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Introduction to digital signal processing, ed. 2 extended
ID: 177166
Richard G. Lyons
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Manual, which is a comprehensive lecture in the field of digital signal processing. It contains the basics of signal theory and discrete systems, uniform sampling, discrete Fourier transform, fast Fourier transform with algorithms and computer programs, design of finite and infinite impulse response filters, special low-band filters, quadrature signals, discrete Hilbert transform, conversion of sampling frequency, signal averaging, digital data formatting and digital signal processing tricks that increase its efficiency.
Recipients of the book: students of mechanical, mechatronic, electrical and electronic faculties, technical universities and students of post-graduate studies in the field of digital signal processing.
Table of Contents:
PREFACE 11
1. SIGNALS AND DISCRETE SYSTEMS 19
1.1. Discrete signals and their notation 20
1.2. The instantaneous value, absolute value and instantaneous signal strength 26
1.3. Operation symbols in signal processing 28
1.4. Introduction to discrete linear systems unchanged in time 30
1.5. Linear discrete systems 30
1.5.1. Example of a linear system 31
1.5.2. An example of a non-linear system 32
1.6. Systems unchanged in time 35
1.6.1. An example of a system unchanged in time 36
1.7. Interchangeability property of linear invariant systems in time 37
1.8. Analysis of linear systems unchanged over time 37
2. IMMUNE SAMPLE 39
2.1. Aliasing: frequency ambiguity in the frequency domain 39
2.2. Sampling of lowband signals 45
2.3. Sampling of bandwidth signals 48
2.4. Spectral reversal in band sampling 57
3. DISCREET CONVERTATION OF FOURIER 62
3.1. Understanding the DFT 63 equation
3.1.1. Example 1 DFT 66
3.2. Symmetry DFT 75
3.3. DFT 77 linearity
3.4. DFT amplitude spectrum signal 77
3.5. Frequency axis DFT 79
3.6. The transfer claim 79
3.6.1. Example 2 DFT 80
3.7. Reverse DFT 82
3.8. Leakage DFT 83
3.9. Windows 91
3.10. Loss coming from DFT 98 surges
3.11. DFT resolution, zeros refining and frequency sampling 99
3.12. Improvement of the signal / noise ratio using DFT 103
3.12.1. Improvement of the signal / noise ratio of a single DFT 104
3.12.2. Improvement of the signal / noise ratio resulting from averaging multiple DFT 107
3.13. DFT rectangular functions 107
3.13.1. DFT rectangular function in the general form 108
3.13.2. DFT symmetrical rectangular function 114
3.13.3. DFT rectangular function with unit values alone 116
3.13.4. Time and frequency axes associated with rectangular functions 119
3.13.5. Alternate DFT forms of a rectangular function with unit values alone 121
3.13.6. Inverse DFT of the rectangular function in the general form 121
3.13.7. Inverse DFT of the symmetrical rectangular function 124
3.14. DFT of complex stimulation 126
3.15. DFT of actual cosine stimulation 129
3.16. A single-track DFT of excitation being a true cosine signal 131
3.17. Interpretation of DFT 133
Literature to chapter 3 136
4. FASTIER TRANSFORMATION FAST. 137
4.1. The relationship between FFT and DFT 138
4.2. Tips on how to use FFT in practice 139
4.2.1. Sampling fast enough and long enough 139
4.2.2. Pre-processing of time data before determining FFT 140
4.2.3. Correcting FFT results 141
4.2.4. Interpretation of FFT 142 results
4.2.5. Software implementing FFT 143
4.2.6. Derivation of the FFT algorithm with base 2 144
4.3. Bitwise reversal of the FFT 151 I / O index
4.4. FFT butterfly structures with base 2 152
Literature to chapter 4 160
5. FILTERS WITH THE FINISHED PULSON ANSWER 162
5.1. Introduction to filters with finite impulse response - SOI 163 filters
5.2. The weave operation in SOI 168 filters
5.3. Designing low-pass SOI 178 filters
5.3.1. Window design 178
5.3.2. Application of window functions in the design of SOI 186 filters
5.4. Design of bandpass filters SOI 192
5.5. Designing high-pass SOI 195 filters
5.6. Remesis method for designing SOI 196 filters
5.7. Bandwidth SOI 198 filters
5.8. Phase characteristics of SOI 200 filters
5.9. A general description of the discrete plexus 205
5.10. Discrete plexus in time domain 206
5.10.1. The weave statement 210
5.10.2. Application of the weave statement 213
Literature to chapter 5 216
6. FILTERS WITH INFINITE IMPULSE ANSWER 218
6.1. Introduction to filters with infinite impulse response 219
6.2. Laplace transform 222
6.2.1. The poles and zeros on the plane are stability 229
6.3. Transformation from 236
6.3.1. Poles and zeros in the plane for stability 238
6.3.2. The use of the Z transformation for the analysis of NOI 240 filters
6.3.3. Alternative NOI 248 filter structures
6.4. Designing of NOI filters using impulse response invulnerability 250
6.4.1. Example of Impulse Response invulnerability - Method 1 257
6.4.2. Example of impulse response invulnerability design - Method 2 260
6.5. Designing of NOI filters by biline transformation 267
6.5.1. Example of filter design with the use of biline transform 273
6.6. Optimized method of designing NOI 277 filters
6.7. Pitfalls lurking in the construction of digital NOI 279 filters
6.8. Improving NOI filters - cascading 281
6.8.1. Properties of cascade and parallel filters 281
6.8.2. Cascade connection of NOI 283 filters
6.9. A short comparison of NOI and SOI 286 filters
Literature to chapter 6 287
7. SPECIALIZED LOWERPROOF FILTERS SOI 289
7.1. Frequency sampling filters: forgotten art 290
7.1.1. Cascade combination of comb filter and complex digital resonator 292
7.1.2. Multi-section complex filters FSF 297
7.1.3. Ensuring the stability of FSF 301 filters
7.1.4. Multiflex FSF filters with real coefficients of 304
7.1.5. Multiflex FSF filters with real and linear coefficients of 307 phase
7.1.6. Where we were and where we are going with the FSF 309 filters
7.1.7. Effective FSF filter with real coefficients of 310
7.1.8. Modeling of FSF 312 filters
7.1.9. Correction of characteristics using coefficients in the 313 transition band
7.1.10. Alternative filter structures FSF 315
7.1.11. The advantages of FSF 316 filters
7.1.12. Example of an FSF Type IV 318 filter
7.1.13. When to use FSF 319 filters
7.1.14. Designing of FSF 322 filters
7.1.15. Summary of FSF 325 filters
7.2. Interpolated SOI 325 low-pass filters
7.2.1. Selection of the optimal M 330 extension factor
7.2.2. Estimate the number of links in the SOI 331 filter
7.2.3. Modeling of the ISOI 332 filter characteristics
7.2.4. Implementation problems of ISOI 335 filters
7.2.5. Example of ISOI 336 filter design
Literature to chapter 7 338
8. SQUARES SQUARES 340
8.1. Why square signals? 341
8.2. Notation of complex numbers 341
8.3. Representation of real signals using complex indications 347
8.4. A handful of thoughts about the negative frequencies 351
8.5. Quadrature signals in the frequency domain 352
8.6. Banded quadrature signals in the 355 frequency domain
8.7. Complex frequency conversion down 357
8.8. An example of complex frequency conversion down 359
8.9. An alternative method of down-frequency conversion 363
Literature to chapter 8 365
9. HILBERT'S DISCREET TRANSFORM 366
9.1. Denis of the Hilbert transformation 367
9.2. Why do we deal with the Hilbert transformation? 369
9.3. Pulse response of the Hilbert transformer 374
9.4. Designing a discreet Hilbert 376 transformer
9.4.1. Hilbert transformation in time domain: implementation of SOI 376 filter
9.4.2. Hilbert transformation in the frequency domain 380
9.5. Generation of analytical signal in time domain 382
9.6. Comparison of analytical methods of signal generation 384
Literature to chapter 9 385
10. CONVERSION OF SAMPLE FREQUENCY 386
10.1. Decimation 387
10.2. Interpolation 392
10.3. Combination of decimation and interpolation 395
10.4. Polyphase filters 396
10.5. Cascade integration comb filters 402
10.5.1. Recursive summary filter 403
10.5.2. Filter structures CIC 404
10.5.3. Improved attenuation of CIC 409 filters
10.5.4. Implementation aspects of CIC 410 filters
10.5.5. Compensating SOI 412 filters
Literature to chapter 10 414
11. MULTIPURATION OF SIGNALS 416
11.1. Coherent averaging 417
11.2. Non-coherent averaging 423
11.3. Averaging multiple FFTs 426
11.4. Filtering aspects of time averaging 435
11.5. Exponential averaging 436
Literature to chapter 11 442
12. REPRESENTATIONS OF DIGITAL DATA AND THEIR EFFECTS 443
12.1. Fixed-point binary representations 443
12.1.1. Figures in figure 444
12.1.2. Hexadecimal numbers 445
12.1.3. Fractional binary numbers 446
12.1.4. Binary sign-module representation 447
12.1.5. Representation of the supplement to two 447
12.1.6. Representation with a binary offset 449
12.2. Precision and dynamic range of binary numbers 450
12.3. The effects of the finite length of the fixed-point word binary 450
12.3.1. Quantization errors in A / C converters 451
12.3.2. Data overflow 458
12.3.3. Clip 462
12.3.4. Data rounding 465
12.4. Floating point binary representations 466
12.4.1. Floating point dynamics range 470
12.5. Block floating point representation of binary 472
Literature to chapter 12 472
13. DIGITAL PROCESSING INSTRUMENTS OF SIGNALS 474
13.1. Frequency shift without multiplication 474
13.1.1. Frequency shift of s / 2 474
13.1.2. Frequency shift of s / 4 476
13.1.3. Filtration and decimation after moving down by fąşs / 4 479
13.2. Quick approximation of the vector module 482
13.3. Fracturing in the frequency domain 486
13.4. Fast multiplication of complex numbers 489
13.5. Calculation of two N-point real FFTs 490
13.5.1. Realization of two N-point FFT 490
13.5.2. Realization of 2N-point real FFT 497
13.6. Calculation of inverse FFT using a simple FFT 501
13.6.1. The first method of calculating the reverse FFT 501
13.6.2. The second method of calculating the inverse FFT 503
13.7. Simplified structure of the SOI 504 filter
13.8. Quantum noise reduction of the A / C 504 converter
13.8.1. Oversampling 506
13.8.2. Dithering 508
13.9. A / C converter 511 testing techniques
13.9.1. Determining quantization noise using FFT 511
13.9.2. Detection of lost 514 codes
13.10. Rapid SOI filtration using FFT 515
13.11. Generation of random data with a normal distribution 517
13.12. Oxygen phase filtration 519
13.13. Improving the characteristics of SOI 520 filters
13.14. Interpolation of band signal 522
13.15. Peak location algorithm in the 524 spectrum
13.16. Calculation of FFT 526 rotation rates
13.17. Detection of a single tone 529
13.17.1. Goertzel 530 algorithm
13.17.2. Example of using the Goertzel 532 algorithm
13.17.3. Advantages of the Goertzel 532 algorithm
13.18. Sliding DFT 533
13.18.1. The DFT 534 sliding algorithm
13.18.2. Stability of SDFT 538
13.18.3. Reduction of leakage SDFT 539
13.18.4. Little known property of SDFT 540
13.19. Zoom FFT 541
13.20. Practical spectrum analyzer 545
13.21. Effective approximation arctangent 548
13.22. 550 frequency demodulation algorithms
13.23. Removing a fixed component 552
13.23.1. Removing a constant component from data block 553
13.23.2. Removing a fixed component in real-time systems 553
13.23.3. Removing a constant component with real-time quantization 555
13.24. Improving the quality of traditional CIC 556 filters
13.24.1. Non-recursive CIC 557 filters
13.24.2. Non-recursive CIC filters for factor R being the prime number 560
13.25. Smoothing impulse interference 561
13.26. Efficient calculation of polynomial 563
13.27. Designing of very high order SOI filters 564
13.28. Time domain interpolation using FFT 567
13.28.1. Calculation of interpolated real signals 568
13.28.2. Calculation of interpolated analytical signals 570
13.29. Frequency translation by decimation 571
13.30. Automatic gain control 571
13.31. Estimated envelope detection 574
13.32. Quadrature oscillator 575
13.33. Two-mode averaging 578
Literature to chapter 13 579
A. ARITHMETIC NUMBERS OF BANDS 583
A.1. Representation of graces of real and complex numbers 583
A.2. Arithmetic representation of complex numbers 584
A.3. Arithmetic operations on complex numbers 586
A.3.1. Addition and subtraction of complex numbers 586
A.3.2. Multiplication of complex numbers 587
A.3.3. Coupling of complex number 587
A.3.4. Dividing complex numbers 588
A.3.5. Inverse of a complex number 588
A.3.6. Exponentiation of complex numbers 589
A.3.7. The elements of the complex number 589
A.3.8. Natural logarithms of complex number 590
A.3.9. The base 10 logarithm of the complex number 590
A.3.10. The logarithm of the complex number 10, expressed in the natural logarithm 590
A.4. Some practical implications of using complex numbers 591
Literature to Appendix A 592
B. THE EXPRESSION OF A GEOMETRIC RANGE 593
C. REVERSING TIME AND DFT 595
D. AVERAGE VALUE, VARIATION AND STANDARD DEVIATION 598
D.1. Statistical measures 598
D.2. Standard deviation or rms value, continuous sinusoid 601
D.3. Mean value and variance of random signals 602
D.4. The probability density function of a normal distribution 605
Literature to Appendix D 606
E. DECYBELE (dB and dBm) 607
E.1. Use of a logarithmic measure to determine the relative strength of the signal 607
E.2. Some useful decibel numbers 612
E.3. Absolute power expressed in decibels 612
F. TERMINOLOGY OF DIGITAL FILTERS 614
Literature to Appendix F 624
G. CONSIDERATIONS ON SAMPLE FILTERS IN THE FIELD OF FREQUENCY 624
G.1. Impulse response of comb filter 625
G.2. Impulse response of a single fused FSF 626 filter
G.3. Phase dependencies in multi-sectional FSF 627 filters
G.4. Multifunction function of the FSF 628 filter
G.5. The function of the actual transmittance of the FSF 629 filter
G.6. Frequency characteristics of the FSF Type-IV 631 filter
H. TABLES SUPPORTING PROJECTING SAFETY FILTERS IN THE AREA OF FREQUENCY 633
Index 643
Recipients of the book: students of mechanical, mechatronic, electrical and electronic faculties, technical universities and students of post-graduate studies in the field of digital signal processing.
Table of Contents:
PREFACE 11
1. SIGNALS AND DISCRETE SYSTEMS 19
1.1. Discrete signals and their notation 20
1.2. The instantaneous value, absolute value and instantaneous signal strength 26
1.3. Operation symbols in signal processing 28
1.4. Introduction to discrete linear systems unchanged in time 30
1.5. Linear discrete systems 30
1.5.1. Example of a linear system 31
1.5.2. An example of a non-linear system 32
1.6. Systems unchanged in time 35
1.6.1. An example of a system unchanged in time 36
1.7. Interchangeability property of linear invariant systems in time 37
1.8. Analysis of linear systems unchanged over time 37
2. IMMUNE SAMPLE 39
2.1. Aliasing: frequency ambiguity in the frequency domain 39
2.2. Sampling of lowband signals 45
2.3. Sampling of bandwidth signals 48
2.4. Spectral reversal in band sampling 57
3. DISCREET CONVERTATION OF FOURIER 62
3.1. Understanding the DFT 63 equation
3.1.1. Example 1 DFT 66
3.2. Symmetry DFT 75
3.3. DFT 77 linearity
3.4. DFT amplitude spectrum signal 77
3.5. Frequency axis DFT 79
3.6. The transfer claim 79
3.6.1. Example 2 DFT 80
3.7. Reverse DFT 82
3.8. Leakage DFT 83
3.9. Windows 91
3.10. Loss coming from DFT 98 surges
3.11. DFT resolution, zeros refining and frequency sampling 99
3.12. Improvement of the signal / noise ratio using DFT 103
3.12.1. Improvement of the signal / noise ratio of a single DFT 104
3.12.2. Improvement of the signal / noise ratio resulting from averaging multiple DFT 107
3.13. DFT rectangular functions 107
3.13.1. DFT rectangular function in the general form 108
3.13.2. DFT symmetrical rectangular function 114
3.13.3. DFT rectangular function with unit values alone 116
3.13.4. Time and frequency axes associated with rectangular functions 119
3.13.5. Alternate DFT forms of a rectangular function with unit values alone 121
3.13.6. Inverse DFT of the rectangular function in the general form 121
3.13.7. Inverse DFT of the symmetrical rectangular function 124
3.14. DFT of complex stimulation 126
3.15. DFT of actual cosine stimulation 129
3.16. A single-track DFT of excitation being a true cosine signal 131
3.17. Interpretation of DFT 133
Literature to chapter 3 136
4. FASTIER TRANSFORMATION FAST. 137
4.1. The relationship between FFT and DFT 138
4.2. Tips on how to use FFT in practice 139
4.2.1. Sampling fast enough and long enough 139
4.2.2. Pre-processing of time data before determining FFT 140
4.2.3. Correcting FFT results 141
4.2.4. Interpretation of FFT 142 results
4.2.5. Software implementing FFT 143
4.2.6. Derivation of the FFT algorithm with base 2 144
4.3. Bitwise reversal of the FFT 151 I / O index
4.4. FFT butterfly structures with base 2 152
Literature to chapter 4 160
5. FILTERS WITH THE FINISHED PULSON ANSWER 162
5.1. Introduction to filters with finite impulse response - SOI 163 filters
5.2. The weave operation in SOI 168 filters
5.3. Designing low-pass SOI 178 filters
5.3.1. Window design 178
5.3.2. Application of window functions in the design of SOI 186 filters
5.4. Design of bandpass filters SOI 192
5.5. Designing high-pass SOI 195 filters
5.6. Remesis method for designing SOI 196 filters
5.7. Bandwidth SOI 198 filters
5.8. Phase characteristics of SOI 200 filters
5.9. A general description of the discrete plexus 205
5.10. Discrete plexus in time domain 206
5.10.1. The weave statement 210
5.10.2. Application of the weave statement 213
Literature to chapter 5 216
6. FILTERS WITH INFINITE IMPULSE ANSWER 218
6.1. Introduction to filters with infinite impulse response 219
6.2. Laplace transform 222
6.2.1. The poles and zeros on the plane are stability 229
6.3. Transformation from 236
6.3.1. Poles and zeros in the plane for stability 238
6.3.2. The use of the Z transformation for the analysis of NOI 240 filters
6.3.3. Alternative NOI 248 filter structures
6.4. Designing of NOI filters using impulse response invulnerability 250
6.4.1. Example of Impulse Response invulnerability - Method 1 257
6.4.2. Example of impulse response invulnerability design - Method 2 260
6.5. Designing of NOI filters by biline transformation 267
6.5.1. Example of filter design with the use of biline transform 273
6.6. Optimized method of designing NOI 277 filters
6.7. Pitfalls lurking in the construction of digital NOI 279 filters
6.8. Improving NOI filters - cascading 281
6.8.1. Properties of cascade and parallel filters 281
6.8.2. Cascade connection of NOI 283 filters
6.9. A short comparison of NOI and SOI 286 filters
Literature to chapter 6 287
7. SPECIALIZED LOWERPROOF FILTERS SOI 289
7.1. Frequency sampling filters: forgotten art 290
7.1.1. Cascade combination of comb filter and complex digital resonator 292
7.1.2. Multi-section complex filters FSF 297
7.1.3. Ensuring the stability of FSF 301 filters
7.1.4. Multiflex FSF filters with real coefficients of 304
7.1.5. Multiflex FSF filters with real and linear coefficients of 307 phase
7.1.6. Where we were and where we are going with the FSF 309 filters
7.1.7. Effective FSF filter with real coefficients of 310
7.1.8. Modeling of FSF 312 filters
7.1.9. Correction of characteristics using coefficients in the 313 transition band
7.1.10. Alternative filter structures FSF 315
7.1.11. The advantages of FSF 316 filters
7.1.12. Example of an FSF Type IV 318 filter
7.1.13. When to use FSF 319 filters
7.1.14. Designing of FSF 322 filters
7.1.15. Summary of FSF 325 filters
7.2. Interpolated SOI 325 low-pass filters
7.2.1. Selection of the optimal M 330 extension factor
7.2.2. Estimate the number of links in the SOI 331 filter
7.2.3. Modeling of the ISOI 332 filter characteristics
7.2.4. Implementation problems of ISOI 335 filters
7.2.5. Example of ISOI 336 filter design
Literature to chapter 7 338
8. SQUARES SQUARES 340
8.1. Why square signals? 341
8.2. Notation of complex numbers 341
8.3. Representation of real signals using complex indications 347
8.4. A handful of thoughts about the negative frequencies 351
8.5. Quadrature signals in the frequency domain 352
8.6. Banded quadrature signals in the 355 frequency domain
8.7. Complex frequency conversion down 357
8.8. An example of complex frequency conversion down 359
8.9. An alternative method of down-frequency conversion 363
Literature to chapter 8 365
9. HILBERT'S DISCREET TRANSFORM 366
9.1. Denis of the Hilbert transformation 367
9.2. Why do we deal with the Hilbert transformation? 369
9.3. Pulse response of the Hilbert transformer 374
9.4. Designing a discreet Hilbert 376 transformer
9.4.1. Hilbert transformation in time domain: implementation of SOI 376 filter
9.4.2. Hilbert transformation in the frequency domain 380
9.5. Generation of analytical signal in time domain 382
9.6. Comparison of analytical methods of signal generation 384
Literature to chapter 9 385
10. CONVERSION OF SAMPLE FREQUENCY 386
10.1. Decimation 387
10.2. Interpolation 392
10.3. Combination of decimation and interpolation 395
10.4. Polyphase filters 396
10.5. Cascade integration comb filters 402
10.5.1. Recursive summary filter 403
10.5.2. Filter structures CIC 404
10.5.3. Improved attenuation of CIC 409 filters
10.5.4. Implementation aspects of CIC 410 filters
10.5.5. Compensating SOI 412 filters
Literature to chapter 10 414
11. MULTIPURATION OF SIGNALS 416
11.1. Coherent averaging 417
11.2. Non-coherent averaging 423
11.3. Averaging multiple FFTs 426
11.4. Filtering aspects of time averaging 435
11.5. Exponential averaging 436
Literature to chapter 11 442
12. REPRESENTATIONS OF DIGITAL DATA AND THEIR EFFECTS 443
12.1. Fixed-point binary representations 443
12.1.1. Figures in figure 444
12.1.2. Hexadecimal numbers 445
12.1.3. Fractional binary numbers 446
12.1.4. Binary sign-module representation 447
12.1.5. Representation of the supplement to two 447
12.1.6. Representation with a binary offset 449
12.2. Precision and dynamic range of binary numbers 450
12.3. The effects of the finite length of the fixed-point word binary 450
12.3.1. Quantization errors in A / C converters 451
12.3.2. Data overflow 458
12.3.3. Clip 462
12.3.4. Data rounding 465
12.4. Floating point binary representations 466
12.4.1. Floating point dynamics range 470
12.5. Block floating point representation of binary 472
Literature to chapter 12 472
13. DIGITAL PROCESSING INSTRUMENTS OF SIGNALS 474
13.1. Frequency shift without multiplication 474
13.1.1. Frequency shift of s / 2 474
13.1.2. Frequency shift of s / 4 476
13.1.3. Filtration and decimation after moving down by fąşs / 4 479
13.2. Quick approximation of the vector module 482
13.3. Fracturing in the frequency domain 486
13.4. Fast multiplication of complex numbers 489
13.5. Calculation of two N-point real FFTs 490
13.5.1. Realization of two N-point FFT 490
13.5.2. Realization of 2N-point real FFT 497
13.6. Calculation of inverse FFT using a simple FFT 501
13.6.1. The first method of calculating the reverse FFT 501
13.6.2. The second method of calculating the inverse FFT 503
13.7. Simplified structure of the SOI 504 filter
13.8. Quantum noise reduction of the A / C 504 converter
13.8.1. Oversampling 506
13.8.2. Dithering 508
13.9. A / C converter 511 testing techniques
13.9.1. Determining quantization noise using FFT 511
13.9.2. Detection of lost 514 codes
13.10. Rapid SOI filtration using FFT 515
13.11. Generation of random data with a normal distribution 517
13.12. Oxygen phase filtration 519
13.13. Improving the characteristics of SOI 520 filters
13.14. Interpolation of band signal 522
13.15. Peak location algorithm in the 524 spectrum
13.16. Calculation of FFT 526 rotation rates
13.17. Detection of a single tone 529
13.17.1. Goertzel 530 algorithm
13.17.2. Example of using the Goertzel 532 algorithm
13.17.3. Advantages of the Goertzel 532 algorithm
13.18. Sliding DFT 533
13.18.1. The DFT 534 sliding algorithm
13.18.2. Stability of SDFT 538
13.18.3. Reduction of leakage SDFT 539
13.18.4. Little known property of SDFT 540
13.19. Zoom FFT 541
13.20. Practical spectrum analyzer 545
13.21. Effective approximation arctangent 548
13.22. 550 frequency demodulation algorithms
13.23. Removing a fixed component 552
13.23.1. Removing a constant component from data block 553
13.23.2. Removing a fixed component in real-time systems 553
13.23.3. Removing a constant component with real-time quantization 555
13.24. Improving the quality of traditional CIC 556 filters
13.24.1. Non-recursive CIC 557 filters
13.24.2. Non-recursive CIC filters for factor R being the prime number 560
13.25. Smoothing impulse interference 561
13.26. Efficient calculation of polynomial 563
13.27. Designing of very high order SOI filters 564
13.28. Time domain interpolation using FFT 567
13.28.1. Calculation of interpolated real signals 568
13.28.2. Calculation of interpolated analytical signals 570
13.29. Frequency translation by decimation 571
13.30. Automatic gain control 571
13.31. Estimated envelope detection 574
13.32. Quadrature oscillator 575
13.33. Two-mode averaging 578
Literature to chapter 13 579
A. ARITHMETIC NUMBERS OF BANDS 583
A.1. Representation of graces of real and complex numbers 583
A.2. Arithmetic representation of complex numbers 584
A.3. Arithmetic operations on complex numbers 586
A.3.1. Addition and subtraction of complex numbers 586
A.3.2. Multiplication of complex numbers 587
A.3.3. Coupling of complex number 587
A.3.4. Dividing complex numbers 588
A.3.5. Inverse of a complex number 588
A.3.6. Exponentiation of complex numbers 589
A.3.7. The elements of the complex number 589
A.3.8. Natural logarithms of complex number 590
A.3.9. The base 10 logarithm of the complex number 590
A.3.10. The logarithm of the complex number 10, expressed in the natural logarithm 590
A.4. Some practical implications of using complex numbers 591
Literature to Appendix A 592
B. THE EXPRESSION OF A GEOMETRIC RANGE 593
C. REVERSING TIME AND DFT 595
D. AVERAGE VALUE, VARIATION AND STANDARD DEVIATION 598
D.1. Statistical measures 598
D.2. Standard deviation or rms value, continuous sinusoid 601
D.3. Mean value and variance of random signals 602
D.4. The probability density function of a normal distribution 605
Literature to Appendix D 606
E. DECYBELE (dB and dBm) 607
E.1. Use of a logarithmic measure to determine the relative strength of the signal 607
E.2. Some useful decibel numbers 612
E.3. Absolute power expressed in decibels 612
F. TERMINOLOGY OF DIGITAL FILTERS 614
Literature to Appendix F 624
G. CONSIDERATIONS ON SAMPLE FILTERS IN THE FIELD OF FREQUENCY 624
G.1. Impulse response of comb filter 625
G.2. Impulse response of a single fused FSF 626 filter
G.3. Phase dependencies in multi-sectional FSF 627 filters
G.4. Multifunction function of the FSF 628 filter
G.5. The function of the actual transmittance of the FSF 629 filter
G.6. Frequency characteristics of the FSF Type-IV 631 filter
H. TABLES SUPPORTING PROJECTING SAFETY FILTERS IN THE AREA OF FREQUENCY 633
Index 643
177166
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