---
title: "Speech characteristics and 7-bit Hamming code"
subject: "Wireless Communication"
chapter: 6
key: "semester_7/wireless_communication:speech-hamming-code"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/speech-hamming-code
site: BCT Engineering
---

# Speech characteristics and 7-bit Hamming code

Wireless Communication · Chapter 6: Speech and Channel Coding

- Asked in: 2080 Chaitra, 3+5 marks
- Video: [Error Detection and Correction in Hamming Code](https://www.youtube.com/watch?v=N8Yy0-4YMS4) — TutorialsPoint
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/speech-hamming-code
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-6

## Question

Explain the characteristics of speech. Explain 7-bit Hamming code method with relevant example.

## Short answer

Speech has 300–3400 Hz bandwidth, non-uniform amplitude, high sample correlation, formants, and quasi-stationary 10–30 ms frames. The (7,4) Hamming code adds parity bits p1=d1⊕d2⊕d4, p2=d1⊕d3⊕d4, p3=d2⊕d3⊕d4; data 1011 gives codeword 0110011, and syndrome 101 corrects bit 5.

## Answer

#### Characteristics of speech

- Most energy and intelligibility in 300–3400 Hz.
- Non-uniform amplitude pdf: small amplitudes are more likely.
- Strong correlation between adjacent samples, so speech is predictable.
- Non-flat spectrum with formant peaks.
- Voiced sounds are quasi-periodic (pitch 80–350 Hz); unvoiced sounds are noise-like.
- Quasi-stationary over 10–30 ms; about 40–60% silence in conversation.

#### 7-bit Hamming code

The **(7,4) Hamming code** is a linear block code that adds 3 parity bits to 4 data bits. Minimum distance d_min = 3, so it **corrects any single-bit error** (or detects two). Parity bits sit at positions that are powers of 2:

| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Bit | p1 | p2 | d1 | p3 | d2 | d3 | d4 |

Even-parity equations (each parity covers the positions whose binary index has that bit set):

```text
 p1 = d1 ⊕ d2 ⊕ d4   (positions 1,3,5,7)
 p2 = d1 ⊕ d3 ⊕ d4   (positions 2,3,6,7)
 p3 = d2 ⊕ d3 ⊕ d4   (positions 4,5,6,7)
```

**Example – encoding:** data 1011 → d1 = 1, d2 = 0, d3 = 1, d4 = 1.

```text
 p1 = 1 ⊕ 0 ⊕ 1 = 0
 p2 = 1 ⊕ 1 ⊕ 1 = 1
 p3 = 0 ⊕ 1 ⊕ 1 = 0
 Codeword (p1 p2 d1 p3 d2 d3 d4) = 0 1 1 0 0 1 1
```

**Example – error correction:** suppose bit 5 is flipped; received word = 0 1 1 0 **1** 1 1.

```text
 s1 = r1 ⊕ r3 ⊕ r5 ⊕ r7 = 0⊕1⊕1⊕1 = 1
 s2 = r2 ⊕ r3 ⊕ r6 ⊕ r7 = 1⊕1⊕1⊕1 = 0
 s3 = r4 ⊕ r5 ⊕ r6 ⊕ r7 = 0⊕1⊕1⊕1 = 1
 Syndrome (s3 s2 s1) = 101 = 5
```

The syndrome points to position 5, so that bit is inverted back to 0, giving 0110011 and data **1011**. A syndrome of 000 means no error.

Code rate = 4/7 ≈ 0.57. Such block codes protect the most important speech-coder bits in mobile systems.

## Check yourself

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

1. What does the (7,4) Hamming code add to 4 data bits, and what can it do?
   A. 3 parity bits; correct any single-bit error
   B. 4 parity bits; correct two errors
   C. 3 parity bits; correct any two errors
   D. 1 parity bit; correct one error
   Answer: A. d_min = 3, so it corrects any single error (or detects two). (Key point: Hamming parameters)

2. At which positions do parity bits sit in the 7-bit Hamming code?
   A. 1, 2, 3
   B. 5, 6, 7
   C. Powers of 2: 1, 2, 4
   D. Even positions
   Answer: C. Parity bits p1, p2, p3 are at positions 1, 2 and 4. (Key point: Parity positions)

3. For data 1011, what is the codeword (p1 p2 d1 p3 d2 d3 d4)?
   A. 1011010
   B. 0110011
   C. 0111001
   D. 1100110
   Answer: B. p1 = 1^0^1 = 0, p2 = 1^1^1 = 1, p3 = 0^1^1 = 0 giving 0 1 1 0 0 1 1. (Key point: Encoding example)

4. What does a syndrome of 101 mean?
   A. No error
   B. Error in position 3
   C. Two errors
   D. Error at position 5, so invert that bit
   Answer: D. The syndrome read as binary 101 = 5 points to bit 5; syndrome 000 means no error. (Key point: Syndrome)

## Related in Wireless Communication

- [Speech characteristics and linear predictive coder](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-lpc) — Wireless Communication, chapter 6, asked 5×
- [Speech characteristics in coder design](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-characteristics-coder-design) — Wireless Communication, chapter 6, asked 3×
- [Speech characteristics; formant and channel vocoder](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-formant-channel-vocoder) — Wireless Communication, chapter 6
- [Characteristics of speech signal](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-characteristics) — Wireless Communication, chapter 6
- [Formant vocoder and speech characteristics](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aformant-vocoder-speech) — Wireless Communication, chapter 6

## Related in other subjects

- [Hamming weight and distance; (7,4) cyclic code for 1011](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ahamming-weight-cyclic-1011) — Communication Systems, chapter 8, asked 2×
- [Construct a (7,4) Hamming code](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Ahamming-74-construct) — Data Communication, chapter 8
- [Forward error correction using Hamming code](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afec-hamming) — Data Communication, chapter 8
- [Hamming distance and weight; (6,3) code check for 100101](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ahamming-6-3-h-100101) — Communication Systems, chapter 8