Transforms and Fast Algorithms for Signal Analysis and Representations

1 Introduction. - 1. 1 Discrete linear transforms. - 1. 2 Fast algorithms. - 1. 3 New transforms. - 1. 4 Organization of the book. - References. - 2 Polynomial Transforms and Their Fast Algorithms. - 2. 1 Basic number theory. - 2. 2 Basic polynomial theory. - 2. 3 1D polynomial transform. - 2. 4 Fast polynomial transform. - 2. 5 MD polynomial transform and fast algorithm. - 2. 6 Chapter summary. - References. - 3 Fast Fourier Transform Algorithms. - 3. 1 Introduction. - 3. 2 Radix-2 and split-radix algorithms. - 3. 3 Generalized split-radix algorithm. - 3. 4 Prime factor algorithms. - 3. 5 Generalized 2D split-radix algorithms. - 3. 6 Fast algorithms for generalized DFT. - 3. 7 Polynomial transform algorithms for MD DFT. - 3. 8 Chapter summary. - 4 Fast Algorithms for 1D Discrete Hartley Transform. - 4. 1 Introduction. - 4. 2 Split-radix algorithms. - 4. 3 Generalized split-radix algorithms. - 4. 4 Radix-2 algorithms for type-II -III and -IV DHTs. - 4. 5 Prime factor algorithms. - 4. 6 Radix-q algorithms. - 4. 7 Fast algorithms using type-I DHT. - 4. 8 Chapter summary. - 5 Fast Algorithms for MD Discrete Hartley Transform. - 5. 1 Introduction. - 5. 2 Split-radix algorithms for 2D type-I DHT. - 5. 3 Fast algorithms for 2D type-II -III and -IV DHTs. - 5. 4 Fast algorithms based on type-I DHT. - 5. 5 PT-based radix-2 algorithm for MD type-I DHT. - 5. 6 PT-based radix-2 algorithm for MD type-II DHT. - 5. 7 PT-based radix-q algorithm for MD type-I DHT. - 5. 8 PT-based radix-q algorithm for MD type-II DHT. - 5. 9 Chapter summary. - References. - 6 Fast Algorithms for 1D Discrete Cosine Transform. - 6. 1 Introduction. - 6. 2 Radix-2 algorithms. - 6. 3 Prime factor algorithms. - 6. 4 Radix-q algorithms. - 6. 5 Fast algorithms based on type-I bCT. - 6. 6 Chapter summary. - 7 Fast Algorithms for MD Discrete Cosine Transform. - 7. 1 Introduction. - 7. 2 Algorithms for 2Dtype-I -II and -III DCTs. - 7. 3 Prime factor algorithm for MD DCT. - 7. 4 PT-based radix-2 algorithm for MD type-II DCT. - 7. 5 PT-based radix-2 algorithm for MD type-III DCT. - 7. 6 PT-based radix-q algorithm for MD type-II DCT. - 7. 7 PT-based radix-q algorithm for MD type-III DCT. - 7. 8 Chapter summary. - 8 Integer Transforms and Fast Algorithms. - 8. 1 Introduction. - 8. 2 Preliminaries. - 8. 3 Integer DCT and fast algorithms. - 8. 4 Integer DHT and fast algorithms. - 8. 5 MD Integer DCT and fast algorithms. - 8. 6 MD Integer DHT and fast algorithms. - 8. 7 Chapter summary. - References. - 9 New Methods of Time-Frequency Analysis. - 9. 1 Introduction. - 9. 2 Preliminaries. - 9. 3 Harmonic transform. - 9. 4 Tomographic time-frequency transform. - 9. 5 Chapter summary. - References. Language: English