---
title: "PCM, DPCM and DM comparison; SQNR of PCM"
subject: "Communication Systems"
chapter: 4
key: "semester_6/communication_systems:pcm-dpcm-dm-compare-sqnr"
source: https://www.bctengineer.com/q/semester_6/communication_systems/pcm-dpcm-dm-compare-sqnr
site: BCT Engineering
---

# PCM, DPCM and DM comparison; SQNR of PCM

Communication Systems · Chapter 4: Pulse Modulation

- Asked in: 2079 Chaitra, 3+5 marks
- Video: [L 88 | Conclusion PCM DPCM DM ADM | Difference Between PCM DPCM DM ADM | Communication System I GATE](https://www.youtube.com/watch?v=7QnqpLucb34) — Dopamine
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/pcm-dpcm-dm-compare-sqnr
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-4

## Question

Compare Pulse Code Modulation (PCM), Differential Pulse Code Modulation (DPCM) and Delta Modulation. Find the Signal to Quantization Noise ratio (SQNR) of Pulse Code Modulation (PCM).

## Short answer

PCM quantizes each sample with n bits; DPCM codes the prediction error with fewer bits; DM sends 1-bit sign of difference with oversampling. For uniform PCM, SQNR = (3P/mp²) 2^{2n}. For a full-scale sinusoid, SQNR_dB = 1.76 + 6.02n dB; each additional bit increases SQNR by about 6 dB.

## Answer

#### Comparison of PCM, DPCM and DM

| Point | PCM | DPCM | DM |
|---|---|---|---|
| What is coded | Each sample value | Difference between sample and its prediction | Sign of difference only |
| Bits per sample | $n$ (e.g. 8) | Fewer than PCM (e.g. 4) | 1 |
| Sampling rate | $\ge 2W$ (Nyquist) | $\ge 2W$ | Much higher than $2W$ (oversampling) |
| Predictor | None | Linear predictor | One-sample delay (accumulator) |
| Quantization noise | Granular, $\Delta^2/12$ | Granular, smaller (prediction gain) | Granular + slope overload |
| SQNR | $1.76 + 6.02n$ dB | PCM value + $10\log G_p$ | $3f_s^3/(8\pi^2 f_m^2 W)$ |
| Bandwidth | Highest ($nW$) | Less than PCM | Can be less, but needs high $f_s$ |
| Complexity | Moderate | Most complex | Simplest |
| Use | Telephony (64 kbps), CD | Speech, video coding | Simple voice links |

#### SQNR of PCM

Let $m(t)$ have peak value $m_p$ and be quantized uniformly into $L = 2^n$ levels.

**Step size:** $\Delta = \dfrac{2m_p}{L}$

**Noise power:** the error $q$ is uniform in $(-\Delta/2, \Delta/2)$:

$$
N_q = \int_{-\Delta/2}^{\Delta/2}\frac{q^2}{\Delta}\,dq = \frac{\Delta^2}{12} = \frac{m_p^2}{3L^2}
$$

**SQNR:** with signal power $P$,

$$
\text{SQNR} = \frac{P}{N_q} = \frac{3L^2P}{m_p^2} = \frac{3P}{m_p^2}\,2^{2n}
$$

For a full-scale sinusoid, $P = m_p^2/2$:

$$
\text{SQNR} = 1.5\times 2^{2n} \quad\Rightarrow\quad \text{SQNR}_{dB} = 1.76 + 6.02\,n
$$

Each extra bit adds about 6 dB. Example: 8-bit PCM gives $1.76 + 48.16 = 49.92$ dB.

## Check yourself

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

1. How does the sampling rate of DM compare with PCM?
   A. DM does not sample
   B. DM samples at exactly 2W
   C. DM oversamples, much higher than 2W
   D. DM samples below 2W
   Answer: C. DM uses 1 bit so needs high oversampling to track the signal. (Key point: DM vs PCM sampling)

2. How does DPCM SQNR relate to PCM SQNR with same bits?
   A. PCM value plus 10 log Gp dB
   B. Equal to 6.02 n only
   C. PCM value minus 10 log Gp dB
   D. Equal to PCM
   Answer: A. Prediction gain adds to the SQNR. (Key point: DPCM SQNR)

3. What is the PCM quantization noise power?
   A. Delta^2/3
   B. mp^2/L
   C. Delta^2/12 = mp^2/(3L^2)
   D. Delta/12
   Answer: C. Uniform error over one step gives Delta^2/12. (Key point: PCM noise power)

4. What is SQNR (dB) of full-scale sine PCM with n bits?
   A. 6.02 n - 1.76
   B. 1.76 + 3.01 n
   C. 1.76 + 6.02 n
   D. 3.01 n
   Answer: C. SQNR = 1.5 x 2^(2n); 8 bits gives 49.92 dB. (Key point: PCM SQNR)

## Related in Communication Systems

- [Delta modulation encoder/decoder; PCM vs DM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adm-encoder-decoder-pcm-vs-dm) — Communication Systems, chapter 4
- [DPCM vs delta modulation; E1 hierarchy](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adpcm-vs-dm-e1) — Communication Systems, chapter 4
- [PCM vs DM SQNR for 6cos(5000πt) with 128 levels](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apcm-dm-6cos5000pit-128) — Communication Systems, chapter 4
- [SQNR of delta modulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adm-sqnr-derive) — Communication Systems, chapter 4, asked 2×
- [SQNR of delta modulation for a single-tone signal](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adm-sqnr-single-tone) — Communication Systems, chapter 4
- [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×

## Related in other subjects

- [Quantization noise and quantization error](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Aquantization-noise-error) — Digital Control System, chapter 1
- [Pulse stuffing and complete TDM PCM system](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultiplexing-pulse-stuffing-tdm-pcm) — Telecommunications, chapter 3
- [CT ratio for 33/6.6 kV star/delta (300:5)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Adifferential-ct-33-6-6kv-300) — Switchgear and Protection, chapter 7
- [Single-pulse PWM: modulation index and Fourier series](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Asingle-pulse-pwm-fourier) — Power Electronics, chapter 5