History

The revision numbering is major.minor.bugfix. Pure bugfix updates are not listed here.

1.0.2 (May 18, 2012)

first public revision

1.1.0 (June 7, 2015)

• TSK filters
• frequency shifters
• further minor changes

2.0.0alpha (May 28, 2018)

• redone: TSK/SKF filters
• 8-pole ladder filters
• expanded: nonlinearities
• expanded: phasers and flangers (now found under the title multinotch filters)
• Butterworth transformations of the 1st and 2nd kinds
• classical signal processing filters (Butterworth, Chebyshev, elliptic)
• redone: shelving filters
• redone: Hilbert transformers
• crossovers
• state-space form
• transient responses
• many further smaller changes

2.1.0 (October 28, 2018)

• generalized ladder filters
• elliptic filters of order $2^N$ (discussed as order-$2^N$ elliptic rational functions)
• elliptic shelving filter (and elliptic rational function) midslope steepness derivation

Index

• 1-pole
  • Jordan, 37, 278
• 1-pole filter, 7, 199
  • transposed, 30
• 2-pole filter, 95
• 4-pole filter, 133
• 8-pole ladder filter, 158
• allpass filter, 29, 119
  • SKF, 158
  • TSK, 158
• allpass substitution, 92
• amplitude
  • elliptic, 351
  • of oscillations around $\infty$, 344
• amplitude response, 13, 51
• analytic filter, 453, 456
• analytic signal, 453
• antisaturator, 211
• arctangent scale, 313
• bandpass filter, 95, 293, 303
• barberpole, 502
• BIBO, 21
• bilinear transform, 57
  • inverse, 58
  • topology-preserving, 81
  • unstable, 89
• bisection, 189
• BLT, 57
• BLT integrator, see trapezoidal integrator
• Butterworth filter, 103, 286, 294, 319
  • 1st kind of, 286
  • 2nd kind of, 294
• Butterworth transformation, 283, 285
  • 1st kind of, 286
  • 2nd kind of, 294
• canonical form, 79
• cascade decomposition, 275
• Chebyshev filter, 337, 344
  • type I, 337
  • type II, 344
• Chebyshev polynomial, 332
  • double-reciprocated, 344
  • renormalized, 335
• comb filter, 493
• complex exponential, 5
• complex impedances, 12
• complex sinusoid, 1
• controllable canonical form, 271
• coupled-form resonator, 253
• crossover, 437
• cutoff, 8, 14
  • of a pole, 109
  • of a zero, 109
  • parameterization of, 15, 275
• cutoff modulation, 40, 264
• damping
  • in SVF, 100
  • of a pole, 109
  • of a zero, 109
• DC offset, 2
• degree
  • of transformation, 383
• degree equation, 383
• delayless feedback, 73
• DF1, 79
• DF2, 79
• diagonal form, 247, 278
• differentiator, 91
• diode clipper, 208
• diode ladder filter, 164, 200
• Dirac delta, 4
• direct form, 79
• discrimination factor, 387
• eigenfunction, 9
• elliptic filter, 400
  • minimum Q, 405
• elliptic function, 351
  • evaluation of, 374
  • normalized, 363
  • normalized-argument, 372
• elliptic modulus, 350
• elliptic rational function, 384
  • normalized, 389
  • renormalized, 394
• ellitic integral, 350
• EMQF, 405
• equiripple, 309
• equiripples, 332
• even roots/poles, 288, 322, 449
• filter
  • 1-pole, 7, 199
  • 2-pole, 95
  • 4-pole, 133
  • allpass, 29, 119
  • analytic, 453, 456
  • bandpass, 95, 293, 303
  • Butterworth, 103, 286, 294, 319
  • comb, 493
  • elliptic, 405
  • highpass, 18, 95, 138, 292, 303
  • highpass TSK, 154
  • ladder, 133, 275, 305
  • lowpass, 7, 95, 133, 290, 302
  • lowpass SKF, 155
  • lowpass TSK, 154
  • multimode, 25, 95, 141, 276
  • multinotch, 487
  • normalized bandpass, 111
  • notch, 119
  • peaking, 121
  • Sallen-Key, 152, 154
  • shelving, 27, 118, 410
  • SKF, 154
  • stable, 21
  • tilting, 410
  • transposed, 30
  • TSK, 152
  • unit-gain bandpass, 111
• fixed-point iteration, 184
• Fourier integral, 3
• Fourier series, 2
• Fourier transform, 3
• frequency response, 13, 51
• frequency shifter, 468
• gain element, 8
• generalized SVF, 271
• hard clipper, 177, 198
• harmonics, 2
• Hermitian, 3
• highpass filter, 18, 95, 138, 292, 303
• Hilbert transform, 453
• Hilbert transformer, 453, 456
• hyperbolic functions, 325
• imaginary Riemann circle, 312
• instantaneous gain, 75
• instantaneous offset, 75
• instantaneous response, 75
• instantaneous smoother, 85
• instantaneously unstable
  • feedback, 85
• integrator, 8
  • BLT, see integrator, trapezoidal
  • naive, 47
  • trapezoidal, 53, 269
• integratorless feedback, 239
• Jacobian elliptic function, 351
  • evaluation of, 374
  • normalized, 363
  • normalized-argument, 372
• Jordan 1-pole, 37, 278
• Jordan 2-pole, 253, 278
• Jordan cell, 256
  • real, 259
• Jordan chain, 39, 257
• Jordan normal form, 256
• ladder filter, 133, 275
  • 2-pole allpass, 158
  • 8-pole, 158
  • bandpass, 146
  • diode, 164, 200
  • generalized, 305
  • highpass, 145
  • modes of, 141
  • OTA, 201
  • transistor, 199
• Landen transformation, 374
• Laplace integral, 5
• Laplace transform, 5
• linearity, 11
• Linkwitz-Riley crossover, 439
• lowpass filter, 7, 14, 95, 133, 290, 302
• LP to BP substitution, 114, 294
• LP to BP transformation, 114
• LP to BS substitution, 117
• LP to HP substitution, 24
• LP to HP transformation, 24
• matrix exponential, 244
• maximum phase, 24
• MIMO
  • SKF, 155
• minimax approximation, 472, 473
• minimum phase, 24
• minimum Q, 405
• modular angle, 350
• modulus
  • ellitpic, 350
• multimode filter, 25, 95, 141, 276
• multinotch filter, 487
• N-th degree transformation, 383
• naive integrator, 47
• Newton-Raphson method, 186
• nonstrictly proper, 11
• normalized bandpass filter, 111
• notch filter, 119
• observable canonical form, 273
• odd roots/poles, 288, 322, 449
• OTA ladder filter, 201
• parallel representation, 278
• partial fraction expansion, 278
• partials, 2
• passband, 14, 97, 111
• peaking filter, 121
• phase response, 13, 51
• phase splitter, 468
• pole, 19, 35, 53
  • cutoff of, 109
  • damping of, 109
• preimage
  • of a representation, 320
• prewarping, 62, 115
• prewarping point, 65
• principal values, 326
• quarter period
  • imaginary, 354
• quarter-period, 353
• real diagonal form, 252, 278
• real Riemann circle, 310
• reference gain, 431
• Remez algorithm, 472
• representation, 320
• resonance, 100, 106
• Riemann circle
  • imaginary, 312
  • real, 310
• Riemann sphere, 309
  • rotations of, 314
• rolloff, 15, 21
• Sallen-Key
  • highpass, 155
  • lowpass, 155
  • MIMO, 155
• Sallen-Key filter, 152, 154
• saturator, 174
  • asymptotically linear, 176
  • bounded, 175
  • bounded-range, 175
  • compact-range monotonic, 175
  • slower than linear, 176
  • unbounded, 176
  • unbounded-range, 176
• selectivity factor, 387
• selfoscillation, 101, 128, 136, 180
• selfoscillation point, 129
• serial cascade, 275
• shelving band, 417
• shelving filter, 118, 410
  • 1-pole, 27
• SKF, 154
  • allpass, 158
  • highpass, 155
  • lowpass, 155
  • MIMO, 155
• soft clipper, 177
• spectrum, 2
• stability, 21, 35, 269
  • time-varying, 42
• state space, 239
• state-space form, 237
• state-variable filter, 95
• steady state, 33
• steady-state response, 33
• stopband, 14, 97
• substitution
  • LP to BP, 114, 294
  • LP to BS, 117
  • LP to HP, 24
• summator, 8
• SVF, 95
  • generalized, 271
• tilting filter, 410
• time-invariant, 10
• time-varying system, 42
• topology, 42
• topology-preserving transform, 59, 81
• TPBLT, 81
• TPT, 59, 81
• transfer function, 11, 33, 50, 182
• transfer matrix, 242, 267
• transformation
  • LP to BP, 114
  • LP to HP, 24
• transient response, 33, 245, 268
• transistor ladder filter, 199
• transition band, 14, 97, 417
• transposition, 30, 243
• trapezoidal integrator, 53, 269
• trigonometric functions, 325
• TSK
  • allpass, 158
• TSK filter, 152
  • highpass, 154
  • lowpass, 154
• unit delay, 48
• unit-gain bandpass filter, 111
• waveshaper, 173
• z-integral, 46
• z-transform, 46
• zero, 19, 53
  • cutoff of, 109
  • damping of, 109
• zero-delay feedback, 74, 183