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Questions and Answers
What are the most commonly used analog signals in communication systems?
What are the most commonly used analog signals in communication systems?
What happens to signals when they are corrupted by noise?
What happens to signals when they are corrupted by noise?
Which type of system is used to process signals in communication?
Which type of system is used to process signals in communication?
Which of the following statements is true regarding communication systems?
Which of the following statements is true regarding communication systems?
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What role does the independent variable, t, play in info bearing signals?
What role does the independent variable, t, play in info bearing signals?
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What is referred to as the zero-energy state of a physical system?
What is referred to as the zero-energy state of a physical system?
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How does the initial state of a system influence its response to inputs?
How does the initial state of a system influence its response to inputs?
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Which of the following best describes 'state' in the context of mechanical systems?
Which of the following best describes 'state' in the context of mechanical systems?
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What occurs when an input is applied to a system with predetermined initial conditions?
What occurs when an input is applied to a system with predetermined initial conditions?
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Which mechanical component is not typically classified as part of a mechanical system?
Which mechanical component is not typically classified as part of a mechanical system?
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What is the professional title of Tahir Aja Zarma?
What is the professional title of Tahir Aja Zarma?
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Which department does Tahir Aja Zarma belong to?
Which department does Tahir Aja Zarma belong to?
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What is the email address of Tahir Aja Zarma?
What is the email address of Tahir Aja Zarma?
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What is the phone number format provided for Tahir Aja Zarma?
What is the phone number format provided for Tahir Aja Zarma?
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What is the room number of Tahir Aja Zarma at Nile University?
What is the room number of Tahir Aja Zarma at Nile University?
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Which of the following describes an electronic system?
Which of the following describes an electronic system?
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Which characteristic is NOT typically associated with electronic systems?
Which characteristic is NOT typically associated with electronic systems?
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What type of system is a phone network primarily considered?
What type of system is a phone network primarily considered?
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Which of the following examples is NOT an electronic system?
Which of the following examples is NOT an electronic system?
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Which term best describes a system that does not change over time?
Which term best describes a system that does not change over time?
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Which characteristic is NOT required for a physical realizable signal?
Which characteristic is NOT required for a physical realizable signal?
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Which of the following signals violates the characteristics of physical realizability?
Which of the following signals violates the characteristics of physical realizability?
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What is a necessary property of a physical realizable signal?
What is a necessary property of a physical realizable signal?
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Which of the following statements about real-world signals is true?
Which of the following statements about real-world signals is true?
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Which of the following is a common characteristic of a continuous, real-valued signal?
Which of the following is a common characteristic of a continuous, real-valued signal?
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What is a key characteristic of a system?
What is a key characteristic of a system?
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From a communication engineer's perspective, what defines a system?
From a communication engineer's perspective, what defines a system?
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Why is feedback important in systems?
Why is feedback important in systems?
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Which of the following best describes a system?
Which of the following best describes a system?
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What is commonly referred to as unwanted signals in systems?
What is commonly referred to as unwanted signals in systems?
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Study Notes
Introduction to Signals and Systems
- Signals used to convey information, central to communication and signal processing
- Signals can be viewed in time or frequency domain
- A signal is any physical quantity varying in time, space, or other independent variables (IVs), often time
- Theoretical signals described mathematically, graphically, or in tabular form
- Real signals often difficult to describe precisely, approximated
Signal Classification
- Deterministic and Random Signals: Signal value known or unknown at all times
- Periodic Signals: x(t) = x(t + T)
- Non-Periodic Signals: x(t) ≠ x(t + T)
- Analog (Continuous-Time): Exist for all times 't'
- Example: x(t) = A cos(2πfct + θ)
- Discrete: Exist at discrete times only
Important Signal Types
- Energy Signals: Finite energy, E₀ < ∞. Energy can be calculated in time or frequency domain. All time-limited signals of finite amplitude are energy signals. Energy depends on load
- Power Signals: Finite average power, P₀ < ∞. Power is the time-averaged (mean) of the squared amplitude
- Examples:
- Most periodic signals are power type.
- Energy signals have zero power and vice versa
Signal Properties
- Even Signals: Symmetric about the y-axis (x(t) = x(-t))
- Odd Signals: Symmetric about the origin (x(t) = -x(-t))
- Any signal can be written as a sum of even and odd parts
- Sum of two even signals is even; sum of two odd signals is odd
Important Signal Types (cont'd)
- Complex exponentials: Include harmonicas represented as ejωt = cos(ωt) ± j sin(ωt)
- Unit step function: u(t): u(t)=1 for t ≥ 0, u(t)=0 for t<0. Commonly denoted by u(t)
- Ramp function: r(t): r(t) = t u(t)
- Rectangular pulse function: rect(t)
- Triangular pulse function: A(t) or tri(t);
- Sign function: sgn(t); sgn(t)=1 for t>0, sgn(t)=-1 for t<0, and sgn(t)=0 if t=0
- Sinc function: sinc(t) = sin(at) / (at)
- Impulse function (Delta function): D(t) or δ(t)
System Classification
- A system is an entity that processes inputs to yield outputs.
- System can be Physical (hardware realization) or algorithmic (software realization)
- Systems can be time-invariant / variant, causal / non-causal, linear/non-linear
System Properties (cont'd)
- Causal: Output at time t depends only on input values up to that time (not future input values)
- Non-causal: Output depends on input values in the future, as well as in the past
- Linearity: Additivity and homogeneity (i.e. Ax(t)=A*y(t))
- Principle of superposition: Linear systems satisfy both these rules.
Common Operations on Signals
- Amplitude scaling: Multiplying the signal by a constant (K * g(t)).
- Time Shifting: Displacing the signal in time (g(t ± T)), shifting left (+) or right (-) by T
- Time Scaling: Implies a-fold expansion or compression (g(at) / g(t/a)) where 1/a may slow down /speeds up
- Reflection/Folding: Reflecting the signal about the vertical axis (g(-t))
Systems Important Concepts
- State: Variables needed to determine the energy level of the system
- Initial conditions: state of the system before applying any input
- Frequency function: (or the frequency response) describes how a system responds to sinusoidal input signals.
- Time function: Describes how the system responds to general inputs.
Signal & Spectra
- Spectral Density: Describes how power or energy is distributed over different frequencies. (Includes Energy and Power spectral Density)
- Examples: energy spectral density or power spectral density
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Description
Explore the fundamental concepts of signals and systems in communication and signal processing. Learn about different types of signals, their classification, and how they can be represented mathematically. This quiz covers topics from deterministic and random signals to energy and power signals.
