Overview

Chapter - 1: Signals ==============1.Deterministic and random signals2.Analog and Digital Signals3.Unit impulse Function - Elementary Signals4.Unit step Function5.Unit Ramp and Parabolic & Singularity Functions 6. Exponential Functions - Elementary Signals7. Signum Function - Elementary Signals8. Rectangular Function - Elementary Signals9. Triangular Function - Elementary Signals10. Sinusoidal Functions - Elementary Signals11. Sinc & Sampling Functions - Elementary Signals12. Periodic & Non Periodic Signals- Classification13.Even and Odd Signals14.Causal and Non Causal Signals16.Rectangular Function E & P17.Unit step Function E & P18.Unit Ramp Function E & P19.Power of Sinusoidal Signal20.Effect of shifting and Scaling on E & P21.Observation Points on E & P22.Operations on Independent Variable of Signal23. GATE Previous Problems with Solutions Set - 1 24. GATE Previous Problems with Solutions Set - 2Chapter - 2: Systems================15. 1. Systems Classification - Linear & Nonlinear Systems16. 2. Systems Classification - Time Variant & time Invariant Systems17. 3. Static & Dynamic & Causal & Non Causal Systems18. 4. Examples19. 5. Stable & Unstable Systems20. 6. Examples21 7. Invertible & Non Invertible Systems23. 9. GATE Previous Problems with Solutions Set - 124. 10.GATE Previous Problems with Solutions Set - 225. 11.GATE Previous Problems with Solutions Set - 3 Chapter - 3: Fourier Series==================1. Fourier Series Introduction2.Orthogonality in Vectors3.Orthogonality in Signals4.Orthogonal Signal Space & Signal Approximation5.Mean Square Error and Complete Set6.Orthonormal Set7.Complete Set Example - 18.Complete Set Example - 29.Orthogonality in Complex Functions10.Full Wave Rectified signal EFS11.Dirichlet's Conditions for Fourier Series12.TFS and EFS Expansion Example13.Symmetric Conditions14.Check the Symmetry Conditions for Examples15 GATE Previous Problems with Solutions Set - 116.GATE Previous Problems with Solutions Set - 2 17.Exponentials periodic signal TFS & EFS18.Triangular Periodic Signal TFS & EFS19.Frequency SpectrumChapter - 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 Function5. 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 Transform13. Differentiation in Time property of Fourier Transform14. Integration in Time domain Property of Fourier Transform15. Differentiation in Frequency domain Property of Fourier Transform16. Conjugation Property of Fourier Transform17. 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 - 125. GATE Previous Problems with Solutions Set - 2 Chapter - 5: Laplace Transform=====================1. Laplace Transform of impulse function with ROC2. LT of unit step Function with ROC3. LT of left side unit step Function with ROC4. LT of Exponential Functions with ROC5. LT of Complex Exponentials & cos and sin Functions with ROC6. LT and ROC of both side Exponentials7. LT and ROC of damped sin Function8. LT and ROC of Damped cos Function9. LT and ROC of Hyperbolic sin and cos Functions10. Linearity Property of LT11. Time shifting Property of LT12. Frequency shifting Property of LT13. Time scaling and Time Reversal Property of LT14. Time Differentiation Property of LT15. Differentiation in S-domain Property of LT16. Conjugation property of LT17. Initial and Final value Theorems of LT18. Convolution Property of LT19. GATE Previous Problems with Solutions Set - 120. Laplace Transform Example Set - 121. Laplace Transform Example Set - 2Chapter - 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 - 3Chapter - 7: Discrete Fourier Transform==========================1. DTFT(Discrete Time Fourier Transform)2. DTFT of Impulse & Unit step Functions3. DTFT of DT Exponential Sequence4. DFT-Discrete Fourier Transform5. DFT example6. GATE Previous Problems with Solutions Set - 17. GATE Previous Problems with Solutions Set - 2Chapter - 8: Sampling Theorem=======================33. 1. Sampling Theorem Definition.34. 2. Nyquist Condition - NR Calcutions35. 3. Time Domain & Frequency Domain Analysis(spectral)36. 4. GATE Previous Problems with Solutions Set - 1Chapter - 9: Signal Transmission Through LTI System===================================1.Distortionless transmission system and frequency respons2.Impulse Response of Distortionless transmission system3.Filter Characteristics of LTI Systems4.Signal Bandwidth vs System Bandwidth.Chapter - 10: Convolution & Correlation===========================1.Convolution & Examples2.Convolution Graphical procedure exponential with unit step3.Convolution Graphical procedure two rectangular signals4.Triangular and rectangular convolution

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