---
title: "Uniform vs non-uniform quantization; 16-level PCM numerical"
subject: "Communication Systems"
chapter: 4
key: "semester_6/communication_systems:uniform-nonuniform-16-level-pcm"
source: https://www.bctengineer.com/q/semester_6/communication_systems/uniform-nonuniform-16-level-pcm
site: BCT Engineering
---

# Uniform vs non-uniform quantization; 16-level PCM numerical

Communication Systems · Chapter 4: Pulse Modulation

- Asked in: 2073 Chaitra (CS II), 4+6 marks
- Video: [Examples of Quantization & Calculation of Parameters based on Quantization in Digital Communication](https://www.youtube.com/watch?v=zA8nw9owtbQ) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/uniform-nonuniform-16-level-pcm
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-4

## Question

Differentiate between uniform and non-uniform quantization. The information in an analog waveform with maximum frequency 4 kHz is to be transmitted over a 16-level PCM system.
a) What would be the maximum number of bits per sample?
b) What is the minimum sampling rate and bit rate?

## Short answer

Uniform quantization uses a constant step size, giving poor SQNR for weak signals; non-uniform uses small steps near zero and larger steps at high amplitudes, providing nearly constant SQNR via companding. For 16-level PCM: bits per sample = log₂16 = 4 bits; minimum sampling rate = 8 kHz; bit rate = 4 × 8000 = 32 kbps.

## Answer

#### Uniform vs non-uniform quantization

| Point | Uniform | Non-uniform |
|---|---|---|
| Step size | Constant $\Delta$ over the whole range | Small near zero, larger at high amplitudes |
| Noise power | $\Delta^2/12$, same at all levels | Varies; small for weak signals |
| SQNR | Proportional to signal power; poor for weak signals | Nearly constant over wide range |
| Realisation | Uniform ADC | Compressor + uniform ADC + expander (companding) |
| Laws | Linear | µ-law ($\mu = 255$), A-law ($A = 87.6$) |
| Bits for toll-quality speech | About 12–13 | 8 |
| Used in | Instrumentation, video, audio with uniform pdf | Telephony (speech) |

Non-uniform quantization suits speech because small amplitudes are much more likely and the dynamic range is large.

#### Numerical
**Given:** $f_{max} = W = 4$ kHz, $L = 16$ levels.

**a) Bits per sample**
$$
n = \log_2 L = \log_2 16 = 4\ \text{bits}
$$

**b) Minimum sampling rate and bit rate**
$$
\begin{aligned}
f_{s,min} &= 2W = 2 \times 4 = 8\ \text{kHz} \\
R_b &= nf_s = 4 \times 8000 = 32\ \text{kbps}
\end{aligned}
$$

**Answer: (a) 4 bits/sample; (b) $f_s = 8$ kHz (8000 samples/s), $R_b = 32$ kbps.**

## Check yourself

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

1. How does the step size differ in non-uniform quantization?
   A. Constant over the whole range
   B. Small near zero and larger at high amplitudes
   C. Large near zero and small at high amplitudes
   D. Random
   Answer: B. Non-uniform quantizers use fine steps for weak signals, which are most likely in speech. (Key point: Step size)

2. Non-uniform quantization is realised by:
   A. Expander at the transmitter only
   B. Compressor, uniform quantizer, then expander at the receiver
   C. A higher sampling rate
   D. Anti-aliasing filter
   Answer: B. Companding compresses before a uniform ADC and expands after decoding. (Key point: Companding)

3. For 16 levels, bits per sample are:
   A. 16
   B. 8
   C. 4
   D. 2
   Answer: C. n = log2 16 = 4. (Key point: Bits per sample)

4. For W = 4 kHz and 16 levels, the minimum sampling rate and bit rate are:
   A. 8 kHz and 32 kbps
   B. 4 kHz and 16 kbps
   C. 8 kHz and 128 kbps
   D. 16 kHz and 64 kbps
   Answer: A. fs = 2W = 8 kHz and Rb = 4 x 8000 = 32 kbps. (Key point: Rates)

## Related in Communication Systems

- [Non-uniform quantization; PCM numerical (4 kHz, ±2.4 V, 64 kHz)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anonuniform-companding-pcm-4khz-64khz) — Communication Systems, chapter 4
- [Bits per sample and information rate (4.5 kHz, 8 levels)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Abits-info-rate-4-5khz-8-levels) — Communication Systems, chapter 6
- [SQNR for uniform quantization in terms of levels and bits](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asqnr-uniform-levels-bits) — Communication Systems, chapter 4, asked 2×
- [Uniform vs non-uniform quantization; companding laws](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Auniform-nonuniform-companding-laws) — Communication Systems, chapter 4
- [Entropy and information rate of 6-level PCM signal](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aentropy-info-rate-5khz-six-levels) — Communication Systems, chapter 6
- [Need for non-uniform quantization; SQNR of DM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anonuniform-quantization-dm-sqnr) — Communication Systems, chapter 4, asked 2×