Learn signals and systems: LTI, convolution, Fourier/Laplace and quizzes
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144
Sub Topics
205
MCQs
95
MCOs
154
True/False
95
Fill Blanks
27
Rearrange
85
Matching
39
Comprehensions
80
Flashcard Decks
Curriculum
What You'll Learn
01 Introduction to Signals and Systems 3 topics
1 Basic Concepts and Definitions
- Signals: Definition and Classification
- Systems: Definition and Properties
- Signal Operations and Transformations
2 Signal Models and Classifications
- Continuous-Time vs. Discrete-Time Signals
- Periodic vs. Aperiodic Signals
- Energy vs. Power Signals
- Deterministic vs. Random Signals
3 Elementary Signals
- Unit Step Function
- Unit Impulse Function
- Exponential and Sinusoidal Signals
- Complex Exponentials
02 Linear Time-Invariant Systems 3 topics
1 System Properties
- Linearity
- Time Invariance
- Causality
- Stability
- Memory
2 Impulse Response and Convolution
- Impulse Response for Continuous-Time Systems
- Impulse Response for Discrete-Time Systems
- Convolution Integral (Continuous-Time)
- Convolution Sum (Discrete-Time)
- Properties of Convolution
3 Differential and Difference Equations
- Representation of Continuous-Time Systems
- Representation of Discrete-Time Systems
- Solution Methods
03 Fourier Series Analysis 3 topics
1 Continuous-Time Fourier Series
- Trigonometric Form
- Exponential Form
- Convergence Properties
- Fourier Series Coefficients
2 Properties of Continuous-Time Fourier Series
- Linearity
- Time Shifting
- Time Scaling
- Modulation
- Differentiation and Integration
3 Discrete-Time Fourier Series
- Definition and Properties
- Relationship with Continuous-Time Fourier Series
04 Fourier Transform 3 topics
1 Continuous-Time Fourier Transform
- Definition and Existence Conditions
- Common Transform Pairs
- Spectrum Representation
2 Properties of Continuous-Time Fourier Transform
- Linearity
- Time Shifting and Frequency Shifting
- Time Scaling
- Duality
- Convolution and Multiplication
- Differentiation and Integration
- Parseval's Theorem
3 Discrete-Time Fourier Transform
- Definition and Properties
- Relationship with Continuous-Time Fourier Transform
- Periodicity of DTFT
05 Sampling Theory 3 topics
1 Sampling of Continuous-Time Signals
- Ideal Sampling
- Nyquist-Shannon Sampling Theorem
- Aliasing
- Reconstruction of Continuous-Time Signals
2 Practical Sampling Considerations
- Anti-Aliasing Filters
- Quantization
- Sample-and-Hold Circuits
3 Discrete-Time Processing of Continuous-Time Signals
- Digital-to-Analog Conversion
- Analog-to-Digital Conversion
06 Laplace Transform 4 topics
1 Definition and Region of Convergence
- Unilateral Laplace Transform
- Bilateral Laplace Transform
- Region of Convergence (ROC)
2 Properties of the Laplace Transform
- Linearity
- Time Shifting
- Frequency Shifting
- Scaling
- Differentiation and Integration
- Convolution
- Initial and Final Value Theorems
3 Inverse Laplace Transform
- Partial Fraction Expansion
- Complex Integration
4 System Analysis Using Laplace Transform
- Transfer Functions
- Stability Analysis
- Transient Response Analysis
- Steady-State Response Analysis
07 Z-Transform 4 topics
1 Definition and Region of Convergence
- Unilateral Z-Transform
- Bilateral Z-Transform
- Region of Convergence (ROC)
2 Properties of the Z-Transform
- Linearity
- Time Shifting
- Scaling in Z-domain
- Differentiation in Z-domain
- Convolution
- Initial and Final Value Theorems
3 Inverse Z-Transform
- Partial Fraction Expansion
- Power Series Expansion
- Contour Integration
4 System Analysis Using Z-Transform
- Transfer Functions
- Stability Analysis
- Transient Response Analysis
- Steady-State Response Analysis
08 Discrete Fourier Transform 3 topics
1 Definition and Properties
- DFT Pair
- Relationship with DTFT
- Periodicity and Symmetry Properties
2 Fast Fourier Transform (FFT)
- Decimation in Time (DIT)
- Decimation in Frequency (DIF)
- Computational Efficiency
3 Applications of DFT
- Linear Filtering
- Spectral Analysis
- Correlation and Convolution
09 State-Space Analysis 3 topics
1 State-Space Representation
- Continuous-Time State Equations
- Discrete-Time State Equations
- State Transition Matrix
2 Solution of State Equations
- Continuous-Time Solution Methods
- Discrete-Time Solution Methods
3 System Properties in State-Space
- Controllability
- Observability
- Stability Analysis
10 Filter Design and Analysis 4 topics
1 Filter Classifications
- Lowpass, Highpass, Bandpass, Bandstop
- FIR vs. IIR Filters
- Linear Phase Filters
2 Analog Filter Design
- Butterworth Filters
- Chebyshev Filters
- Elliptic Filters
- Bessel Filters
3 Digital Filter Design
- FIR Filter Design Methods
- IIR Filter Design Methods
4 Filter Implementation Structures
- Direct Form
- Cascade Form
- Parallel Form
- Lattice Form
11 Random Signals and Noise 4 topics
1 Probability and Random Variables
- Probability Density Functions
- Cumulative Distribution Functions
- Statistical Averages
2 Random Processes
- Stationary Processes
- Ergodic Processes
- Autocorrelation Functions
- Cross-correlation Functions
3 Power Spectral Density
- Definition and Properties
- Relationship with Autocorrelation
- Wiener-Khinchin Theorem
4 Response of Linear Systems to Random Inputs
- Mean and Correlation Function of System Output
- Power Spectral Density of System Output
- Signal-to-Noise Ratio Analysis
12 Applications of Signal Processing 4 topics
1 Communications Systems
- Modulation and Demodulation
- Multiplexing Techniques
- Digital Communications
2 Control Systems
- Feedback Control
- Stability Analysis
- PID Controllers
3 Image and Audio Processing
- Two-Dimensional Signals and Systems
- Image Enhancement and Restoration
- Audio Signal Processing
4 Biomedical Applications
- ECG Signal Processing
- EEG Signal Analysis
- Medical Imaging
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