Schaum's Outline of Theory and Problems of Signals and Systems

This powerful study guide gives you 571 problems in signals and systems, fully solved step-by-step! From SchaumOs, the original study guide, and studentsO favorite with over 30 million guides soldNthis solution-packed timesaver helps you master every type of problem you will face on your tests, from simple questions on linear time-invariant systems to complex Fourier analysis of discrete-time systems and state space analysis. Go directly to the answers you need with a complete index. Compatible with any classroom text, SchaumOs Outline of Signals and Systems is so complete itOs the perfect tool for graduate or professional exam prep! Cover......Page 1 Preface......Page 6 Contents......Page 8 1.2 Discrete-Time Signals......Page 11 1.2.2 Some Fundamental Sequences......Page 12 1.2.4 Periodic & Aperiodic Sequences......Page 13 1.2.6 Signal Manipulations......Page 14 Transformations of Independent Variable......Page 15 1.2.7 Signal Decomposition......Page 16 Memoryless System......Page 17 Linear Systems......Page 18 Shift-Invariance......Page 19 Stability......Page 20 Associative Property......Page 21 Direct Evaluation......Page 22 Graphical Approach......Page 23 1.5 Difference Equations......Page 25 1.2 Discrete-Time Signals......Page 28 1.3 Discrete-Time Systems......Page 35 1.4 Convolution......Page 45 1.5 Difference Equations......Page 53 1.2 Discrete-Time Signals......Page 58 1.3 Discrete-Time Systems......Page 59 1.4 Convolution......Page 60 Answers to Supplementary Problems......Page 62 2.2 Frequency Response......Page 65 Symmetry......Page 67 Linear Phase......Page 68 2.4 Interconnection of Systems......Page 69 2.5 Discrete-Time Fourier Transform......Page 71 Periodicity......Page 72 Time-Reversal......Page 73 2.7.1 LSI Systems & LCCDEs......Page 74 2.7.2 Performing Convolutions......Page 75 2.7.4 Inverse Systems......Page 76 2.2 Frequency Response......Page 77 2.3 Filters......Page 80 2.4 Interconnection of Systems......Page 84 2.5 Discrete-Time Fourier Transform......Page 87 2.6 DTFT Properties......Page 97 2.7 Applications......Page 102 2.3 Filters......Page 106 2.5 Discrete-Time Fourier Transform......Page 107 2.6 DTFT Properties......Page 108 Answers to Supplementary Problems......Page 109 3.2.1 Periodic Sampling......Page 111 3.2.2 Quantization & Encoding......Page 114 3.3 Digital-to-Analog Conversion......Page 116 3.4 Discrete-Time Processing of Analog Signals......Page 118 3.5.1 Sample Rate Reduction by Integer Factor......Page 120 3.5.2 Sample Rate Increase by Integer Factor......Page 121 3.5.3 Sample Rate Conversion by Rational Factor......Page 123 3.2 & 3.3 A/D & D/A Conversion......Page 124 3.4 Discrete-Time Processing of Analog Signals......Page 134 3.5 Sample Rate Conversion......Page 142 3.2 & 3.3 A/D & D/A Conversion......Page 148 3.5 Sample Rate Conversion......Page 149 Answers to Supplementary Problems......Page 150 4.2 Definition of z-Transform......Page 152 Time Reversal......Page 156 Conjugation......Page 157 Initial Value Theorem......Page 158 4.4.1 Partial Fraction Expansion......Page 159 4.4.2 Power Series......Page 160 4.5 One-Sided z-Transform......Page 161 4.2 Computing z-Transforms......Page 162 4.3 Properties......Page 167 4.4 Inverse z-Transforms......Page 174 4.5 One-Sided z-Transforms......Page 179 Applications......Page 181 4.2 z-Transforms......Page 188 4.3 Properties......Page 189 4.5 One-Sided z-Transforms......Page 190 Answers to Supplimentary Problems......Page 191 5.2 System Function......Page 193 Causality......Page 194 Realizable Systems......Page 195 5.2.2 Inverse Systems......Page 196 5.2.3 Unit Sample Response for Rational System Functions......Page 197 5.2.4 Frequency Response for Rational System Functions......Page 198 5.3 Systems with Linear Phase......Page 199 Type I Linear Phase Filters......Page 200 z-Transform of Linear Phase Systems......Page 201 5.4 Allpass Filters......Page 203 5.5 Minimum Phase Systems......Page 204 5.6 Feedback Systems......Page 205 5.2 System Function......Page 206 5.3 Systems with Linear Phase......Page 214 5.4 Allpass Filters......Page 219 5.5 Minimum Phase......Page 222 5.6 Feedback......Page 226 5.2 System Function......Page 228 5.5 Minimum Phase......Page 229 5.6 Feed back......Page 230 Answers to Supplementary Problems......Page 231 6.2 Discrete Fourier Series......Page 233 Shift......Page 234 Periodic Convolution......Page 235 6.3 Discrete Fourier Transform......Page 236 Circular Shift......Page 237 Circular Convolution......Page 238 Circular vs Linear Convolution......Page 240 6.5 Sampling DTFT......Page 241 6.6 Linear Convolution using DFT......Page 242 Overlap-Add......Page 243 Overlap-Save......Page 244 6.2 Discrete Fourier Series......Page 245 6.3 Discrete Fourier Transform......Page 247 6.4 DFT Properties......Page 250 6.5 Sampling DTFT......Page 259 6.6 Linear Convolution using DFT......Page 261 Applications......Page 263 6.4 DFT Properties......Page 268 6.6 Linear Convolution using DFT......Page 269 Answers to Supplementary Problems......Page 270 7.2.1 Decimation-in-Time FFT......Page 272 7.2.2 Decimation-in-Frequency FFT......Page 276 7.3 FFT Algorithms for Composite N......Page 277 7.4 Prime Factor FFT......Page 281 7.2 Radix-2 FFT Algorithms......Page 283 7.3 FFT Algorithms for Composite N......Page 288 7.4 Prime Factor FFT......Page 292 7.2 Radix-2 FFT Algorithms......Page 295 Answers to Supplementary Problems......Page 296 8.2 Digital Networks......Page 297 8.3.3 Linear Phase Filters......Page 299 8.4 Structures for IIR Systems......Page 301 8.4.1 Direct Form......Page 302 8.4.2 Cascade Structure......Page 304 8.4.3 Parallel Structure......Page 305 8.4.5 Allpass Filters......Page 306 8.5.1 FIR Lattice Filters......Page 308 8.5.2 All-Pole Lattice Filters......Page 310 8.5.3 IIR Lattice Filters......Page 311 Fixed Point......Page 312 Quantization Errors in Fixed-Point Number Systems......Page 313 8.6.2 Quantization of Filter Coefficients......Page 314 8.6.3 Round-Off Noise......Page 316 8.6.5 Overflow......Page 319 8.3 Structures for FIR Systems......Page 320 8.4 Structures for IIR Systems......Page 329 8.5 Lattice Filters......Page 343 8.6 Finite Word-Length Effects......Page 351 8.3 Structures for FIR Systems......Page 362 8.5 Lattice Filters......Page 363 8.6 Finite Word-Length Effects......Page 364 Answers to Supplementary Problems......Page 365 9.2 Filter Specifications......Page 368 9.3.1 Linear Phase FIR Design using Windows......Page 369 9.3.2 Frequency Sampling Filter Design......Page 372 9.3.3 Equiripple Linear Phase Filters......Page 373 9.4 IIR Filter Design......Page 376 9.4.1 Analog Low-Pass Filter Prototypes......Page 377 9.4.2 Design of IIR Filters from Analog Filters......Page 383 Impulse Invariance......Page 384 Bilinear Transformation......Page 385 9.5 Filter Design based on Least Squares Approach......Page 386 9.5.1 Pade Approximation......Page 387 9.5.2 Prony's Method......Page 388 9.5.3 FIR Least-Squares Inverse......Page 389 9.3 FIR Filter Design......Page 390 9.4 IIR Filter Design......Page 402 9.5 Least-Squares Filter Design......Page 428 9.3 FIR Filter Design......Page 434 9.4 IIR Filter Design......Page 435 9.5 Least-Squares Filter Design......Page 436 Answers to Supplementary Problems......Page 437 Index......Page 439 Backcover......Page 447 Confusing Textbooks? Missed Lectures? Tough Test Questions? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you Signals And Systems -- Linear Time-invariant Systems -- Laplace Transform And Continuous-time Lti Systems -- The Z-transform And Discrete-time Lti Systems -- Fourier Analysis Of Continuous-time Signals And Systems -- Fourier Analysis Of Discrete-time Signals And Systems -- State Space Analysis -- Appendices: -- Review Of Matrix Theory -- Properties Of Linear Time-invariant Systems And Various Transforms -- Review Of Complex Numbers. Hwei P. Hsu. Includes Index. I purchased this outline as a supplement for a class text Signals and Systems, by Alan Oppenheim. The information is a significant help and the instructor actually recommended this outline as she gives us some additional problems to try on our own that is similar to what we are doing in class. This is a great study aid. I am happy with the purchase, it's always great to see several different examples worked out so you can recognize what's going on.