Fourier Transforms

1 Signals and Systems. - 1. 1 Waveforms and Sequences. - 1. 2 Basic Signal Examples. - 1. 3 Random Signals. - 1. 4 Systems. - 1. 5 Linear Combinations. - 1. 6 Shifts. - 1. 7 Two-Dimensional Signals. - 1. 8 Sampling Windowing and Extending. - 1. 9 Probability Functions. - 1. 10 Problems. - 2 The Fourier Transform. - 2. 1 Basic Definitions. - 2. 2 Simple Examples. - 2. 3 Cousins of the Fourier Transform. - 2. 4 Multidimensional Transforms. - 2. 5 * The DFT Approximation to the CTFT. - 2. 6 The Fast Fourier Transform. - 2. 7 * Existence Conditions. - 2. 8 Problems. - 3 Fourier Inversion. - 3. 1 Inverting the DFT. - 3. 2 Discrete Time Fourier Series. - 3. 3 Inverting the Infinite Duration DTFT. - 3. 4 Inverting the CTFT. - 3. 5 Continuous Time Fourier Series. - 3. 6 Duality. - 3. 7 Summary. - 3. 8 * Orthonormal Bases. - 3. 9 * Discrete Time Wavelet Transforms. - 3. 10 * Two-Dimensional Inversion. - 3. 11 Problems. - 4 Basic Properties. - 4. 1 Linearity. - 4. 2 Shifts. - 4. 3 Modulation. - 4. 4 Parseval's Theorem. - 4. 5 The Sampling Theorem. - 4. 6 The DTFT of a Sampled Signal. - 4. 7 * Pulse Amplitude Modulation (PAM). - 4. 8 The Stretch Theorem. - 4. 9 * Downsampling. - 4. 10 * Upsampling. - 4. 11 The Derivative and Difference Theorems. - 4. 12 Moment Generating. - 4. 13 Bandwidth and Pulse Width. - 4. 14 Symmetry Properties. - 4. 15 Problems. - 5 Generalized Transforms and Functions. - 5. 1 Limiting Transforms. - 5. 2 Periodic Signals and Fourier Series. - 5. 3 Generalized Functions. - 5. 4 Fourier Transforms of Generalized Functions. - 5. 5 * Derivatives of Delta Functions. - 5. 6 * The Generalized Function ?(g(t)). - 5. 7 Impulse Trains. - 5. 8 Problems. - 6 Convolution and Correlation. - 6. 1 Linear Systems and Convolution. - 6. 2 Convolution. - 6. 3 Examples of Convolution. - 6. 4 The Convolution Theorem. - 6. 5 Fourier Analysis of Linear Systems. - 6. 6 The Integral Theorem. - 6. 7Sampling Revisited. - 6. 8 Correlation. - 6. 9 Parseval's Theorem Revisited. - 6. 10 * Bandwidth and Pulsewidth Revisited. - 6. 11 * The Central Limit Theorem. - 6. 12 Problems. - 7 Two Dimensional Fourier Analysis. - 7. 1 Properties of 2-D Fourier Transforms. - 7. 2 Two Dimensional Linear Systems. - 7. 3 Reconstruction from Projections. - 7. 4 The Inversion Problem. - 7. 5 Examples of the Projection-Slice Theorem. - 7. 6 Reconstruction. - 7. 7 * Two-Dimensional Sampling Theory. - 7. 8 Problems. - 8 Memoryless Nonlinearities. - 8. 1 Memoryless Nonlinearities. - 8. 2 Sinusoidal Inputs. - 8. 3 Phase Modulation. - 8. 4 Uniform Quantization. - 8. 5 Problems. - A Fourier Transform Tables. Language: English