Signals and Sytems from Udemy

In this course, we start our journey form discussing the general representation of signals and systems which is really important.

We will be representing our signals as mathematical functions having an independent variable. And this representation will be the most of the first unit.

Then, we are going to classify our signals, such as periodic/non-periodic, even/odd etc etc. This part will be also really crucial, since the kind of the signal allows us to choose the path to move on as we proceed to the solution.

Common Signals will be explained .

The Chapter for coming signals provides in-depth treatment of singularity functions such as unit pulse, unit step, and unit ramp signals. All of these signals are defined graphically and mathematically in the CT (Continuous Time) and DT (Discrete Time) domains. Signal properties and relationships between singularity functions are also explained. And other signals like signum function, sinc function etc. are also covered.

Properties of Systems: All system properties such as linearity, time invariance, causality, stability, memory and reversibility are well explained using a lot of examples.

You also have the opportunity to ask any question you have in your mind to the instructor 24/7.

We will be replying your messages and questions within 24 hours. (as soon as possible)

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What's inside

Syllabus

1 - Signals and Systems Overview

1.2.1 Examples and Mathematical Representation of Signals

1.2.2 Signal Energy and Power

1.3.1 Transformation of the Independent Variable

Example - 1 Transformation of the Independent Variable

Quiz for Transformation of the Independent Variable

1.3.2 Periodic Signals

Quiz for Periodic Signals

Example - 2 Periodic Signals

1.3.3 Even and Odd Signals

1.4.1 Continuous Time Complex Exponential and Sinusoidal Signals

Example - 3 - Continuous Time Complex Exponential and Sinusoidal Signals

1.4.2 General Complex Exponential Signals

1.4.3 Discrete Time Complex Exponentials and Sinusoidal Signals

1.4.4 Periodicity Properties of Discrete-Time Complex Exponentials

Example - 4 - Periodicity of a Discrete-Time Exponential

1.5.1 Discrete Time Unit Step and Unit Impulse Function

1.5.2 Continuous Time Unit Step and Unit Impulse Function

Example - 5 - Unit Step and Unit Impulse Signals

1.6.1 Continuous and Discrete Time System Examples

1.6.2 Interconnections of Systems

1.7.1 Basic System Properties - I

1.7.2 Basic System Properties - II

End of the Unit 1 Problems : 1

End of the Unit 1 Problems : 2

End of the Unit 1 Problems : 3

End of the Unit 1 Problems : 4

End of the Unit 1 Problems : 5

2 - Linear and Time Invariant Systems (LTI Systems)

2.1 Intro

2.2.1 The Representation of Discrete-Time Signals in terms of Unit Impulses

2.2.2 The Discrete Time Unit Impulse Response and Convolution-Sum Representation

2.2.2 Example - 1

2.2.2 Example - 2

2.2.2 Example - 3

3 - Fourier series and Transform

3.1 Expressing the Idea in Mathematical Terms

3.2 Finding out the coefficients a0, an and bn

3.3 Some Observations on the Result (symmetry)

3.4 Example - 1

3.4.1 Example - 2

3.5 Complex Fourier Series

3.6 Complex Fourier series - 2

3.7 Review Fourier Series

3.8 Example -3

4.1 Fourier Transform -1

4.2 Fourier Transform - 2

The Preparation you might need for Fourier series and transform

E.1 Fundamentals of Functions

E.2 Fundamentals of Complex Numbers

E.3 Orthogonal Functions

E.4 Orthogonal Functions and More Integrals

E.5 The Single Period Idea

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Signals and Sytems with these activities:

Review Complex Numbers

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Strengthen your understanding of complex numbers, which are fundamental to representing and analyzing signals in the frequency domain.

Browse courses on Complex Numbers

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Review the definition of complex numbers and their representation in rectangular and polar forms.
Practice performing basic arithmetic operations with complex numbers.
Solve problems involving Euler's formula and complex exponentials.

Review Calculus Fundamentals

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Solidify your calculus foundation, as it's essential for understanding signal transformations and system analysis.

Browse courses on Calculus

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Review differentiation and integration techniques.
Practice solving differential equations.
Work through examples of Fourier series and transforms.

Signals and Systems (2nd Edition)

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Supplement the course material with a comprehensive textbook that provides in-depth explanations and examples.

View Signals and Systems (Second Edition) on Amazon

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Read the relevant chapters corresponding to the course syllabus.
Work through the examples and practice problems in the book.
Use the book as a reference for clarifying concepts and solving problems.

Four other activities

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Solve Convolution Problems

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Master convolution, a fundamental operation in LTI systems, through repetitive problem-solving.

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Find practice problems on convolution from textbooks or online resources.
Solve a variety of convolution problems, varying the input signals and system impulse responses.
Check your solutions and identify areas where you need more practice.

Create a Signals and Systems Cheat Sheet

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Consolidate your understanding by creating a concise cheat sheet of key formulas, concepts, and properties.

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Review the course material and identify the most important formulas and concepts.
Organize the information into a clear and concise format.
Include examples and diagrams to illustrate the concepts.

Analyze a Real-World Signal

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Apply your knowledge to analyze a real-world signal, such as an audio signal or a sensor reading.

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Choose a real-world signal to analyze.
Collect data for the signal.
Apply signal processing techniques to analyze the signal's properties.
Interpret the results and draw conclusions about the signal.

Schaum's Outline of Signals and Systems

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Reinforce your understanding and problem-solving skills with a Schaum's Outline.

View Schaum's Outline of Signals and Systems, Fourth... on Amazon

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Read the relevant chapters corresponding to the course syllabus.
Work through the solved problems in the book.
Attempt the practice problems and check your solutions.

Career center

Learners who complete Signals and Sytems will develop knowledge and skills that may be useful to these careers:

Signal Processing Engineer

A Signal Processing Engineer analyzes, designs, and develops signal processing systems. This work involves manipulating signals to extract information, enhance quality, or prepare signals for transmission. A strong understanding of signal representation, signal classification (periodic/non-periodic, even/odd), and common signals is essential to this role. This course helps build a foundation in these areas, particularly with its in-depth treatment of singularity functions and properties of systems. The course's coverage of continuous time and discrete time domains directly applies to the design and implementation of signal processing algorithms and systems. Those who want to become Signal Processing Engineers may find this course especially beneficial.

See salaries and explore the career path for Signal Processing Engineer

Control Systems Engineer

A Control Systems Engineer designs and implements systems that regulate and control the behavior of other systems. This often involves feedback loops, sensors, actuators, and sophisticated algorithms. The course material relating to the properties of systems is very relevant to the work of a control systems engineer. Properties such as linearity, time invariance, causality and stability are directly applicable to designing stable and reliable control systems. A Control Systems Engineer will use the skills learned in this course to model, analyze, and optimize control systems. Aspiring Control Systems Engineers should consider this course.

See salaries and explore the career path for Control Systems Engineer

Systems Engineer

A Systems Engineer focuses on designing, integrating, and managing complex systems throughout their lifecycle. This includes understanding how different components interact and ensuring that the entire system meets specified requirements. The course's emphasis on system properties such as linearity, time invariance, causality, and stability directly relates to what a Systems Engineer does. The course provides a solid foundation for understanding and analyzing system behavior. Systems Engineers will use course topics such as signal representation to understand the inputs and outputs of components, and the classification of signals to model complex systems. Aspiring Systems Engineers may find this course particularly helpful.

See salaries and explore the career path for Systems Engineer

Telecommunications Engineer

A Telecommunications Engineer designs and maintains telecommunications systems, including networks, transmission systems, and communication protocols. Understanding signal characteristics, transmission, and manipulation is paramount. This course may be useful because it covers signal representation as mathematical functions, signal classification, and common signals, which are fundamental to telecommunications. This foundation is crucial for understanding signal behavior in communication channels. The course's exploration of continuous and discrete time signals directly relates to both analog and digital communication systems. Aspiring Telecommunications Engineers may find this course beneficial.

See salaries and explore the career path for Telecommunications Engineer

Robotics Engineer

A Robotics Engineer designs, builds, and programs robots for various applications. This field requires a strong understanding of signals and systems, as robots rely on processing sensory data and controlling actuators through complex control loops. This course may provide a strong foundation through its coverage of signal representation, common signals, and system properties. The course's exploration of continuous and discrete time signals directly applies to robotic systems that operate in real-time. A future Robotics Engineer may find this course especially helpful.

See salaries and explore the career path for Robotics Engineer

Acoustic Engineer

An Acoustic Engineer analyzes and controls sound and vibration. This profession requires a detailed understanding of signal processing techniques to measure, model, and mitigate noise. This course helps individuals better understand the mathematical representation of signals and classifying them. It also helps individuals better understand the properties of systems. All of these are crucial for analyzing and manipulating acoustic signals. An Acoustic Engineer may find this course beneficial.

See salaries and explore the career path for Acoustic Engineer

Audio Engineer

An Audio Engineer records, mixes, and masters audio for music, film, and other media. This role requires a deep understanding of signal processing techniques to enhance audio quality, remove noise, and create special effects. This course helps to understand signal representation and classification, which are crucial for analyzing and manipulating audio signals. The course's treatment of Fourier Transforms provide the math tools for working with audio in the frequency domain. This is at the heart of the audio engineer's work. Audio Engineers may find this course beneficial.

See salaries and explore the career path for Audio Engineer

Research Scientist

A Research Scientist conducts research in a specific field, often at a university or research institution. A deep understanding of signals and systems can be valuable in many scientific disciplines. This course helps in its exploration of signal representation, transformations, and system properties. These are useful for analyzing experimental data and developing new models. Those who wish to be Research Scientists should consider taking this course.

See salaries and explore the career path for Research Scientist

Biomedical Engineer

A Biomedical Engineer applies engineering principles to solve problems in medicine and biology. This role includes the design of medical devices, the development of imaging techniques, and the analysis of biological signals. This course helps Biomedical Engineers learn about signal representation and classification. It can also help them understand system properties, all applicable to processing physiological signals such as EEG and ECG data. Those interested in becoming Biomedical Engineers may find this course valuable.

See salaries and explore the career path for Biomedical Engineer

Image Processing Engineer

An Image Processing Engineer develops algorithms and systems to analyze, enhance, and manipulate digital images. This work involves techniques such as filtering, compression, and feature extraction. This course helps to understand the mathematical representation of signals, as well as how to classify them. These skills are applicable to processing image data. The course's coverage of Fourier Transforms may be useful, as this is used in image enhancement and restoration. Aspiring Image Processing Engineers may find this course beneficial.

See salaries and explore the career path for Image Processing Engineer

Data Scientist

A Data Scientist analyzes large datasets to extract meaningful insights and build predictive models. While seemingly disparate, signal processing techniques can be applied to time series data and other types of signals to identify patterns and anomalies. This course may provides a foundational understanding of signal representation, signal classification, and system properties. This knowledge can be leveraged to develop and apply signal processing techniques to data analysis problems. A Data Scientist may find this course useful.

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Machine Learning Engineer

A Machine Learning Engineer develops and implements machine learning models. This role requires a strong understanding of algorithms and data structures. Some machine learning techniques are inspired by signal processing. This course may give Machine Learning Engineers a foundational understanding of signal representation, signal classification, and system properties that they can leverage. Specifically, machine learning engineers can use the provided knowledge of Fourier Transforms to build spectrograms to generate audio data sets. A Machine Learning Engineer may benefit from this course.

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Software Engineer

A Software Engineer designs, develops, and tests software applications. This role requires a strong understanding of algorithms and data structures. Signal processing techniques are often implemented in software. This course may give Software Engineers foundational understanding of signal representation, signal classification, and system properties that they can leverage to develop software for signal processing applications. A Software Engineer looking to work in the field of signal processing may find this course beneficial.

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Aerospace Engineer

An Aerospace Engineer designs and develops aircraft, spacecraft, and related systems. This role requires a strong understanding of signals and systems for navigation, control, and communication. This course covers representation of signals, transformations, and system properties useful for analyzing and controlling the behavior of aerospace systems. An Aerospace Engineer may find this course useful.

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Financial Analyst

A Financial Analyst analyzes financial data, provides investment recommendations, and manages financial risk. Time series analysis, a form of signal processing, is used to forecast financial trends. This course may provide a high level understanding of signal representation, transformations, and system properties which can be applied to financial time series data. The financial analyst can leverage their knowledge of linear time invariant systems to understand how an investment portfolio responds to different market forces. Financial analysts looking to expand their understanding might find this course useful.

See salaries and explore the career path for Financial Analyst

Signals and Sytems

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