---
title: "Sub-band coding"
subject: "Wireless Communication"
chapter: 6
key: "semester_7/wireless_communication:sub-band-coding"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/sub-band-coding
site: BCT Engineering
---

# Sub-band coding

Wireless Communication · Chapter 6: Speech and Channel Coding

- Asked in: 2080 Bhadra, 6 marks
- Video: [suband coding techniques](https://www.youtube.com/watch?v=goW36BquXzo) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/sub-band-coding
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-6

## Question

Explain sub-band coding with transmitter and receiver.

## Short answer

Sub-band coding splits speech into frequency bands using a filter bank, decimates each band, and codes each with ADPCM using bits allocated by perceptual importance. The receiver decodes, interpolates, filters and sums bands; QMF filters cancel aliasing, giving good quality at 16–32 kbps.

## Answer

**Sub-band coding (SBC)** is a frequency-domain speech coding method in which the speech band is split into several frequency sub-bands by a filter bank, and each sub-band is coded separately with a number of bits matched to its perceptual importance and energy.

**Idea:** speech energy and its importance to the ear are not uniform over 0–4 kHz. Low bands (with pitch and the first formants) get more bits; high bands get fewer. Quantization noise is also kept within each band, so it is masked by the speech in that band.

```text
 TRANSMITTER
         +-[BPF1]-[↓D]-[ADPCM, n1 bits]-+
 s(n) ---+-[BPF2]-[↓D]-[ADPCM, n2 bits]-+-[MUX]-> channel
         +-[BPFk]-[↓D]-[ADPCM, nk bits]-+

 RECEIVER
            +-[decode1]-[↑D]-[BPF1]-+
 ch->[DEMUX]+-[decode2]-[↑D]-[BPF2]-+-(Σ)-> s^(n)
            +-[decodek]-[↑D]-[BPFk]-+
   (↓D: decimate, ↑D: interpolate)
```

**Transmitter**

1. Speech sampled at 8 kHz is passed through a bank of *k* band-pass filters (often **quadrature mirror filters**, QMF), e.g. 4–8 bands.
2. Each band output is **decimated** (down-sampled) to its Nyquist rate, so the total sample rate stays 8 kHz.
3. Each sub-band is encoded, usually with **ADPCM**, using a bit allocation nᵢ based on band energy and perception (e.g. 4–5 bits in low bands, 2 bits in high bands).
4. Coded bits of all bands are multiplexed and transmitted.

**Receiver**

1. The bit stream is demultiplexed into the sub-band streams.
2. Each stream is decoded, **interpolated** (up-sampled) and passed through the matching synthesis filter.
3. The band outputs are added to reconstruct the speech. QMF filters cancel the aliasing created by decimation.

**Advantages:** noise in each band is controlled separately; bits are allocated to what the ear hears; good quality at 16–32 kbps (ITU G.722 wideband audio uses two-band SBC with ADPCM at 64 kbps).
**Disadvantage:** filter bank adds delay and complexity.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the main idea of sub-band coding?
   A. Send only the pitch
   B. Split speech into bands and code each with bits matched to its importance and energy
   C. Use one quantizer for the whole band
   D. Remove all high frequencies
   Answer: B. Bit allocation per band follows perceptual importance and energy. (Key point: Idea of SBC)

2. Why is each sub-band decimated at the transmitter?
   A. To add delay
   B. To raise the sampling rate
   C. To remove the ADPCM
   D. To reduce each band to its Nyquist rate so total sample rate stays 8 kHz
   Answer: D. Narrow bands need fewer samples, so total rate does not increase. (Key point: Decimation)

3. Which bands normally get more bits?
   A. Low bands with pitch and first formants
   B. High-frequency bands
   C. All bands equally
   D. The band with least energy
   Answer: A. Low bands are more important perceptually and get 4-5 bits, high bands about 2. (Key point: Bit allocation)

4. What do quadrature mirror filters achieve?
   A. Increase the bit rate
   B. Cancel aliasing created by decimation
   C. Detect pitch
   D. Generate noise
   Answer: B. QMF banks are designed so aliasing from decimation cancels at reconstruction. (Key point: QMF role)

5. What is the correct receiver order for each band?
   A. Filter, decode, interpolate
   B. Interpolate, decode, add
   C. Decode, interpolate, synthesis filter, then add all bands
   D. Add, decode, filter
   Answer: C. Each stream is decoded, up-sampled, filtered, and the bands are summed. (Key point: Receiver steps)

## Related in Wireless Communication

- [OFDM transmitter and receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aofdm-transmitter-receiver) — Wireless Communication, chapter 4, asked 5×
- [Spread spectrum and DSSS transmitter/receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspread-spectrum-dsss-tx-rx) — Wireless Communication, chapter 4
- [DPSK transmitter/receiver and PN sequence](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adpsk-pn-sequence) — Wireless Communication, chapter 4
- [OQPSK transmitter/receiver and π/4-QPSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aoqpsk-pi4-qpsk) — Wireless Communication, chapter 4

## Related in other subjects

- [Why DPCM over PCM; DPCM transmitter and receiver](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adpcm-preferred-transmitter-receiver) — Communication Systems, chapter 4, asked 2×
- [Stereo FM transmitter and receiver; output of mono receiver](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Astereo-fm-mono-receiver) — Communication Systems, chapter 3