The development of communications technologies has led to an ever-increasing requirement for a wider bandwidth of microwave signal processing systems. To overcome the inherent electronic speed limitations, photonic techniques have been developed for the processing of ultra-broadband microwave signals. A dispersive delay line (DDL) is able to introduce different time delays to different spectral components, which are used to implement signal processing functions, such as time reversal, time delay, dispersion compensation, Fourier transformation and pulse compression. An electrical DDL is usually implemented based on a surface acoustic wave (SAW) device or a synthesized C-sections microwave transmission line, with a bandwidth limited to a few GHz. However, an optical DDL can have a much wider bandwidth up to several THz. Hence, an optical DDL can be used for the processing of an ultra-broadband microwave signal. In this thesis, we will focus on using a DDL based on a linearly chirped fiber Bragg grating (LCFBG) for the processing of broadband microwave signals. Several signal processing functions are investigated in this thesis. 1) A broadband and precise microwave time reversal system using an LCFBG-based DDL is investigated. By working in conjunction with a polarization beam splitter, a wideband microwave waveform modulated on an optical pulse can be temporally reversed after the optical pulse is reflected by the LCFBG for three times thanks to the opposite dispersion coefficient of the LCFBG when the optical pulse is reflected from the opposite ends. A theoretical bandwidth as large as 273 GHz can be achieved for the time reversal. 2) Based on the microwave time reversal using an LCFBG-based DDL, a microwave photonic matched filter is implemented for simultaneously generating and compressing an arbitrary microwave waveform. A temporal convolution system for the calculation of real time convolution of two wideband microwave signals is demonstrated for the first time. 3) The dispersion of an LCFBG is determined by its physical length. To have a large dispersion coefficient while maintaining a short physical length, we can use an optical recirculating loop incorporating an LCFBG. By allowing a microwave waveform to travel in the recirculating loop multiple times, the microwave waveform will be dispersed by the LCFBG multiple times, and the equivalent dispersion will be multiple times as large as that of a single LCFBG. Based on this concept, a time-stretch microwave sampling system with a record stretching factor of 32 is developed. Thanks to the ultra-large dispersion, the system can be used for single-shot sampling of a signal with a bandwidth up to a THz. The study in using the recirculating loop for the stretching of a microwave waveform with a large stretching factor is also performed. 4) Based on the dispersive loop with an extremely large dispersion, a photonic microwave arbitrary waveform generation system is demonstrated with an increased the time-bandwidth product (TBWP). The dispersive loop is also used to achieve tunable time delays by controlling the number of round trips for the implementation of a photonic true time delay beamforming system.