The thesis summarizes a selection of my research within Synthetic Aperture Radar (SAR). Mainly the research is aimed at applying and developing signal processing methods to single channel and multi channel SAR for wideband systems. SAR systems can generate images looking very similar to optical pictures, i.e. photos, and sometimes with much finer resolution compared to optical systems orbiting Earth. SAR has also for instance been used to obtain fine resolution images of the moon, Venus and the satellites of Saturn. Other applications for SAR has is to detect changes in ice sheets and deforestation. In this thesis, SAR systems capable of very high resolution imaging are con- sidered, and data from such systems, namely the VHF system CARABAS-II and the UHF system LORA, is used. High resolution imaging in this thesis refers to high resolution with regard to wavelength, this independent of system operating frequency. Two of the topics in this thesis are related to detection and parameter estimation of moving objects in SAR, the first one using CARABAS-II data and the second with LORA data. On the CARABAS-II data, a speed estimation and refocusing method is introduced and applied to single channel CARABAS-II data. The results show good estimation accuracy as well as good ability to focus the object and suppress forest clutter by ap- plying the refocusing algorithm. The results on LORA data are satisfactory especially with regard to forest clutter suppression. The ability to detect and focus images of ships allow for surveillance of coastal areas and help in rescue of ships lost at sea. Detection and location of cars and trucks allow for traffic monitoring to obtain statistics of how many cars travel the roads and their speed. In the thesis, two more important aspects for SAR processing is presented. One paper presents windowing of UWB SAR images. A strong object such as a power line in a SAR image cause ringing on both sides of the power line. This ringing can cause a small house to be covered by these so called side lobes. Applying a window can make these side lobes in the image much suppressed, however if windowing too much, the power line will smear over the image, covering the small house. The last topic in the thesis concern with theoretical limits for measurement accuracy of parameters for a moving object in a SAR image. These parameters are position, velocity, radar cross section and phase. The theoretical expressions are verified using simulations for a single channel system for estimation accuracy of target speed and relative speed.