Signals and Systems from Basics to Advance Level from Udemy

Chapter - 1: Signals

1.Deterministic and random signals

2.Analog and Digital Signals

3.Unit impulse Function - Elementary Signals

4.Unit step Function

5.Unit Ramp and Parabolic & Singularity Functions

6. Exponential Functions - Elementary Signals

7. Signum Function - Elementary Signals

8. Rectangular Function - Elementary Signals

9. Triangular Function - Elementary Signals

10. Sinusoidal Functions - Elementary Signals

11. Sinc & Sampling Functions - Elementary Signals

12. Periodic & Non Periodic Signals- Classification

13.Even and Odd Signals

14.Causal and Non Causal Signals

16.Rectangular Function E & P

17.Unit step Function E & P

18.Unit Ramp Function E & P

19.Power of Sinusoidal Signal

20.Effect of shifting and Scaling on E & P

21.Observation Points on E & P

22.Operations on Independent Variable of Signal

23. GATE Previous Problems with Solutions Set - 1

24. GATE Previous Problems with Solutions Set - 2

Chapter - 2: Systems

15. 1. Systems Classification - Linear & Nonlinear Systems

16. 2. Systems Classification - Time Variant & time Invariant Systems

17. 3. Static & Dynamic & Causal & Non Causal Systems

18. 4. Examples

19. 5. Stable & Unstable Systems

20. 6. Examples

21 7. Invertible & Non Invertible Systems

23. 9. GATE Previous Problems with Solutions Set - 1

24. 10.GATE Previous Problems with Solutions Set - 2

25. 11.GATE Previous Problems with Solutions Set - 3

Chapter - 3: Fourier Series

1. Fourier Series Introduction

2.Orthogonality in Vectors

3.Orthogonality in Signals

4.Orthogonal Signal Space & Signal Approximation

5.Mean Square Error and Complete Set

6.Orthonormal Set

7.Complete Set Example - 1

8.Complete Set Example - 2

9.Orthogonality in Complex Functions

10.Full Wave Rectified signal EFS

11.Dirichlet's Conditions for Fourier Series

12.TFS and EFS Expansion Example

13.Symmetric Conditions

14.Check the Symmetry Conditions for Examples

15 GATE Previous Problems with Solutions Set - 1

16.GATE Previous Problems with Solutions Set - 2

17.Exponentials periodic signal TFS & EFS

18.Triangular Periodic Signal TFS & EFS

19.Frequency Spectrum

Chapter - 4: Fourier Transform

1. Introduction to Fourier Transforms & Dirichlet s conditions

2. Fourier Transform of Unit Impulse function and One sided Exponential.

3. Fourier Transform of Two sided Exponential.

4. Fourier Transform of Signum Function

5. Fourier Transform of Unit Step function & Sinusoidal Functions.

6. Fourier Transform of Rectangular & Sinc & Fampling Functions.

7. Fourier Transform of Triangular Function.

8. Fourier Transform of Trapezoidal Signal.

9. Linearity property of Fourier Transform

10. Time scaling property of Fourier Transform

11. Time shifting property of Fourier Transform

12. Frequency shifting property of Fourier Transform

13. Differentiation in Time property of Fourier Transform

14. Integration in Time domain Property of Fourier Transform

15. Differentiation in Frequency domain Property of Fourier Transform

16. Conjugation Property of Fourier Transform

17. Duality Property of Fourier Transform

18. Modulation Property of Fourier Transform

19. Area Under time and Frequency Domain Signals.

20. Time Convolution Property of Fourier Transform

21. Frequency Convolution Property of Fourier Transform

22. Parseval's relation

23. Fourier Transform of Periodic Signal

24. GATE Previous Problems with Solutions Set - 1

25. GATE Previous Problems with Solutions Set - 2

Chapter - 5: Laplace Transform

1. Laplace Transform of impulse function with ROC

2. LT of unit step Function with ROC

3. LT of left side unit step Function with ROC

4. LT of Exponential Functions with ROC

5. LT of Complex Exponentials & cos and sin Functions with ROC

6. LT and ROC of both side Exponentials

7. LT and ROC of damped sin Function

8. LT and ROC of Damped cos Function

9. LT and ROC of Hyperbolic sin and cos Functions

10. Linearity Property of LT

11. Time shifting Property of LT

12. Frequency shifting Property of LT

13. Time scaling and Time Reversal Property of LT

14. Time Differentiation Property of LT

15. Differentiation in S-domain Property of LT

16. Conjugation property of LT

17. Initial and Final value Theorems of LT

18. Convolution Property of LT

19. GATE Previous Problems with Solutions Set - 1

20. Laplace Transform Example Set - 1

21. Laplace Transform Example Set - 2

Chapter - 6: Z-Transform

1. Z-Transform and ROC of unit impulse and step Functions

2. ZT and ROC of u(-n) and -u(-n-1)

3. ZT and ROC of exponentials a^nu(n) and -a^nu(-n-1)

4. ZT and ROC of complex exponentials and coswn.u(n)

5. ZT and ROC of sinwn.u(n)

6. ZT Properties - Linearity

7. ZT Properties - Time shifting

8. ZT properties - Multiplication with exponential

9. ZT Properties - Time Reversal

10. ZT Properties - Time Expansion

11. ZT Properties - Differentiation in Z-Domain

12. ZT Properties - Conjugation

13. ZT Properties - Convolution

14. ZT Properties - Initial value Theorem

15. ZT Properties - Final value Theorem

16. GATE Previous Problems with Solutions Set - 1

17. GATE Previous Problems with Solutions Set - 2

18. GATE Previous Problems with Solutions Set - 3

Chapter - 7: Discrete Fourier Transform

1. DTFT(Discrete Time Fourier Transform)

2. DTFT of Impulse & Unit step Functions

3. DTFT of DT Exponential Sequence

4. DFT-Discrete Fourier Transform

5. DFT example

6. GATE Previous Problems with Solutions Set - 1

7. GATE Previous Problems with Solutions Set - 2

Chapter - 8: Sampling Theorem

33. 1. Sampling Theorem Definition.

34. 2. Nyquist Condition - NR Calcutions

35. 3. Time Domain & Frequency Domain Analysis(spectral)

36. 4. GATE Previous Problems with Solutions Set - 1

Chapter - 9: Signal Transmission Through LTI System

1.Distortionless transmission system and frequency respons

2.Impulse Response of Distortionless transmission system

3.Filter Characteristics of LTI Systems

4.Signal Bandwidth vs System Bandwidth.

Chapter - 10: Convolution & Correlation

1.Convolution & Examples

2.Convolution Graphical procedure exponential with unit step

3.Convolution Graphical procedure two rectangular signals

4.Triangular and rectangular convolution

What's inside

Syllabus

Signals

Unit impulse Function - Elementary Signals

Deterministic and Random Signals

Analog and Digital Signals

Unit Ramp and Parabolic & Singularity Functions

Unit step Function

Exponential Functions - Elementary Signals

Signum Function - Elementary Signals

Rectangular Function - Elementary Signals

Triangular Function - Elementary Signals

Sinusoidal Functions - Elementary Signals

Sinc & Sampling Functions - Elementary Signals

Periodic & Non Periodic Signals- Classification

Even and Odd Signals

Causal and Non Causal Signals

Rectangular Function E & P

Unit step Function E & P

Unit Ramp Function E & P

Power of Sinusoidal Signal

Energy and Power Signals

Effect of shifting and Scaling on E & P

Observation Points on E & P

Operations on Independent Variable of Signal

GATE Previous Problems with Solutions Set - 1

GATE Previous Problems with Solutions Set - 2

IES Discussion Part - 1

IES Discussion Part - 2

IES Discussion Part - 3

IES Discussion Part - 4

IES Discussion Part - 5

Orthogonality in Complex Functions

IES Discussion Part - 6

IES Discussion Part - 7

Full Wave Rectified signal EFS

IES Discussion Part - 8

IES Discussion Part - 9

Dirichlet's Conditions for Fourier Series

IES Discussion Part - 10

IES Discussion Part - 11

TFS and EFS Expansion Example

IES Discussion Part - 12

IES Discussion Part - 13

Symmetric Conditions

IES Discussion Part - 14

IES Discussion Part - 15

Check the Symmetry Conditions for Examples

IES Discussion Part - 16

IES Discussion Part - 17

Exponentials periodic signal TFS & EFS

Systems

Systems Classification - Linear & Nonlinear Systems

Systems Classification - Time Variant & time Invariant Systems

Static & Dynamic & Causal & Non Causal Systems

Examples

Stable & Unstable Systems

Invertible & Non Invertible Systems

GATE Previous Problems with Solutions Set - 3

IES Discussion Part - 18

IES Discussion Part - 19

IES Discussion Part - 20

IES Discussion Part - 21

LIT systems with Properties - 1

LIT systems with Properties - 2

LIT systems with Properties - 3

LIT systems with Properties - 4

LIT systems with Properties - 5

LIT systems with Properties - 6

LIT systems with Properties - 7

Fourier Series

Fourier Series Introduction

Orthogonality in Vectors

Orthogonality in Signals

Orthogonal Signal Space & Signal Approximation

Mean Square Error and Complete Set

Orthonormal Set

Complete Set Example - 1

Complete Set Example - 2

Triangular Periodic Signal TFS & EFS

Frequency Spectrum

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 Systems from Basics to Advance Level with these activities:

Review Trigonometry Fundamentals

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Strengthen your understanding of trigonometric functions, which are essential for analyzing sinusoidal signals and Fourier transforms.

Browse courses on Trigonometry

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Review trigonometric identities and formulas.
Practice solving problems involving sine, cosine, and tangent.
Understand the unit circle and its relationship to trigonometric functions.

Signals and Systems

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Deepen your understanding of signals and systems concepts with a comprehensive textbook.

View Signals and Systems (Second Edition) on Amazon

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Read the chapters related to the course syllabus.
Work through the example problems in the book.
Attempt the end-of-chapter exercises to test your understanding.

Solve Problems on Fourier Transform Properties

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Reinforce your understanding of Fourier Transform properties by solving a variety of problems.

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Find practice problems related to linearity, time shifting, and scaling.
Work through problems involving convolution and duality.
Check your solutions against provided answers or online resources.

Four other activities

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Create a Cheat Sheet for Transform Properties

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Improve retention by compiling a cheat sheet summarizing the key properties of Fourier, Laplace, and Z-transforms.

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Review the properties of each transform (Fourier, Laplace, Z).
Organize the properties into a concise and easy-to-read format.
Include examples of how to apply each property.
Use the cheat sheet as a quick reference during problem-solving.

Linear Systems and Signals

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Supplement your learning with a textbook that provides a clear introduction to linear systems and signals.

View Signal Processing and Linear Systems (The... on Amazon

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Read the chapters relevant to the course topics.
Solve the practice problems provided in the book.
Use the book as a reference for understanding key concepts.

Create a Visual Guide to Laplace Transforms

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Solidify your knowledge of Laplace Transforms by creating a visual guide that explains key concepts and properties.

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Summarize the definition and properties of Laplace Transforms.
Create diagrams illustrating the region of convergence (ROC).
Provide examples of common Laplace Transform pairs.
Share your guide with peers for feedback.

Implement a Signal Processing Algorithm

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Apply your knowledge of signals and systems by implementing a signal processing algorithm in software.

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Choose a signal processing algorithm (e.g., filtering, noise reduction).
Implement the algorithm in a programming language (e.g., Python, MATLAB).
Test the algorithm with real-world signals.
Analyze the performance of the algorithm.

Career center

Learners who complete Signals and Systems from Basics to Advance Level 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 includes areas like audio processing, image processing, and communications. This course, "Signals and Systems from Basics to Advance Level", is highly relevant to this role as it covers fundamental concepts such as signal classification, Fourier series, Fourier transforms, Laplace transforms, and Z transforms. Understanding the properties of signals, systems, and their transformations can give you a competitive advantage as a signal processing engineer. Specifically, the course's coverage of topics like the Discrete Fourier Transform and Sampling Theorem will be directly applicable to many real-world signal processing challenges.

See salaries and explore the career path for Signal Processing Engineer

Control Systems Engineer

A control systems engineer designs and implements systems to control dynamic processes. They work in industries like aerospace, robotics, and manufacturing. For a role as control systems engineer, the course "Signals and Systems from Basics to Advance Level" is a perfect launchpad. The course content provides a strong understanding of system characteristics, stability analysis, and signal transformations. The sections on Laplace transforms and Z transforms are particularly relevant, as these form the mathematical bedrock for analyzing and designing control systems. A firm grasp of these concepts can help you excel in the practical application of control theory.

See salaries and explore the career path for Control Systems Engineer

Radar Systems Engineer

A radar systems engineer designs, develops, and tests radar systems for various applications, such as air traffic control, weather forecasting, and military surveillance. The course "Signals and Systems from Basics to Advance Level" is highly relevant, as radar systems rely heavily on signal processing techniques. Understanding signal modulation, demodulation, filtering, and detection is crucial for radar system design. The course's syllabus has numerous relevant topics. This will help prepare one to specialize in radar.

See salaries and explore the career path for Radar Systems Engineer

Telecommunications Engineer

A telecommunications engineer designs and maintains telecommunications infrastructure. This can include designing networks, developing modulation techniques, and ensuring signal integrity. The course "Signals and Systems from Basics to Advance Level" builds a solid foundation for a career as a telecommunications engineer. The course covers essential topics such as signal transmission through linear time-invariant systems, Fourier transforms, and sampling theory. For instance, the course's treatment of signal bandwidth and system bandwidth is particularly relevant. Understanding these topics can help you to design efficient and reliable communication systems.

See salaries and explore the career path for Telecommunications Engineer

Image Processing Specialist

An image processing specialist develops algorithms and systems to analyze, enhance, and manipulate digital images. They may work in fields like medical imaging, computer vision, or satellite imaging. The course "Signals and Systems from Basics to Advance Level" covers fundamental concepts applicable to image processing. Understanding Fourier transforms, signal transformations, and system properties helps with designing image processing algorithms. In particular, the course's coverage of two-dimensional signal processing concepts related to Fourier transforms, along with convolution, can directly help image processing.

See salaries and explore the career path for Image Processing Specialist

Audio Engineer

An audio engineer records, mixes, and masters audio for music, film, and other media. They often need a deep understanding of signal processing techniques. The course "Signals and Systems from Basics to Advance Level" gives you a background in the mathematics of audio signals. It also helps with understanding concepts such as Fourier analysis and filtering. Learning about topics such as the Discrete Fourier Transform and signal transmission through linear time-invariant systems can help you to manipulate and improve audio signals.

See salaries and explore the career path for Audio Engineer

Robotics Engineer

A robotics engineer designs, builds, and programs robots for a variety of applications. The principles of signals and systems are crucial for developing robot control systems, sensor data processing, and communication systems. "Signals and Systems from Basics to Advance Level" helps in this field. The course's coverage of linear time-invariant systems, Laplace transforms, and Z transforms provides the mathematical tools to design stable and responsive robot control algorithms. Understanding signal characteristics and system responses can help with robot design.

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Data Scientist

A data scientist analyzes large datasets to extract insights and build predictive models. While seemingly unrelated, the signal processing techniques taught in "Signals and Systems from Basics to Advance Level" can be surprisingly useful in data science, especially when dealing with time-series data or sensor data. The course provides a strong foundation in signal transformations, frequency analysis, and system modeling. For example, the Fourier transform concepts covered in the course can be applied to feature extraction and anomaly detection in time-series data. This course may help with the mathematical side of data science.

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Embedded Systems Engineer

An embedded systems engineer designs and develops software and hardware for embedded systems. These are specialized computer systems often found in devices like appliances, automobiles, and industrial equipment. The content from "Signals and Systems from Basics to Advance Level" may provide a foundation for understanding the signal processing aspects of embedded systems, particularly in areas like sensor interfacing and data acquisition. The course's exploration of Z transforms and discrete-time systems is especially relevant, as these are commonly used in embedded system design. Developing an understanding of this is a great introduction into this career.

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Geophysicist

A geophysicist studies the Earth's physical properties using techniques such as seismic surveys, gravity measurements, and electromagnetic methods. The course "Signals and Systems from Basics to Advance Level" provides valuable tools for analyzing geophysical data. The signal processing techniques covered in the course, such as Fourier analysis and filtering, can be applied to process seismic signals, gravity data, and electromagnetic measurements to extract information about the Earth's subsurface structure. It can provide the foundational signal knowledge that a geophysicist requires.

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Biomedical Engineer

A biomedical engineer applies engineering principles to solve problems in medicine and biology. This includes designing medical devices, developing imaging techniques, and analyzing biological signals. "Signals and Systems from Basics to Advance Level" may be helpful for analyzing and processing physiological signals, such as electrocardiograms (ECG) or electroencephalograms (EEG). The course's coverage of Fourier analysis, filtering, and signal transformations can provide insights into the characteristics of these signals and help in developing algorithms for their analysis. This may be a good introduction to biomedical enineering signals and systems work.

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Acoustic Engineer

An acoustic engineer deals with the science and technology of sound and vibration. They might design concert halls, develop noise control solutions, or work on audio equipment. The course "Signals and Systems from Basics to Advance Level" may provide a foundation for understanding the behavior of sound waves and designing acoustic systems. The course's coverage of Fourier analysis and signal transformations, along with signal classification, can be helpful for analyzing and manipulating audio signals. While further study on acoustics is needed, this may be a good place to start.

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Seismologist

A seismologist studies earthquakes and seismic waves to understand the Earth's structure and predict seismic events. "Signals and Systems from Basics to Advance Level" is a launchpad for working with signals from the earth. The course's coverage of signal processing techniques, such as Fourier analysis and filtering, can be applied to analyze seismic waves and extract information about the location, magnitude, and characteristics of earthquakes. This provides the foundation to understand the signals.

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Financial Analyst

A financial analyst analyzes financial data, provides investment recommendations, and helps organizations make sound financial decisions. While "Signals and Systems from Basics to Advance Level" may seem far removed from finance, the underlying mathematical concepts related to time series analysis and signal processing can be valuable. The course may provide a new perspective for analyzing financial data, identifying patterns, and building predictive models, particularly when dealing with high-frequency trading data or other time-dependent financial variables. Learning about signals may encourage an interdisciplinary approach.

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Meteorologist

A meteorologist studies the atmosphere and weather patterns to forecast weather conditions. While seemingly unrelated, the signal processing techniques covered in "Signals and Systems from Basics to Advance Level" may provide insights into analyzing weather data, which often involves time-series analysis and spatial data processing. The course's coverage of Fourier transforms and signal transformations could be relevant for analyzing weather patterns and identifying trends. The course may introduce ways to analyze complex data.

See salaries and explore the career path for Meteorologist

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Signals and Systems from Basics to Advance Level.

Signals and Systems (Second Edition)

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Comprehensive resource for understanding signals and systems. It covers a wide range of topics, including Fourier analysis, Laplace transforms, and Z-transforms. It is commonly used as a textbook in undergraduate and graduate courses. This book provides additional depth and breadth to the existing course.

Signals and Systems (Second Edition)

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Signals and Systems (Second Edition)

Kindle Edition

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Signal Processing and Linear Systems

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Provides a clear and accessible introduction to linear systems and signals. It covers the fundamentals of signal processing, including Fourier analysis, Laplace transforms, and Z-transforms. It useful reference tool for students and professionals. This book is helpful in providing background and prerequisite knowledge.

Signal Processing and Linear Systems (The Oxford...

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Signals and Systems from Basics to Advance Level

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