads from left to right. The blue card is coded bits per sample. The middle card applies this page's rule. The green card is coded stream rate. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only coded bits per sample, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 1.5 bits/sample.
- 2
Name the relationship. stream rate = 8,000 samples/s x coded bits/sample / 1,000
- 3
Substitute with units. 8,000 x 1.5 / 1,000 = 12.0 kbit/s
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change coded bits per sample
Try Predict the direction of stream rate = 8,000 samples/s x coded bits/sample / 1,000. Test another coded bits per sample, then compare coded stream rate.
Observe More coded bits preserve more detail but increase the narrowband stream in direct proportion. Reset coded bits per sample to 1.5 and compare coded stream rate.
Explain More coded bits preserve more detail but increase the narrowband stream in direct proportion.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Calculate mono PCM at 8000 samples/s for 8 and 16 bits/sample, then apply the stated 0.5–1.5 bits/sample speech-model range.
The raw stream doubles from 64 to 128 kbps with bit depth, while the model-coded estimate falls to about 4–12 kbps; Nyquist remains 4 kHz.
PCM rate is a direct product of sample rate, word length, and channels; a speech codec reduces redundancy in represented samples but cannot recreate frequencies excluded by sampling.
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.
| 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.
Technical boundaries: This one-channel rate budget omits packet and codec headers, framing, silence suppression, compute energy, algorithmic delay, loss recovery, audio quality, clock error, and variable-rate bursts.