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# ENG201 Linear Systems Analysis and Design SUSS Assignment Sample Singapore

ENG201 Linear Systems Analysis and Design course focus on the analysis, design and construction of linear systems. It covers topics such as the Laplace Transform, transfer functions, state-space models and digital control. The course emphasizes problem-solving and system identification techniques that are required for the successful implementation of linear control systems. Topics discussed include frequency response analysis, stability concepts, root locus methods, optimal control, feedback theory and servo systems. Students gain a comprehensive understanding of concepts through practical application with the use of computer-aided analysis methods and hardware experiments in the laboratory. The course also covers topics such as system optimization, simulation and fault management. At the end of the course, students will be capable of designing linear control systems and applying appropriate techniques to ensure the successful operation of these systems.

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## Unlock the secrets to success in your ENG201 Linear Systems Analysis and Design course by studying sample assignments!

Singaporeassignmenthelp.com provides sample assignments for ENG201 Linear Systems Analysis and Design to help you understand the principles, methodologies and techniques used in linear control systems. With our assignment samples, you can gain a better understanding of concepts such as transfer functions, Laplace transforms, state-space models and digital control. You will become familiar with the different problem-solving techniques used in linear control systems and learn how to design efficient, reliable and robust control systems.

In this session, we’ll go over a few assignment objectives. Specifically, these are:

### Assignment Objective 1: Sketch the signal waveforms and system responses.

To truly understand a system and its responses, it is crucial to sketch out the signal waveforms. This visual representation allows us to study the behavior of the system under various conditions and inputs. By examining the waveforms, we can identify patterns, trends, and outliers that give us insights into the system’s strengths and weaknesses.

The system responses can also be sketched out to provide a clear picture of how the system reacts to different inputs. With this information, we can diagnose issues, optimize performance, and even design new systems. Sketching signal waveforms and system responses may seem like a trivial task, but it can lead to significant improvements in understanding and analysis.

### Assignment Objective 2: Describe the signals and systems using appropriate mathematical expressions.

A signal can be represented mathematically as a function of time, denoted by x(t), where t represents time. Depending on the type of signal, the mathematical expression can vary. For example, a sinusoidal signal can be represented as:

x(t) = A sin(ωt + φ)

where A is the amplitude, ω is the angular frequency, and φ is the phase angle.

A system can be represented mathematically as a function that maps an input signal x(t) to an output signal y(t). This can be denoted as y(t) = H[x(t)], where H is the mathematical representation of the system. The system can be represented in different ways depending on the type of system. For example, a linear time-invariant (LTI) system can be represented as a convolution integral:

y(t) = h(t) * x(t)

where h(t) is the impulse response of the system, which represents the output of the system when the input is a unit impulse. The convolution integral represents the mathematical operation of convolving the input signal x(t) with the impulse response h(t) to obtain the output signal y(t).

### Assignment Objective 3: Calculate the Fourier series, Fourier transform, inverse Fourier transform, Laplace transform and inverse Laplace transform.

As a professional, understanding the intricacies of mathematical concepts such as the Fourier series, Fourier transform, inverse Fourier transform, Laplace transform, and inverse Laplace transform is crucial to creating accurate and reliable models in fields such as engineering, physics, and mathematics. These concepts may seem complex, yet understanding how to calculate and apply them can lead to powerful results.

From analyzing periodic phenomena to solving linear differential equations, the ability to apply these tools is essential in advancing science and technology. While it may take time and effort to master these mathematical concepts, the payoff is invaluable in the context of research and development.

### Assignment Objective 4: Discuss the characteristics and properties of signals and systems.

Signals and systems are fundamental concepts in the field of electrical engineering, telecommunications, and other related fields. A signal is a time-varying or spatially varying quantity that represents some information, while a system is a physical or mathematical entity that processes the signal to achieve a desired output. Here are some of the characteristics and properties of signals and systems:

Characteristics of Signals:

1. Amplitude: The amplitude of a signal is the strength or intensity of the signal at any given point in time or space.
2. Frequency: The frequency of a signal is the number of cycles or oscillations that occur in a second.
3. Phase: The phase of a signal is the position of the signal relative to a reference point.
4. Time-varying: A signal is said to be time-varying if its characteristics change over time.
5. Continuous-time or Discrete-time: Signals can be classified as continuous-time or discrete-time based on whether they are defined at every point in time or at discrete intervals.

Properties of Signals:

1. Linearity: A signal is said to be linear if its response to a sum of inputs is equal to the sum of its individual responses.
2. Time Invariance: A signal is said to be time-invariant if its response to an input signal is the same irrespective of the time at which the input is applied.
3. Causality: A signal is said to be causal if its output at any time depends only on past or current values of the input.
4. Stationarity: A signal is said to be stationary if its statistical properties remain constant over time.

Characteristics of Systems:

1. Linearity: A system is said to be linear if it satisfies the principle of superposition.
2. Time Invariance: A system is said to be time-invariant if its response to an input signal is the same irrespective of the time at which the input is applied.
3. Causality: A system is said to be causal if its output at any time depends only on past or current values of the input.
4. Memory: A system is said to be memoryless if its output at any time depends only on the current value of the input.
5. Stability: A system is said to be stable if its output does not grow unbounded in response to a bounded input.

Properties of Systems:

1. Linearity: A system is said to be linear if it satisfies the principle of superposition.
2. Time Invariance: A system is said to be time-invariant if its response to an input signal is the same irrespective of the time at which the input is applied.
3. Causality: A system is said to be causal if its output at any time depends only on past or current values of the input.
4. Memory: A system is said to be memoryless if its output at any time depends only on the current value of the input.
5. Stability: A system is said to be stable if its output does not grow unbounded in response to a bounded input.

Understanding these characteristics and properties is essential for the design and analysis of signals and systems in various applications.

### Assignment Objective 5: Solve differential equations for modeling and analyzing systems.

Differential equations are mathematical equations that describe the relationship between the rate of change of a system and its current state. They are widely used in physics, engineering, economics, and other fields to model and analyze complex systems.

There are different types of differential equations, but most of them can be solved using one of the following methods:

1. Separation of Variables: This method is used to solve first-order ordinary differential equations of the form dy/dx = f(x)g(y). The method involves separating the variables on each side of the equation and integrating both sides with respect to their respective variables.
2. Integrating Factors: This method is used to solve first-order linear differential equations of the form dy/dx + p(x)y = q(x). The method involves multiplying both sides of the equation by an integrating factor, which is a function that makes the left-hand side of the equation integrable.
3. Laplace Transforms: This method is used to solve linear differential equations of any order. The method involves transforming the differential equation into an algebraic equation using the Laplace transform and then solving for the unknown function.
4. Numerical Methods: This method involves using numerical techniques to approximate the solution of a differential equation. Examples of numerical methods include the Euler method, the Runge-Kutta method, and the finite element method.

In practice, the choice of method depends on the type and complexity of the differential equation, as well as the availability of analytical or numerical tools for solving it.

### Assignment objective 6: Determine the system responses and characteristics.

When it comes to understanding systems, it’s important to delve deeper into their responses and characteristics. This knowledge can help you identify potential issues, optimize these systems, and make informed decisions about their implementation. Understanding the temporal, spatial, and frequency characteristics of these systems can reveal insightful patterns and trends, offering a wealth of valuable data that can help you optimize performance and identify bottlenecks.

Similarly, exploring their dynamic response characteristics will allow you to develop models and simulations that can be used to test hypotheses and make predictions. By mastering these essential features, you can take confidence in knowing that you have a deep understanding of how these systems work, and how to best utilize them.

### Assignmernt Objective 7: Analyze the basic properties of signals and LTI systems.

Signals and Linear Time-Invariant (LTI) Systems are fundamental concepts in signal processing, which is the branch of electrical engineering concerned with the analysis, synthesis, and processing of signals. Here are some of their basic properties:

Signals:

A signal is any time-varying quantity that carries information. In signal processing, a signal is typically represented as a function of time or space or both. Signals can be analog or digital, continuous or discrete, periodic or aperiodic, deterministic or random.

• Amplitude: the strength or magnitude of a signal at any given time or point.
• Frequency: the number of cycles or repetitions of a periodic signal per unit of time.
• Phase: the offset of a signal from a reference point in time or space.
• Energy and Power: The energy of a signal is the integral of the squared magnitude of the signal over all time, while the power is the energy per unit of time.

Linear Time-Invariant (LTI) Systems:

An LTI system is a system whose response to a given input signal is a scaled and time-shifted version of the input signal. LTI systems are important in signal processing because they can be characterized by their impulse response, which is the output of the system when the input is a delta function.

• Linearity: the output of the system is a linear combination of its inputs.
• Time-Invariance: the system’s behavior is independent of the time at which the input is applied.
• Superposition: the output resulting from a sum of inputs is the sum of the individual outputs due to each input.
• Convolution: the output of an LTI system is the convolution of the input signal with the impulse response of the system.

Overall, understanding the properties of signals and LTI systems is crucial for signal-processing applications such as filtering, modulation, and communication.

### Assignment Objective 8: Design LTI systems and signals using the basic signal functions and properties.

Designing an LTI (Linear Time-Invariant) system involves selecting a suitable system function and choosing appropriate input signals to analyze the system’s response. Here are some basic signal functions and properties that can be used for this purpose:

1. Unit impulse function (δ(t)): The unit impulse function is a signal that has an amplitude of 1 at t=0 and zero everywhere else. It is used to determine the impulse response of an LTI system, which is the system’s output when the input is an impulse.
2. Step function (u(t)): The step function is a signal that has an amplitude of 0 for t<0 and 1 for t≥0. It is often used as an input signal to observe the system’s step response, which is the system’s output when the input is a step function.
3. Sinusoidal function (sin(ωt)): The sinusoidal function is a periodic signal that oscillates between -1 and 1 with a frequency of ω. It is commonly used to analyze the frequency response of an LTI system, which is the system’s output when the input is a sinusoidal signal.
4. Exponential function (e^(αt)): The exponential function is a non-periodic signal that grows or decays exponentially with time, depending on the sign of α. It is used to analyze the stability of an LTI system, as an unstable system will exhibit unbounded exponential growth or decay.

Once the appropriate input signal is selected, the system’s output can be computed using the convolution integral:

y(t) = ∫x(τ)h(t-τ)dτ

where x(t) is the input signal, h(t) is the system’s impulse response, and y(t) is the system’s output. The properties of the input signal and system function can be used to simplify the convolution integral and obtain an analytical expression for the system’s output. For example, if the input signal is a sinusoidal function and the system function is a low-pass filter, the output can be expressed as a sinusoidal function with reduced amplitude and phase shift, reflecting the filter’s frequency response.

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