---
title: "PCM bit rate for 4.5 MHz TV signal with 1024 levels"
subject: "Communication Systems"
chapter: 4
key: "semester_6/communication_systems:pcm-tv-4-5mhz-1024"
source: https://www.bctengineer.com/q/semester_6/communication_systems/pcm-tv-4-5mhz-1024
site: BCT Engineering
---

# PCM bit rate for 4.5 MHz TV signal with 1024 levels

Communication Systems · Chapter 4: Pulse Modulation

- Asked in: 2075 Chaitra (CS II), 4 marks
- Video: [A television signal (video plus audio) has a bandwidth of 4.5 MHz. This signal is sampled, quanti…](https://www.youtube.com/watch?v=Zz8-KFw08Jk) — Engineer Thileban Explains
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/pcm-tv-4-5mhz-1024
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-4

## Question

The bandwidth of a TV plus audio signal is 4.5 MHz. If this signal is converted to PCM with 1024 quantization levels, determine bit rate of the resulting PCM signal. Let us assume that the signal is sampled at a rate 20% above the Nyquist rate.

## Short answer

1024 levels give 10 bits per sample. Nyquist rate 9 MHz, sampling at 10.8 MHz (20% above). Bit rate = 10 * 10.8 MHz = 108 Mbps.

## Answer

**Given:** $W = 4.5$ MHz, $L = 1024$, sampling 20% above Nyquist rate.

1. Bits per sample:
$$
n = \log_2 L = \log_2 1024 = 10\ \text{bits}
$$
2. Nyquist rate and actual sampling rate:
$$
\begin{aligned}
f_N &= 2W = 2 \times 4.5 = 9\ \text{MHz} \\
f_s &= 1.2 \times 9 = 10.8\ \text{MHz}
\end{aligned}
$$
3. Bit rate:
$$
R_b = n f_s = 10 \times 10.8 \times 10^6 = 108 \times 10^6\ \text{bps}
$$

**Answer: Bit rate = 108 Mbps.**

## Check yourself

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

1. With L = 1024 levels, the number of bits per sample is:
   A. 8
   B. 10
   C. 12
   D. 1024
   Answer: B. n = log2 1024 = 10. (Key point: Bits per sample)

2. Sampling 20% above the Nyquist rate for W = 4.5 MHz gives fs:
   A. 9 MHz
   B. 10.8 MHz
   C. 5.4 MHz
   D. 11.25 MHz
   Answer: B. Nyquist rate = 9 MHz and 1.2 x 9 = 10.8 MHz. (Key point: Sampling rate)

3. The PCM bit rate is:
   A. 45 Mbps
   B. 90 Mbps
   C. 108 Mbps
   D. 10.8 Mbps
   Answer: C. Rb = n x fs = 10 x 10.8 MHz = 108 Mbps. (Key point: Bit rate)

## Related in Communication Systems

- [PAM, PWM, PPM; PCM of 4.8 MHz TV signal with 512 levels](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apam-pwm-ppm-tv-4-8mhz) — Communication Systems, chapter 4
- [E1 hierarchy; PCM of 4.2 MHz TV signal with 512 levels](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ae1-pcm-tv-4-2mhz-512) — Communication Systems, chapter 4
- [TDM of 24 voice signals: PAM bandwidth and PCM sampling rate](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Atdm-24-voice-pam-pcm) — Communication Systems, chapter 5
- [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
- [PCM: minimum channel bandwidth numerical](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apcm-bandwidth-3khz-0-5pct) — Communication Systems, chapter 4
- [PCM 7-bit at 50 Mbps: maximum message bandwidth](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apcm-7bit-50mbps-bandwidth) — Communication Systems, chapter 4

## Related in other subjects

- [Capacity and Nyquist levels, 3 to 4 MHz, 24 dB](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Anyquist-shannon-bandwidth-3-4mhz) — Data Communication, chapter 1
- [Nyquist levels for 3 to 4 MHz channel](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Anyquist-noiseless-24db) — Data Communication, chapter 1
- [Frequency of a signal sampled at 300 Hz](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Asampled-signal-frequency-300) — Signals and Systems, chapter 4