The first part of this work describes a method for calculating the impulse and step response of a linear system from the real part of its frequency response. The real part is approximated by confluent straight line segments up to a truncation frequency, and by an even inverse power of frequency beyond that. Criteria for choosing a truncation frequency and the required inverse power are discussed. Using the amplitudes of the real part at the junctions of the straight line segments, the truncation frequency, and the inverse power, the impulse and step response can be calculated using the tables and curves given. The second part describes a synthesis procedure. The central idea in this is the description of the real part of the frequency response of systems by the harmonic content of the section up to a truncation frequency, and by an even inverse power of frequency beyond that. In this way real parts corresponding approximately to a wide range of systems with a specified pole-zero excess can be formed. Performance indices relating the transient and frequency performances corresponding to each such real part have been found, and are presented in the form of performance curves. By means of these curves target systems meeting a range of performance indices may be chosen. Prom the frequency response of the target system and the open loop constraint, the frequency response of the required cascade compensation is found. This is then approximated by a rational transfer function from which the necessary compensating network can be synthesised.