Jitter is the deviation of a signal's transitions from ideal time positions. Excess jitter is undesireable in a communication system, as it can lead to increased bit error rate and degraded signal quality. This paper begins with an overview of the present state-of-the-art with respect to jitter analysis of data waveforms: The main characteristics of jitter are described, and corresonding measurement techniques are discussed. Waveform capture using both real-time and equivalent time oscillioscopes are described and compared. The need to interpolate between consecutive samples in order to precisely determine the threshold crossing times for data transitions is discussed, and the interpolation method, using the Fast Fourier Transform (FFT) and zero-padding, is demonstrated using MATLAB (technical programming and plotting software). The concept of jitter spectrum is presented, useful in determining the sources of jitter, showing both individual frequency components of jitter, as well as spectral density curves for jitter contributions spread over a range of frequencies. Presently, the popular method of jitter spectrum analysis performs the FFT on the sequence of time jitter values, with data points only obtained when there is a bit value transition. This method works well when processing signals with uniform spacing of transitions, such as clock signals, but is severely limited when processing pseudo-random binary sequences. This is due to the random occurance of the bit transition, typically with 50% probability at any particular data bit boundary. Therefore the jitter vs. time data no longer represents a uniform time sampled signal; hence the FFT no longer provides a faithful representation of the spectral content of the jitter. A new jitter spectral analysis method is proposed which avoids the limitations of the established method. The new technique calculates jitter values for bit transitions. The sequence of jitter values is now uniform time spaced, and the FFT now provides a more accurate estimate of spectral content. The improved ability of the new method to resolve spectral components of jitter is demonstrated using MATLAB, with plots clearly showing the improvement over the earlier method of ignoring non-transition bit boundaries.