The analysis of the distortion which results when frequency-modulated waves are passed through linear networks is investigated by the Fourier method and the Quasi-steady-state method. The major enphasis is placed on the Fourier method, and extensive digital computer programs are developed to allow this method to be implemented on the modern, high-speed digital computer. In the Fourier method, the frequency-modulated wave which is applied to the input of a linear network is broken up into its Fourier spectrum. Each of the resulting ‘'sideband'' frequencies is then passed through the network and is subjected to alterations in amplitude and phase. The output wave is then synthesized by taking the vector sum of the "weighted" sideband components. In contrast to the single pair of sideband frequencies generated by amplitude modulation, the spectrum of a frequency-modulated wave contains an infinite number of sideband components. Fortunately, only a relatively small number of these sidebands have significant influence on the total makeup of the waveform. The number of significant sidebands is proportional to the value of modulation index. When the modulation index is high, the number of significant sidebands is very large and the number of computations required by the Fourier method becomes enormous. Previously considered to be completely impractical, the Fourier method was usually abandoned in favor of the Quasi-steady-state approach. However, the digital computer techniques developed in the course of this investigation allow for a fast, economical, and convenient analysis based on the Fourier method even when the modulation index is relatively high. Analyses were performed for values of modulation index up to 45 and techniques are discussed for increasing this range. The Quasi-steady-state method is based on the assumption that the frequency of the input wave is changing slowly enough that the frequency of the output wave at any instant is equal to the "instantaneous fregquency' of the input wave. This method is inherently in error since it neglects the transient terms generated by the changing frequency. To compensate for this error, it is the general practice to incorporate correction terms, usually in the form of an infinite series. The Quasi-steady-state method is more effective at low modulating frequencies (high modulation index). While the analysis contained in this paper considers in detail only a first-order correction, the application of higher-order correction terms is discussed. The results obtained from applying both analyses to a complex, multi-section filter indicate that the computer solution of the Fourier method is preferable for intermediate values of modulation index. Experimental verification of the Fourier method is obtained by simulating the system on an analog computer. The advantages of this rather novel approach are discussed in some detail. The agreement between the results predicted by the digital computer and those obtained experimentally leaves no doubt to the validity and accuracy of the analysis. Digital computer programs for analyzing the distortion using each of the above methods are given. Subprograms are also included, some of which can be used independently. Among these are a program that computes Bessel functions of the first kind for positive and negative orders and a program that computes the minimum phase shift of a network from its atténuation. All programs are written in the FORTRAN IV computer language and were executed on the IBM 7040/1401 system. / Ph. D.