Bibliography Practical Signal Processing and Its Applications Downloaded from www.worldscientific.com Abramowitz, Milton, and Irene A. Stegun. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Vol. 55. Courier Corporation, 1964. Arsac, Jacques. Fourier transforms and the theory of distributions. Englewood Cliffs, NJ: Prentice-Hall, 1966. Bateman, Harry. Tables of integral transforms, 1954. Bracewell, Ronald N., Fourier Transforms and Its Applications, Second Edition, McGraw Hill, 1978. Brigham, E. Oran, The fast Fourier transform and its applications. Prentice Hall, 1988. Chen, Wai-Kai. Passive and active filters: theory and implementations. Wiley, 1986. Dwight, Herbert Bristol, Tables of Integrals and Other Mathematical Data, Fourth Edition, The MacMillan Company, 1961. Jackson, Leland B. Digital Filters and Signal Processing: With MATLAB Exercises. Springer Science & Business Media, 2013. Lathi, B. P. Signal processing and linear systems. New York: Oxford University Press, 1998. Lathi, B. P. Linear systems and signals. Vol. 2. New York: Oxford University Press, 2005. Lathi, B. P. and Ding, Zhi, Modern Digital and Analog Communication Systems, Oxford University Press, 4th Edition, 2009. Lighthill, M. J., Introduction to Fourier Analysis and Generalized Functions, Cambridge University Press, 1962. McClellan, James H., Schafer, Ronald W., and Yoder, Mark A., Signal Processing First, Pearson Education, Inc., 2003. Oppenheim, Alan V., and Schafer, Ronald W., Discrete-time Signal Processing, Prentice Hall signal processing series, 3rd Edition, 2010. Oppenheim, Alan V., Willsky Alan, S., and Nawab, S. Hamid, Signals and Systems, Second Edition, Prentice Hall, 1997. Papoulis, Athanasios, The Fourier Integral and its Applications, McGraw-Hill, 1962. Papoulis, Athanasios, Signal Analysis, McGraw Hill, 1977. 605
606 Bibliography Practical Signal Processing and Its Applications Downloaded from www.worldscientific.com Roberts, M. J., Signals and Systems, McGraw Hill, 2004. Stuller, John. Introduction to signals and systems. Thomson-Engineering, 2007. Tan, S. M., Lecture notes on Linear Systems, found at: https://sites.google.com/site/ szemengtan/home/linear-systems. Tervo, Richard, J., Practical Signal Theory and with MATLAB Applications, Wiley, 2014. Wiener, Norbert, The Fourier Integral and certain of its Applications, Cambridge University Press, 1988 (first published in 1933).
Index Practical Signal Processing and Its Applications Downloaded from www.worldscientific.com Abscissa of convergence 403 Active filter circuits 353, 359, 361 Admittance 344, 366, 485, 495 Aliasing 228, 229, 452 Aliasing (eliminating it) 235 Allpass digital filter 307 Allpass digital filter (1st-order) 449 Allpass digital filter (2nd-order) 450 Amplitude quantization 246, 261 Analog filters 340 Analog filters 346, 350, 353, 451, 479 Analog signal 1, 4 Analog-to-digital conversion (ADC) 219, 245, 256 Anti-alias post-filtering 236 Anti-alias pre-filtering 237, 316 Anticausal sequence 28, 96, 372 Anticausal signal 66, 402 Anticausal system 441, 477 Applications of signal processing 3, 37, 74, 134, 196, 255, 295, 344, 431, 463 Autocorrelation 36, 48, 73, 118, 143, 179 Backward difference operation 32, 47, 117, 386 Band-elimination (notch) analog filter 340, 353, 483 Band-elimination (notch) digital filter 277, 280 Band-limited 225 Bandpass analog filter 340, 350, 482 Bandpass digital filter 277, 279, 304, 446 Bandwidth 104, 167, 202, 224, 304 Baseband 226 Bilateral Laplace transform 400 Bilateral Z transform 370 Bilinear transformation 455 Binomial distribution 42 Bode plot 122, 183 Butterworth lowpass filter 453, 462 Capacitor impedance 345, 486 Capacitor with nonzero initial conditions 488 Causal sequence 28, 371, 372 Causal signal 66, 96, 402 Causal system 283, 284, 441, 477 Circular convolution 109, 142 Comb filter 308, 448 Comb function 19, 58, 123, 184 Combined feedback and feed-forward network 293 Communications 2, 69, 110, 172, 201 Compact trigonometric Fourier series 193 Complex exponential function 59, 163, 339, 406 Complex exponential sequence 21, 100, 376 Complex numbers 7, 8 Complex-conjugate poles 394, 423 Complex-conjugate root theorem 432, 469 607
608 Index Conductance 366 Conjugate 7, 32, 70 Conjugation of a sequence 385 Continuous-time Fourier transform (CTFT) 157 Continuous-time signal 5, 55 Continuous-time system 335 Convolution 71, 74, 77, 79, 171 Convolution (discrete-time) 34, 44, 48, 108, 115, 124 Convolution of sequences 384 Convolution of signals 415 Convolution of two pulses 35, 72 Convolution using the FFT 142 Convolution with rectangular pulse 41 Critical (Nyquist) sampling rate 229 Cross-correlation 36, 38, 48, 72, 75, 117, 179 Cumulative integral 69 Cumulative sum 32, 47, 117, 386 Cutoff frequency 278, 341, 365 Decibel (db) scale 150, 211, 251 Decimation (down-sampling) 31, 112, 116, 313, 315 Delta-Sigma (ΔΣ) ADC 260 Demodulation 5, 203 Difference equations 283, 319, 388 Differential equations 417, 498, 501 Digital bandpass filter design 326 Digital communication systems 204 Digital filter building blocks 282 Digital filter design based on analog prototypes 451 Digital filtering concepts 277 Digital filters 295, 321 Digital highpass filter design 325 Digital lowpass filter design 322 Digital signal 1, 4, 5 Digital-to-analog conversion (DAC) 245, 255 Dirac delta function 56 Discrete Convolution 37 Discrete cosine transform (DCT) 145 Discrete Fourier transform (DFT) 126, 128, 130 Discrete time Fourier transform (DTFT) 93, 103, 115, 222 Discrete-time filter networks 282 Discrete-time signal 6, 17 Discrete-time systems 269 Down-sampling (decimation) 31, 112, 116, 313, 315 Eigenfunction 21, 59, 272, 275 Energy of a signal 25, 46, 62, 81, 114 Energy signals 25, 62 Euler's formula 10 Even and odd signals 27, 65 Exponential Fourier series 187 Exponentially decaying sequence 23, 95, 374 Exponentially decaying signal 61, 159, 404 Fast Fourier transform (FFT) 44, 130, 134, 142, 143, 328 Feedback network 285, 288, 353 Feedback system using op-amp 356 Filtering 4, 224, 340 Finite impulse response (FIR) filter 291, 315, 317, 321, 389 Finite-length sequence 29, 137 Finite-length signal 66 FIR filter design (frequency sampling method) 328 FIR filter design (windowing method) 321 First-order analog filters 346 First-order digital filters 295 First-order hold method 242 Flash ADC 259 Fourier series 187 Fourier transform 93, 157 Fourier transform of periodic sequences 123, 135 Fourier transform of periodic signals 184, 187 Fourier transform properties 105, 167 Frequency analysis 269, 335 Frequency resolution 134 Frequency response 273, 341 Frequency response from H(s) 466
Frequency response from H(z) 432 Frequency shift 112, 115, 174, 201, 414, 418 Frequency-domain sampling 207, 328 Fundamental frequency 26, 64, 126, 187, 310 Fundamental period 26, 64 Generalized feedback network 288 Generalized feed-forward network 290 Half-power frequency 347, 350, 489 Half-raised cosine (Hanning) window 321 Hamming window 325 Hanning (half-raised cosine) window 321 Harmonic index 27, 65 Harmonics 27, 65, 127, 188, 310 Highpass analog filter 340, 346, 362, 481 Highpass digital filter 277, 279, 301, 445 Ideal continuous-time filter 224, 340, 341, 342, 343 Ideal discrete-time filter 277 Ideal operational amplifier 357 Image processing 6, 263 Impedance 344, 362, 485, 495 Improper rational function 421 Impulse function 56, 161, 405 Impulse response 76, 270, 291 Impulse sequence 18, 98, 375 Impulse-invariant transformation 452 Inductor impedance 345, 486 Inductor with nonzero initial conditions 487 Infinite impulse response (IIR) filter 288 Infinite-length sequence 29 Infinite-length signal 66 Integrable signals 63 Interpolation (up-sampling) 32, 114, 116, 313 Interpolation filter 314 Inverse continuous-time Fourier transform (ICTFT) 157 Index 609 Inverse discrete Fourier transform (IDFT) 127 Inverse discrete-time Fourier transform (IDTFT) 94 Inverse Laplace transform 400 Inverse Laplace transform of rational functions 420 Inverse Z transform 370, 389 Inverter op-amp circuit 359 Inverting op-amp topology 358 Kirchoff's current law (KCL) 366 Kirchoff's voltage law (KVL) 366 Kronecker delta function 18 Ladder network 496 Laplace transform 400 Laplace transform properties 410 Laplace transforms of basic signals 404 Left-sided sequence 28 Left-sided signal 66 Linear difference equations 283 Linear shift-invariant (LSI) discretetime system 269 Linear system analysis in s-domain 464 Linear time-invariant continuous (LTIC) system 336, 464 Linearity 105, 115, 168, 381, 411 Linear-phase filter 310, 312 Logarithmic successive approximation ADC 258 Long division method 390 Loudspeaker measurement 198 Lowpass analog filter 340, 349, 359, 480 Lowpass digital filter 277, 278, 297, 444 Magnitude 7, 32, 70 Magnitude response from poles & zeros in s plane 469 Magnitude response from poles & zeros in z plane 434 Magnitude spectrum 94, 122, 158, 184 Minimum-phase analog filter 484 Minimum-phase digital filter 451 Mirroring a pole about the jω axis 475
610 Index Modulation in communications 3, 110, 201 Modulation property 110, 115, 172, 202 Moving-window averaging 41 Multiplication of a sequence by n 385 Multiplication of sequence by a 386 Multiplication of sequences 384 Multiplication of signals 415 Negative feedback 356 Node and mesh analysis 491 Non-inverting op-amp topology 357 Non-uniform quantization 253, 262 Normalized cross-correlation 39, 76, 82 Notch (band-elimination) analog filter 343, 353, 483 Notch (band-elimination) digital filter 277, 280, 306, 447 Nyquist (critical) sampling rate 228 Nyquist plot 119, 181, 317 One-port network 362 Open-loop gain 356 Operational amplifier (op-amp) 355 Operational amplifier circuits 256, 357, 359, 359, 361, 362 Orthogonal 77, 129, 189 Oversampling 229, 234, 260 Parseval s Theorem 114, 117, 131, 176, 179, 193 Partial fraction expansion 391, 420 Passband 224, 277, 340 Passive filter circuits 346 Periodic impulse train 19, 57 Periodic signals 26, 38, 44, 64, 74 Phase 7, 20, 32, 58, 70, 310 Phase response from poles & zeros in s plane 474 Phase response from poles & zeros in z plane 438 Phase spectrum 94, 158 Phasor 10 Piano keyboard 196 Plotting a sequence 43 Plotting a spectrum 146, 208 Plotting basic signals 78 Plotting frequency response 319, 362 Plotting impedance function 362 Polar coordinates 6, 120, 181 Poles and zeros 374, 382, 404, 412, 431, 468, 484 Pole-zero diagram 382, 413, 443, 455, 457, 479 Polynomial product 37 Power 25, 36, 44, 62, 72, 81, 193 Power signals 25, 36, 62, 72 Practical applications of signal processing 37, 74, 134, 196, 255, 295, 344, 431, 463 Probability density function 84, 249 Proper rational function 390, 421 Properties of the Fourier transform 115, 177 Properties of the Laplace transform 418 Properties of the Z transform 387 Pseudo-code 290, 292, 295 Quantization 219, 246 Quantization error 250 R-2R ladder digital-to-analog converter 255 Radian frequency 20, 58 Radio communications 5 Ramp function 60, 408 Ramp sequence 22, 26, 377, 385 Rational function 284, 371, 388 Reactance 366 Reciprocating a pole 439 Reconstruction filter 227, 231, 234, 236 Rectangular (rect) pulse 22, 44, 60, 74, 102, 165 Rectangular coordinates 118, 180 Region of convergence (ROC) in s plane 402, 466, 476 Region of convergence (ROC) in z plane 372, 432, 441 Relation between CTFT and DTFT 221 Repeated roots 424 Resistor impedance 345, 486 Right-sided sequence 28 Right-sided signal 66 RLC circuits 344, 482, 483
Sallen-Key circuit 361, 362 Sample delay 282 Sample-and-hold 241 Sampling bandpass signals 238 Sampling theory 219 Sampling-based Fourier transform relationships 223 Scale factor of pole-zero diagram 383, 412 S-domain signal processing 399, 463 Second-order analog filters 350, 361 Second-order digital filters 303 Shift-invariance 272 Short-time normalized cross-correlation 39 Sidelobes of energy 206 Sifting (sampling) property of an impulse function 19, 57, 274 Signals 2, 17, 55 Signal-to-quantization-noise power ratio (SNR ) 249 Signum function 21, 59, 98, 162 Simple complex roots 422 Simple real roots 421 Sinc function 24, 62, 104, 167, 231 Sinusoid 10, 20, 58, 101, 164, 377, 407 Sinusoidal steady-state analysis 467 Solving linear differential equations 498 Specialized digital filters 308 Spectral analysis 134, 204 Spectrum 94, 129, 158 Speech signal 5, 110, 172, 224, 235 S-plane 399, 402, 403, 412 Stability 289, 292, 356, 441, 476 Stabilizing a system 442, 477 State variables and state equations 502 Stopband 224, 277, 340 Strictly proper rational function 420 Successive approximation ADC 256 Summable sequences 26 Summary of CTFT and Fourier series transformations 195 Summary of DTFT and DFT transformations 133 Index 611 Susceptance 366 System stability 441 Table of Fourier transform pairs 103, 165 Table of Fourier transform properties 115, 177 Table of Laplace transform pairs 408 Table of Laplace transform properties 418 Table of V-I characteristics of RLC components 486 Table of Z transform pairs 378 Table of Z transform properties 387 Time advance 29 Time constant 347, 350, 489 Time delay 29, 67, 199, 310, 413 Time differentiation 417, 499 Time integration property 418 Time multiplication property 109, 115, 171, 177 Time reversal 31, 68, 116, 178, 200 Time scaling 31, 68, 112, 174, 177, 414 Time shift 29, 107, 169, 383, 413 Time/frequency duality 108, 170 T-matrices 494 Transfer function 275, 338, 431, 463, 501 Transformed network 346 Transient circuit analysis 491 Transition band 224 Triangular pulse function 23, 61, 75, 105 Trigonometric Fourier series 190 Two-port network 494 Undersampling 229, 238 Uniform quantization 247 Unilateral Laplace transform 400 Unilateral Z transform 371 Unit step function 21, 59, 100, 163, 375, 406 Up-sampling (interpolation) 32, 114, 116, 313 Useful MATLAB code 43, 77, 146, 208, 261, 319, 362 Voltage follower op-amp circuit 358
612 Index Voltage-current (V-I) characteristics 345, 486 Waveform smoothing 41, 44, 74 Windowing function 204 Windowing in time 233 Z-domain signal processing 369, 431 Zero-order hold method 239 Zero-phase filter 311 Zeros and poles 374, 382, 404, 412, 431, 468, 484 Zeros of a comb filter 310 Z transform 370 Z transform properties 381 Z transforms of basic signals 374