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1 | (24) |
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1.1 Synthesis of an Impulse by Cosine Waves |
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1 | (1) |
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1.2 Synthesis of Rectangular Waveforms by Sine and Cosine Waves |
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2 | (2) |
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4 | (1) |
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1.4 Harmonics and Waveforms |
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5 | (3) |
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8 | (1) |
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1.6 Shift of Harmonics on the Time Axis |
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9 | (2) |
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1.7 Complex Exponential Functions and Sine and Cosine Functions |
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11 | (4) |
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1.8 Phases of Cosine and Sine Functions |
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15 | (2) |
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1.9 Synthesis of Sine Wave with Arbitrary Phase |
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17 | (3) |
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1.10 Instantaneous Phase and Frequency |
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20 | (3) |
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23 | (2) |
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2 Fourier Series Expansion |
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25 | (26) |
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2.1 Integrals of Sine and Cosine Functions |
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25 | (3) |
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2.2 Calculations of Fourier Coefficients |
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28 | (4) |
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2.3 Expressing Waveforms by Even Functions |
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32 | (4) |
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2.4 Expressing Waveforms by Odd Functions |
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36 | (2) |
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2.5 Expressing Waveforms by Complex Exponential Functions |
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38 | (3) |
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41 | (5) |
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46 | (3) |
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49 | (2) |
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3 Numerical (Digitized) Waveforms |
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51 | (26) |
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3.1 Fourier Series Expansion of Spectrum |
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51 | (5) |
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3.2 Reproduction of the Continuous Waveform from the Sequence of Sample Values |
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56 | (2) |
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3.3 Frequency Bandwidth and Sampling Frequency |
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58 | (2) |
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3.4 Smoothing of Sample Sequence by Low-Pass Filtering |
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60 | (2) |
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62 | (1) |
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3.6 Smoothing of a Sample Sequence Using the Sampling Theorem |
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63 | (2) |
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3.7 Folding (Aliasing) of the Spectrum |
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65 | (4) |
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3.8 Sampling Frequency Conversion I (Application of the Fourier Transform) |
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69 | (3) |
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3.9 Sampling Frequency Conversion II (Application of LPF) |
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72 | (2) |
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74 | (3) |
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4 Discrete Fourier Transform |
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77 | (30) |
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4.1 Fourier Transform of Discrete Sequence of Numbers |
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77 | (3) |
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4.2 Inverse Discrete Fourier Transform (IDFT) |
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80 | (4) |
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4.3 The DFT and the Fourier Transform |
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84 | (3) |
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87 | (7) |
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4.4.1 Sine and Cosine Waves |
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87 | (1) |
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88 | (1) |
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89 | (2) |
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4.4.4 Symmetric and Antisymmetric Waveforms |
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91 | (1) |
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4.4.5 Sine Waveforms with Noninteger Frequencies |
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92 | (1) |
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4.4.6 Too Wide Sample Spacing |
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92 | (2) |
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94 | (1) |
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4.5 Discrete Cosine Transform (DCT) |
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94 | (6) |
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4.6 Extension of the Discrete Cosine Transform |
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100 | (4) |
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104 | (3) |
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107 | (24) |
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5.1 Decimation in Time Algorithm |
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107 | (4) |
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5.2 Decimation in Frequency Algorithm |
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111 | (3) |
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5.3 2m-Point FFT by Decimation in Time Algorithm |
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114 | (7) |
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5.4 2m-Point FFT by Decimation in Frequency Algorithm |
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121 | (4) |
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5.5 Rearrangement of the Bit-Reversed Order |
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125 | (3) |
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5.6 Speed-Up Technique by Parallel Computation |
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128 | (2) |
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130 | (1) |
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131 | (22) |
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131 | (4) |
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6.2 Uncertainty Principle |
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135 | (3) |
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6.3 Spreading of the Spectrum |
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138 | (1) |
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6.4 Analysis of Short Waves |
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139 | (5) |
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144 | (2) |
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6.6 Removal of Discontinuity by the Adjustment of the Sampling Frequency |
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146 | (2) |
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6.7 Removal of Discontinuity by the Weighting of Sample Sequences |
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148 | (3) |
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151 | (2) |
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153 | (30) |
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7.1 Fourier Transform of a Product of Two Time Functions |
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153 | (2) |
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7.2 Spectra of Tapered Functions |
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155 | (4) |
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7.3 DFT of Short Waveforms |
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159 | (2) |
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161 | (18) |
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161 | (2) |
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7.4.2 Hanning Window (Von Hann Window) |
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163 | (4) |
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167 | (1) |
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7.4.4 Blackman-Harris Window |
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168 | (2) |
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7.4.5 Half-Sine Window and Riesz Window |
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170 | (3) |
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173 | (3) |
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176 | (1) |
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177 | (2) |
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7.5 Comparison of Windows by the Results of Frequency Analysis |
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179 | (2) |
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181 | (2) |
| Appendix |
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183 | (10) |
| References |
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193 | (2) |
| Answers |
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195 | (6) |
| Index |
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201 | |
Lisainfo e-raamatute kohta