ETE-2325 Chapter-1 (Signals and Systems)

1. What is a signal?
   A signal is anything that carries or conveys information, like music, speech, motion pictures, or heartbeat.

2. What is the most common independent variable in signals?
   Time (represented by "t") is the most common independent variable in signals.

3. What is amplitude?
   Amplitude is the value of a signal at a specific time.

4. What is waveform?
   Waveform is the shape or plot of a signal as it changes with time or another independent variable.

5. How is a signal mathematically represented?
   A signal is represented as a function of one or more independent variables.

6. Give an example of a signal as a function of time.
   and are examples of signals that change with time.

7. What are the three ways to classify signals?

   • By the number of sources: One-channel or multichannel signals
   • By the number of dependent variables: One-dimensional or multidimensional signals
   • By whether the signal is continuous or discrete: Analog or discrete signals

8. What are one-channel signals?
   Signals that come from a single source or sensor are one-channel signals.

9. Give an example of a one-channel signal.

• Recording room temperature over time
• The audio output of a mono speaker

10. What are multichannel signals?
Signals that come from multiple sources or sensors are called multichannel signals.

11. Give an example of a multichannel signal.
The audio output of stereo speakers (left and right channels) is an example of a two-channel signal.

12. What are one-dimensional signals?
Signals that depend on only one independent variable are called one-dimensional signals.

13. Give an example of a one-dimensional signal.
Music, speech, and heartbeat signals are examples because they change with time.

14. What are multidimensional signals?
Signals that depend on two or more independent variables are called multidimensional signals.

15. Give an example of a two-dimensional signal.
A photograph, where brightness depends on two spatial coordinates (x, y).

16. Give an example of a three-dimensional signal.
A black-and-white motion picture, where brightness depends on x, y, and time (t).

Types of Signals

17. What are analog or continuous signals?
Signals that change smoothly and continuously over time are called analog signals.

18. What are discrete signals?
Signals that are defined only at specific time intervals are called discrete signals.

19. What is a continuous-time signal?
A signal that is defined for every instant of time. It is written as $x(t)$.

20. What is a discrete-time signal?
A signal that is defined only at specific time points. It is written as $x[n]$.

21. What is a digital signal?
A digital signal is a coded version of a discrete signal, usually represented in binary numbers.

22. What is quantization in digital signals?
Quantization is the process of converting continuous signal values into discrete steps.

Systems and Transformations

23. What is a system?
A system is a process that takes an input signal and produces an output signal.

24. How is a system represented?
A system is denoted by the function $H$ and is written as:

$$\text{Output}=H(\text{Input})$$

25. What are the two main types of systems?

• Continuous-time systems
• Discrete-time systems

26. What is a continuous-time system?
A system that processes continuous-time signals.

27. What is a discrete-time system?
A system that processes discrete-time signals.

28. What is an LTI system?
A Linear Time-Invariant (LTI) system is one that follows the properties of linearity and time-invariance.

29. What is the Laplace Transform used for?
It is used to convert time-domain signals into the s-domain for easier analysis.

Frequency and Electromagnetic Spectrum

30. Why is frequency important in signals?
Frequency helps determine the characteristics of a signal, such as pitch in sound or color in images.

31. Give an example of different electromagnetic signals along with their wavelength and frequency range.

Type of Signal	Wavelength (m)	Frequency Range (Hz)
Radio broadcast	$10^4$ to ${10}^2$	$3 \times 10^4$ to $3\times {10}^6$
Shortwave radio signals	$10^2$ to $10^{-2}$	$3 \times 10^6$ to $3\times {10}^{10}\mathrm{<br>}$
Radar / Space communications	$1$ to $10^{-2}$	$3 \times 10^8$ to $3 \times 10^{10}$
Common-carrier microwave	$1$ to ${10}^{-6}$	$3 \times 10^8$ to $3 \times 10^{11}$
Infrared (IR)	$10^{-3}$ to $10^{-6}$	$3 \times 10^{11}$ to $3.7 \times 10^{14}$
Visible light	$3.9 \times 10^{-7}$ to $8.1 \times 10^{-7}$	$3.7 \times 10^{14}$ to $7.7 \times 10^{14}$
Ultraviolet (UV)	$10^{-7}$ to ${10}^{-8}$	$3 \times 10^{15}$ to $3\times {10}^{16}$
Gamma rays and X-rays	$10^{-9}$ to $10^{-10}$	$3 \times 10^{17}$ to $3 \times 10^{18}$

Importance of Signals and Systems

1. Biomedical

• ECG is used to predict heart diseases.
• EEG is used to study normal and abnormal behaviour of the brain.
• EMG is used to study the condition of muscles.
• X-ray images are used to predict bone fractures and tuberculosis.
• Ultrasonic scan images of the kidney and gall bladder are used to predict stones.
• Ultrasonic scan images of the fetus are used to predict abnormalities in a baby.
• MRI scan is used to study minute inner details of any part of the human body.

2. Speech Processing

• Speech compression and decompression to reduce memory requirements of storage systems.
• Speech compression and decompression for effective use of transmission channels.
• Speech recognition for voice-operated systems and voice-based security systems.
• Speech recognition for conversion of voice to text.
• Speech synthesis for various voice-based warnings or announcements.

4. Communication

• The spectrum analysis of modulated signals helps to identify the information-bearing frequency component that can be used for transmission.
• The analysis of signals received from radars is used to detect flying objects and their velocity.
• Generation and detection of DTMF signals in telephones.
• Echo and noise cancellation in transmission channels.

6. Image Processing

• Image compression and decompression to reduce the memory requirement of storage systems.
• Image compression and decompression for the effective use of transmission channels.
• Image recognition for security systems.
• Filtering operations on images to extract features or hidden information.