Chapter – 1: Signals
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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
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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
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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
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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
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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
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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
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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
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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
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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
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1.Convolution & Examples
2.Convolution Graphical procedure exponential with unit step
3.Convolution Graphical procedure two rectangular signals
4.Triangular and rectangular convolution
