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Photonic signal processing offers the prospect of realizing extremely high multigigahertz sampling frequencies, overcoming inherent electronic limitations. This stems from the intrinsic excellent delay properties of optical delay lines. These processors provide new capabilities for realizing high time-bandwidth operation and high-resolution performance. In-fiber signal processors are inherently compatible with fiber-optic microwave systems and can provide connectivity with built-in signal conditioning. Fundamental principles of photonic signal processing, including sampling, tuning, and noise, are discussed. Structures that can extend the performance of photonic signal processors are presented, including methods for improving the filter shape characteristics of interference mitigation filters, techniques to increase the stopband attenuation of bandpass filters, and methods to achieve large free spectral range. Several photonic signal processors, including high-resolution microwave filters, widely tunable filters, arbitrary waveform generators, and fast signal correlators, are discussed. Techniques to solve the fundamental noise problem in photonic signal processors are described, and coherence-free structures for few-tap notch filters are discussed. Finally, a new concept for realizing multiple-tap coherence-free processor filters, based on a new frequency-shifting technique, is presented. The structure not only eliminates the phase-induced intensity noise limitation, but can also generate a large number of taps to enable the achievement of processors with high performance and high resolution.