Exact Formulation of Window Functions for Analog Network Spectral Analyzers

An equation for the spectral window function for analog network analyzers is derived without assumptions on length of data interval available. The equation, given in terms of filter pole-zero locations for both the filter-bank and heterodyned-input type analyzers, can be programmed on a digital computer without difficulty. As an illustration, the "growth" of a spectral window with increasing length of available data is shown for a special case: a single-tuned circuit followed by a squaring circuit and perfect integrator. The error in using the usual approximation also is indicated. Use of the derived equation for quantitative comparisons of analog and digital analyzers is noted.