A bound involving n-dimensional instantaneous frequency

The author states and proves an integral inequality that bounds the absolute difference epsilon (x)= mod m(x) -m(x) mod where m(x) is the response of a modulated n-dimensional real linear filter w to a complex exponential signal with n-dimensional instantaneous frequency Delta u(x) and m(x)= mod W( Delta u(x)-u/sub 0/) mod where W is the Fourier transform of w. The quantity of epsilon (x) provides an estimate of the error incurred by using m(x) as an estimate of m(x), e.g., if Delta u(x) is unknown. Such estimates may be applied to the problem of measuring the n-dimensional instantaneous frequency of certain nonstationary phase-modulated signals.<
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