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