---
title: "Analog communication components; distortionless transfer function"
subject: "Communication Systems"
chapter: 1
key: "semester_6/communication_systems:analog-components-distortionless-tf"
source: https://www.bctengineer.com/q/semester_6/communication_systems/analog-components-distortionless-tf
site: BCT Engineering
---

# Analog communication components; distortionless transfer function

Communication Systems · Chapter 1: Introduction

- Asked in: 2069 Bhadra (CS I), 2+5+3 marks
- Video: [Distortion Less Transmission of the System](https://www.youtube.com/watch?v=PYZ84ZpMGAI) — TutorialsPoint
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/analog-components-distortionless-tf
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-1

## Question

What are the main components of analog communication system? Describe briefly about each component. Find the transfer function for distortionless system.

## Short answer

Main components: information source, input transducer, transmitter (modulation, amplification), channel (adds noise/distortion), receiver (demodulation), output transducer, destination. A distortionless system yields y(t)=K x(t−t_d). Transfer function: H(f)=K e^{−j2πf t_d}, requiring constant amplitude and linear phase.

## Answer

An **analog communication system** sends a continuous message (speech, music, video) from a source to a destination using continuous signals.

#### Main components

```text
 [Info source]->[Input transducer]->[Transmitter]
                                         |
                    Noise, interference->[Channel]
                                         |
 [Destination]<-[Output transducer]<-[Receiver]
```

1. **Information source:** produces the message, e.g. a speaker's voice or a camera scene. The message may be non-electrical.
2. **Input transducer:** converts the message into an electrical signal (baseband) $m(t)$, e.g. microphone, camera.
3. **Transmitter:** prepares the signal for the channel. It amplifies, filters and **modulates** a high-frequency carrier (AM, FM), then power-amplifies it and couples it to the antenna or line. Modulation gives practical antenna size, multiplexing and channel matching.
4. **Channel:** the medium between transmitter and receiver, e.g. free space, coaxial cable, optical fibre. It attenuates and distorts the signal, and **noise and interference** are added here.
5. **Receiver:** extracts the message from the weak, corrupted received signal. It selects the wanted signal (tuning, filtering), amplifies it (RF/IF amplifiers), **demodulates** it to recover $m(t)$, and amplifies the baseband output.
6. **Output transducer:** converts the electrical signal back into the original form, e.g. loudspeaker, display.
7. **Destination:** the user who receives the message.

#### Transfer function for a distortionless system
A system is **distortionless** if the output has the same shape as the input; only a constant change in amplitude and a constant time delay are allowed:

$$
y(t)=K\,x(t-t_d)
$$

where $K$ is the gain (or attenuation) and $t_d$ is the delay. Taking the Fourier transform and using the time-shift property:

$$
\begin{aligned}
Y(f)&=K\,X(f)\,e^{-j2\pi ft_d}\\
H(f)&=\frac{Y(f)}{X(f)}=K\,e^{-j2\pi ft_d}
\end{aligned}
$$

So the conditions are:
- **Amplitude response:** $\lvert H(f)\rvert=K$, constant over the signal bandwidth (otherwise amplitude distortion).
- **Phase response:** $\theta(f)=-2\pi ft_d$, linear with frequency and passing through the origin (otherwise phase/delay distortion). Equivalently, the group delay $t_d=-\frac{1}{2\pi}\frac{d\theta}{df}$ is constant.

```text
 |H(f)|                       theta(f)
   |                            |\
 K +-------------              | \  slope = -2*pi*td
   |                     ------+--\------> f
   +------------> f             |   \
```

In practice, it is enough for these conditions to hold only over the band occupied by the signal.

## Check yourself

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

1. The transmitter's key task is:
   A. Convert sound to electrical form
   B. Display the message
   C. Demodulate
   D. Modulate a high-frequency carrier, amplify it and couple it to the channel
   Answer: D. Input transducer converts; transmitter modulates and power-amplifies. (Key point: Transmitter)

2. In the channel:
   A. Noise and interference are added and the signal is attenuated
   B. The signal is demodulated
   C. The message is created
   D. Noise is removed
   Answer: A. The channel attenuates, distorts and adds noise. (Key point: Channel)

3. The receiver does what?
   A. Generates the message
   B. Selects, amplifies and demodulates the signal to recover m(t)
   C. Adds the carrier
   D. Converts to digital only
   Answer: B. It recovers the message from the weak received signal. (Key point: Receiver)

4. The transfer function of a distortionless system is:
   A. K e^(j2 pi f t_d)^2
   B. K f
   C. K e^(-j2 pi f t_d) with |H|=K and phase -2 pi f t_d
   D. K/(1+jf)
   Answer: C. Constant magnitude and linear phase. (Key point: Distortionless H(f))

## Related in Communication Systems

- [Impulse response, transfer function and distortionless transmission](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adistortionless-transfer-function) — Communication Systems, chapter 1
- [Function of basic components of a digital communication system](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adcs-basic-components) — Communication Systems, chapter 1
- [Modulation; analog communication system block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amodulation-analog-block-diagram) — Communication Systems, chapter 1, asked 3×
- [Block diagram of analog communication system](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aanalog-comm-block-diagram) — Communication Systems, chapter 1, asked 2×
- [Duplex digital communication system vs analog](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adigital-comm-duplex-vs-analog) — Communication Systems, chapter 1
- [Analog communication block diagram; modulation and its reasons](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aanalog-comm-modulation-reasons) — Communication Systems, chapter 1, asked 3×

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