unitary transforms of the signals

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UNITARY TRANSFORMS UNITARY TRANSFORMS OF THE SIGNALS OF THE SIGNALS 1. General unitary transforms 1. General unitary transforms 2. Unitary transforms utilizing 2. Unitary transforms utilizing sinusoidal basis functions sinusoidal basis functions 2.1. Cosine transform 2.1. Cosine transform 2.2. Sine transform 2.2. Sine transform 2.3. Hartley transform 2.3. Hartley transform 3. Unitary transform using 3. Unitary transform using no sinusoidal functions no sinusoidal functions 3.1. Hadamard transform 3.1. Hadamard transform 3.2. Haar transform 3.2. Haar transform

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1. General unitary transforms2. Unitary transforms utilizing sinusoidal basis functions2.1. Cosine transform2.2. Sine transform2.3. Hartley transform3. Unitary transform using no sinusoidal functions3.1. Hadamard transform3.2. Haar transform

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Page 1: UNITARY TRANSFORMS OF THE SIGNALS

UNITARY TRANSFORMS UNITARY TRANSFORMS OF THE SIGNALSOF THE SIGNALS

1. General unitary transforms1. General unitary transforms2. Unitary transforms utilizing 2. Unitary transforms utilizing

sinusoidal basis functionssinusoidal basis functions2.1. Cosine transform2.1. Cosine transform2.2. Sine transform2.2. Sine transform2.3. Hartley transform2.3. Hartley transform3. Unitary transform using 3. Unitary transform using no sinusoidal functionsno sinusoidal functions3.1. Hadamard transform3.1. Hadamard transform3.2. Haar transform3.2. Haar transform

Page 2: UNITARY TRANSFORMS OF THE SIGNALS

General unitary transformsGeneral unitary transforms

Page 3: UNITARY TRANSFORMS OF THE SIGNALS

The separable transformations

Page 4: UNITARY TRANSFORMS OF THE SIGNALS

Realization of separable 2D unitary transforms

Page 5: UNITARY TRANSFORMS OF THE SIGNALS

2. Unitary transforms utilizing 2. Unitary transforms utilizing sinusoidal basis functionssinusoidal basis functions

2.1. Cosine transform2.1. Cosine transform

2.2. Sine transform2.2. Sine transform

2.3. Hartley transform2.3. Hartley transform

Page 6: UNITARY TRANSFORMS OF THE SIGNALS

Cosine transform

Page 7: UNITARY TRANSFORMS OF THE SIGNALS

Cosine transform basis functions

Page 8: UNITARY TRANSFORMS OF THE SIGNALS
Page 9: UNITARY TRANSFORMS OF THE SIGNALS

Cosine transformCosine transform

Page 10: UNITARY TRANSFORMS OF THE SIGNALS

Sine transform

Page 11: UNITARY TRANSFORMS OF THE SIGNALS

Sine transform basis functions

Page 12: UNITARY TRANSFORMS OF THE SIGNALS

Sine transformSine transform

Page 13: UNITARY TRANSFORMS OF THE SIGNALS

Hartley transform

Page 14: UNITARY TRANSFORMS OF THE SIGNALS

Hartley transformHartley transform

Page 15: UNITARY TRANSFORMS OF THE SIGNALS

3. Unitary transform using 3. Unitary transform using no sinusoidal functions no sinusoidal functions

3.1. Hadamard transform3.1. Hadamard transform

3.2. Haar transform3.2. Haar transform

Page 16: UNITARY TRANSFORMS OF THE SIGNALS

Hadamard matrix

Page 17: UNITARY TRANSFORMS OF THE SIGNALS

Hadamard matrix

Page 18: UNITARY TRANSFORMS OF THE SIGNALS

Hadamard matrix

Page 19: UNITARY TRANSFORMS OF THE SIGNALS

Hadamard matrix

Page 20: UNITARY TRANSFORMS OF THE SIGNALS

Hadamard transform basis functions

Page 21: UNITARY TRANSFORMS OF THE SIGNALS

Hadamard transformHadamard transform

Page 22: UNITARY TRANSFORMS OF THE SIGNALS

Haar matrix

Page 23: UNITARY TRANSFORMS OF THE SIGNALS

Haar matrix

Page 24: UNITARY TRANSFORMS OF THE SIGNALS

Haar transform basis functions

Page 25: UNITARY TRANSFORMS OF THE SIGNALS

Haar transformHaar transform