Spectral Measurements of Sliding Tones

The response of a spectrum analyzer to sliding tones is considered. A sliding tone is defined as a frequency which changes linearly with time. It is assumed that the spectrum analyzer is the equivalent of a bank of filters whose outputs are measured at. a single point in time. The problem of obtaining spectral measurements is treated in the frequency domain. Results are first developed for the spectral density of a finite fixed duration sinusoid of linearly time varying frequency, from an interpretation of the Cornu spiral. This is referred to as the input spectrum. The response of a filter to a sliding tone is then determined by convolution of the input spectrum with the selectivity characteristics of the filter. The filter selectivity characteristic is obtained by Fourier transforming a periodic representation of the filter impulsive response. This approach to computation of the filter response to sliding tones provides a convenient interpretation of the effects of the characteristics of the filter and the input and facilitates computation of the filtering action. In addition it helps suggest filter characteristics that are desirable from a spectral measurement point of view. Results are presented which indicate the response of a variety of filters to a sliding tone input. The contribution of the approach presented to the evaluation of the response of filters to sliding tones has the two major advantages of: 1. Its usefulness for approximate analysis and the interpretation of the effects of filter and signal parameters. 2. The ease and economy of computation of accurate results. For completeness, filter responses to a very rapidly sliding tone are discussed from the time domain point of view.