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Time−Invariant & Time−Variant Discrete Time Systems
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Signals and Systems
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- 1 Introduction to Signals and Systems
- 2 Continuous and Discrete Time Signals
- 3 Addition of Continuous-Time Signals
- 4 Multiplication of Continuous-Time Signals
- 5 Time Scaling of Continuous-Time Signals
- 6 Amplitude Scaling of Continuous-Time Signals
- 7 Time Shifting of Continuous-Time Signals
- 8 Amplitude Shifting of Continuous-Time Signals
- 9 Reversal of Continuous-Time Signals
- 10 Multiple Transformations of Continuous-Time Signals
- 11 Multiple Transformations of CTS (Important Point & Shortcut)
- 12 Multiple Transformations of CTS (Solved Problem 1)
- 13 Multiple Transformations of CTS (Solved Problem 2)
- 14 Even and Odd Signals
- 15 Even and Odd Components of a Signal
- 16 Properties of Even and Odd Signals
- 17 Even and Odd Signals (Solved Problem 1)
- 18 Even and Odd Signals (Solved Problem 2)
- 19 Even and Odd Signals (Solved Problem 3)
- 20 Even and Odd Signals (Solved Problem 4)
- 21 Periodic and Non-Periodic Signals
- 22 Periodic and Non-Periodic Signals (Important Point)
- 23 Calculation of Fundamental Period
- 24 Periodic and Non-Periodic Signals (Solved Problems)
- 25 Effect of Time-Shifting & Time-Scaling on Fundamental Time Period
- 26 Effect of Time-Reversal and Phase Shift on Fundamental Time Period
- 27 Effect of Amplitude-Shifting on Fundamental Time Period
- 28 Effect of Amplitude-Scaling on Fundamental Time Period
- 29 Effect of Amplitude Reversal on Fundamental Time Period
- 30 Conjugate Symmetric Signals
- 31 Conjugate Antisymmetric Signals
- 32 Half-Wave Symmetric Signals
- 33 Half Wave Symmetric Signals (Solved Problems)
- 34 Area of Continuous-Time Signals
- 35 Average Value of Continuous-Time Signals
- 36 Average Value of Continuous-Time Signals (Solved Problems) | Part 1
- 37 Average Value of Continuous-Time Signals (Solved Problems) | Part 2
- 38 Average Value of Continuous Time Signals (Solved Problems) | Part 3
- 39 Energy and Power of Continuous Time Signals
- 40 Energy Signals
- 41 Energy of CT Signals (Solved Problems) | Part 1
- 42 Energy of CT Signals (Solved Problems) | Part 2
- 43 Energy of CT Signals (Solved Problems) | Part 3
- 44 Power Signals
- 45 Power of CT Signals (Solved Problems) | Part 1
- 46 Power of CT Signals (Solved Problems) | Part 2
- 47 Power of CT Signals (Solved Problems) | Part 3
- 48 Power, RMS & Average Values of Standard Signals
- 49 Neither Energy Nor Power (NENP) Signals
- 50 Shortcut for Energy, Power & NENP Signals
- 51 Energy, Power & NENP Signals (Solved Problem 1)
- 52 Energy, Power & NENP Signals (Solved Problem 2)
- 53 Energy, Power & NENP Signals (Solved Problem 3)
- 54 Energy and Power of Discrete-Time Signals
- 55 Orthogonal Signals
- 56 Orthogonal Signals (Solved Problems 1)
- 57 Orthogonal Signals (Solved Problems 2)
- 58 Orthogonal Signals (Solved Problems 3)
- 59 Unit Impulse Signal
- 60 Properties of Impulse Signal (Part 1)
- 61 Properties of Impulse Signal (Part 2)
- 62 Impulse Signal (Solved Problems) | Part 1
- 63 Impulse Signal (Solved Problems) | Part 2
- 64 Unit Step Signal
- 65 Unit Ramp Signal
- 66 Unit Parabolic Signal
- 67 Relation between Unit Impulse and Unit Step Signals
- 68 Signum Function
- 69 Unit Rectangular Function
- 70 Unit Triangular Function
- 71 Sinc Function
- 72 Sampling Property of Unit Impulse Signal
- 73 Exponential Signals (Real and Complex)
- 74 Mathematical Representation of Signal Waveforms (Shortcut)
- 75 Mathematical Representation of Signal Waveforms (Solved Problems)
- 76 Differentiation of Continuous-Time Signals
- 77 Differentiation of Continuous Time Signals (Solved Problems)
- 78 Integration of Continuous-Time Signals
- 79 Integration of Continuous-Time Signals (Solved Problem)
- 80 Graphical Integration - Examples (Part 1)
- 81 Graphical Integration - Examples (Part 2)
- 82 Basic System Properties
- 83 Static and Dynamic Systems
- 84 Static and Dynamic Systems (Solved Problems) | Part 1
- 85 Static and Dynamic Systems (Solved Problems) | Part 2
- 86 Causal and Non-Causal Systems
- 87 Causal and Non-Causal Systems (Solved Problems) | Part 1
- 88 Causal and Non-Causal Systems (Solved Problems) | Part 2
- 89 Time-Invariant and Time-Variant Systems
- 90 Time-Invariant and Time-Variant Systems (Solved Problems) | Part 1
- 91 Time-Invariant and Time-Variant Systems (Solved Problems) | Part 2
- 92 Time-Invariant and Time-Variant Systems (Split System)
- 93 Linear and Non-Linear Systems
- 94 Linear and Non-Linear Systems (Solved Problems) | Part 1
- 95 Linear and Non-Linear Systems (Solved Problems) | Part 2
- 96 Linear and Non-Linear Systems (Solved Problems) | Part 3
- 97 Linear and Non-Linear Systems (Solved Problems) | Part 4
- 98 Linear and Non-Linear Systems (Integral & Differential Operators)
- 99 Linear and Non-Linear Systems (Even & Odd Operators)
- 100 Linear and Non-Linear Systems (Real & Imaginary Operators)
- 101 Linear and Non-Linear Systems (Various Nonlinear Operators)
- 102 Linear and Non-Linear Systems (All Properties)
- 103 Checking System Linearity using Transfer Characteristics
- 104 Invertible and Non-Invertible Systems
- 105 Invertible and Non-Invertible Systems (Solved Problems)
- 106 Stable and Unstable Systems
- 107 Stable and Unstable Systems (Solved Problems) | Part 1
- 108 Stable and Unstable Systems (Solved Problems) | Part 2
- 109 Prerequisites for LTI Systems (Revision of Linearity & Time Variance)
- 110 Prerequisites for LTI Systems (Laplace Transform)
- 111 Linear Time-Invariant (LTI) Systems
- 112 Transfer Function
- 113 Transfer Function Calculation
- 114 Impulse Response and Convolution
- 115 Introduction to Convolution Operation
- 116 Properties of Convolution (Part 1)
- 117 Properties of Convolution (Part 2)
- 118 Properties of Convolution (Part 3)
- 119 Properties of Convolution (Part 4)
- 120 Convolution Operation (Shortcut)
- 121 Convolution (Solved Problem 1)
- 122 Convolution (Solved Problem 2)
- 123 Convolution (Solved Problem 3)
- 124 Convolution (Solved Problem 4)
- 125 Convolution (Solved Problem 5)
- 126 Convolution (Solved Problem 6)
- 127 Static LTI System
- 128 Static LTI System (Solved Problems)
- 129 Causal LTI System
- 130 Causal LTI System (Solved Problems)
- 131 Stable LTI System
- 132 Stable LTI System (Solved Problems) | Part 1
- 133 Stable LTI System (Solved Problems) | Part 2
- 134 Harmonics and LTI System
- 135 Magnitude Distortion in LTI Systems
- 136 Phase Distortion in LTI Systems
- 137 Distortionless LTI System
- 138 Group Delay and Phase Delay
- 139 Group Delay & Phase Delay (Solved Problems)
- 140 Standard Differential Equation for LTI Systems
- 141 Introduction to Fourier Series
- 142 Conditions for Existence of Fourier Series (Dirichlet Conditions)
- 143 Trigonometric Fourier Series
- 144 Trigonometric Fourier Series (Example 1)
- 145 Trigonometric Fourier Series (Example 2)
- 146 Trigonometric Fourier Series (Example 3)
- 147 Trigonometric Fourier Series (Example 4)
- 148 Trigonometric Fourier Series (Example 5)
- 149 Complex Exponential Fourier Series
- 150 Complex Exponential Fourier Series (Example 1)
- 151 Complex Exponential Fourier Series (Example 2)
- 152 Complex Exponential Fourier Series (Example 3)
- 153 Complex Exponential Fourier Series (Example 4)
- 154 Complex Exponential Fourier Series (Example 5)
- 155 Relation between Fourier Coefficients
- 156 Relation between Fourier Coefficients (Solved Problem)
- 157 x(t)−Cn Pairs (Shortcut for Objectives)
- 158 Complex Exponential Fourier Series (Solved MCQ 1)
- 159 Complex Exponential Fourier Series (Solved MCQ 2)
- 160 Complex Exponential Fourier Series (Solved MCQ 3)
- 161 Symmetricities in Fourier Series (Part 1)
- 162 Symmetricities in Fourier Series (Part 2)
- 163 Hidden Symmetry in Fourier Series (Examples)
- 164 Properties of Fourier Series (Part 1)
- 165 Properties of Fourier Series (Part 2)
- 166 Properties of Fourier Series (Part 3)
- 167 Properties of Fourier Series (Part 4)
- 168 Properties of Fourier Series (Part 5)
- 169 Properties of Fourier Series (Part 6)
- 170 Parseval's Power Theorem
- 171 Parseval's Power Theorem (Solved Example)
- 172 Properties of Fourier Series (Solved Problems)
- 173 Fourier Series for LTI Systems
- 174 Introduction to Fourier Transform
- 175 Conditions for Existence of Fourier Transform (Dirichlet Conditions)
- 176 Properties of Fourier Transform (Part 1)
- 177 Properties of Fourier Transform (Part 2)
- 178 Properties of Fourier Transform (Part 3)
- 179 Properties of Fourier Transform (Part 4)
- 180 Properties of Fourier Transform (Part 5)
- 181 Properties of Fourier Transform (Part 6)
- 182 Properties of Fourier Transform (Part 7)
- 183 Properties of Fourier Transform (Part 8)
- 184 Parseval's Energy Theorem
- 185 Duality Property of Fourier Transform
- 186 Fourier Transform of Basic Signals (DC Value)
- 187 Fourier Transform of Basic Signals (Impulse Signal)
- 188 Fourier Transform of Basic Signals (Exponential Signals)
- 189 Fourier Transform of Basic Signals (Signum Function)
- 190 Fourier Transform of Basic Signals (Unit Step Signal)
- 191 Fourier Transform of sgn(t) & u(t) [Important Shortcut]
- 192 Fourier Transform of Basic Signals (Complex Exponential Signal)
- 193 Fourier Transform of Basic Signals (Cosω₀t)
- 194 Fourier Transform of Basic Signals (Sinω₀t)
- 195 Fourier Transform of Basic Signals (Rectangular Function)
- 196 Fourier Transform of Basic Signals (Triangular Function)
- 197 Fourier Transform of Basic Signals (Sampling Function)
- 198 Fourier Transform (Solved Problem 1)
- 199 Fourier Transform (Solved Problem 2)
- 200 Fourier Transform (Solved Problem 3)
- 201 Fourier Transform (Solved Problem 4)
- 202 Fourier Transform (Solved Problem 5)
- 203 Fourier Transform (Solved Problem 6)
- 204 Fourier Transform (Solved Problem 7)
- 205 Fourier Transform (Solved Problem 8)
- 206 Fourier Transform (Solved Problem 9)
- 207 Fourier Transform (Solved Problem 10)
- 208 Calculation of Cn using Fourier Transform
- 209 Fourier Transform for Periodic Signals
- 210 Fourier Transform (Solved Problem 11)
- 211 x(t)−X(ω) Pairs (Shortcut for Objectives)
- 212 Fourier Transform (Solved Problem 12)
- 213 Fourier Transform (Solved Problem 13)
- 214 Fourier Transform (Solved Problem 14)
- 215 Fourier Transform (Solved Problem 15)
- 216 Fourier Transform (Solved Problem 16)
- 217 Fourier Transform (Solved Problem 17)
- 218 Fourier Transform (Solved Problem 18)
- 219 Fourier Transform (Solved Problem 19)
- 220 Fourier Transform (Solved Problem 20)
- 221 Fourier Transform (Solved Problem 21)
- 222 Fourier Transform (Solved Problems 22 & 23)
- 223 Introduction to Laplace Transform
- 224 Relation between Laplace Transform & Fourier Transform
- 225 Condition for Existence of Laplace Transform
- 226 ROC and its Properties
- 227 ROC and Stability
- 228 Shortcut for Region of Convergence (ROC)
- 229 Properties of Laplace Transform (Part 1)
- 230 Properties of Laplace Transform (Part 2)
- 231 Properties of Laplace Transform (Part 3)
- 232 Properties of Laplace Transform (Part 4)
- 233 Properties of Laplace Transform (Part 5)
- 234 Properties of Laplace Transform (Part 6)
- 235 Initial Value Theorem
- 236 Final Value Theorem
- 237 Laplace Transform of Basic Signals (Unit Impulse Signal)
- 238 Laplace Transform of Basic Signals (Unit Step Signal)
- 239 Laplace Transform of Basic Signals (DC Value & Signum Function)
- 240 Laplace Transform of Basic Signals (Exponential Signals)
- 241 Laplace Transform of Basic Signals (Unit Ramp Signal)
- 242 Laplace Transform of Basic Signals [Cosω₀t.u(t)]
- 243 Laplace Transform of Basic Signals [Sinω₀t.u(t)]
- 244 Laplace Transform (Solved Problem 1)
- 245 Laplace Transform (Solved Problem 2)
- 246 Laplace Transform (Solved Problem 3)
- 247 Laplace Transform (Solved Problem 4)
- 248 Laplace Transform (Solved Problem 5)
- 249 Laplace Transform (Solved Problem 6)
- 250 Laplace Transform (Solved Problem 7)
- 251 Laplace Transform (Solved Problems 8 & 9)
- 252 Laplace Transform (Solved Problem 10)
- 253 Laplace Transform (Solved Problem 11)
- 254 Inverse Laplace Transform
- 255 Inverse Laplace Transform (Solved Problem)
- 256 ROC and Stability of Causal LTI Systems
- 257 Laplace Transform to Solve Differential Equations
- 258 Laplace Transform (Solved Problem 12)
- 259 Laplace Transform (Solved Problem 13)
- 260 Laplace Transform (Solved Problem 14)
- 261 Sampling Theorem
- 262 Nyquist Rate & Nyquist Interval
- 263 Properties of Nyquist Rate
- 264 Nyquist Rate (Solved Problem 1)
- 265 Nyquist Rate (Solved Problem 2)
- 266 Nyquist Rate (Solved Problem 3)
- 267 Reconstruction of Signals
- 268 Reconstruction of a Signal Using Practical LPF
- 269 Frequency Components Present in S(f)
- 270 Reconstruction of Signals (Solved Problem 2)
- 271 Reconstruction of Signals (Solved Problem 3)
- 272 Sampling Theorem for Band Pass Signals
- 273 Operations on Discrete Time Signals (Time Shifting)
- 274 Operations on DTS (Time Compression, Time Expansion & Time Reversal)
- 275 Operations on DTS (Amplitude Scaling & Amplitude Reversal)
- 276 Addition of Discrete Time Signals
- 277 Multiplication of Discrete Time Signals
- 278 Multiple Operations on Discrete Time Signals (Part 1)
- 279 Multiple Operations on Discrete Time Signals (Part 2)
- 280 Even and Odd Discrete Time Signals
- 281 Even and Odd Parts of Discrete Time Signal
- 282 Conjugate Symmetric and Conjugate Antisymmetric DTS
- 283 Periodic Discrete Time Signals
- 284 Periodic Discrete Time Signals (Solved Problems)
- 285 Discrete Time Energy Signals
- 286 Discrete Time Energy Signals (Solved Problems)
- 287 Discrete Time Power Signals
- 288 Discrete Time Power Signals (Solved Problems)
- 289 Unit Impulse Sequence
- 290 Unit Step & Unit Ramp Sequences
- 291 Discrete Time Signum Function
- 292 Discrete Time Convolution
- 293 Discrete Time Convolution (Tabular Method)
- 294 Static & Dynamic Discrete Time Systems
- 295 Causal and Non-Causal Discrete Time Systems
- 296 Time−Invariant & Time−Variant Discrete Time Systems
- 297 Linear and Non−Linear Discrete Time Systems
- 298 Stable & Unstable Discrete Time Systems
- 299 Discrete Time Signals & Systems (Solved Problem 1)
- 300 Discrete Time Signals & Systems (Solved Problem 2)
- 301 Discrete Time Signals & Systems (Solved Problem 3)
- 302 Discrete Time Signals & Systems (Solved Problem 4)
- 303 Discrete Time Signals & Systems (Solved Problem 5)
- 304 Discrete Time Signals & Systems (Solved Problem 6)
- 305 Introduction to Z-Transform
- 306 Condition for Existence of Z-Transform
- 307 Properties of Z-Transform (Part 1)
- 308 Properties of Z-Transform (Part 2)
- 309 Properties of Z-Transform (Part 3)
- 310 Properties of Z-Transform (Part 4)
- 311 Properties of Z-Transform (Part 5)
- 312 Properties of Z-Transform (Initial Value Theorem)
- 313 Properties of Z-Transform (Final Value Theorem)