United States of America As Represented by the Secretary of the Air Force

William S McCormick

James B Tsui

James B Y Tsui

John M Emmert

John J Schamus

A Fourier transformation system usable for example in an electronic warfare radio receiver for analyzing spectral content of multiple transmitter-sourced brief duration incoming signals for characteristics including frequency component and frequency component amplitude content. The Fourier transformation system includes a plurality of approximated Kernel function values disposed at a plurality of locations about a real-imaginary coordinate axis origin and displaced from the origin by magnitudes having real and imaginary component lengths of unity and powers of two. Multiplication involving a power of two component during a Fourier transformation are achieved in a simple manner commensurate with a multiplication by unity in complexity but involving a binary number shift multiplication operation in lieu of a full fledged digital multiplication. Signal results comparisons with more simplified and more complex Kernel function approximations are also included.

Quadbit kernel function algorithm and receiver

In multiple frequency estimation, the bandwidth and resolution of Fast Fourier Transform (FFT) based frequency estimators are limited by A/D converter sampling rate constraints and also by real-time computational requirements. The disclosed configuration uses a Modified Chinese Remainder Theorem of a paper entitled, 'A Noise Insensitive Solution to an Ambiguity Problem in Spectra Estimation' by McCormick et al and a subsampling approach of U.S. Pat. No. 5,099,194 entitled, 'Digital Frequency Measurement Receiver With Bandwidth Improvement Through Multiple Sampling of Real Signals' to resolve the frequency ambiguity problem. The configuration extends these ideas to the multiple frequency case. It significantly extends system bandwidth by operating I FFT units in parallel at specific sampling rates chosen to maximize system bandwidth for a fixed level of noise protection. Each FFT unit output is processed by a 'peak detecting' algorithm that detects the M remainders of the M frequencies for the sampling frequency, F.sub.i, of that particular FFT unit. Using a multiple frequency ambiguity resolution algorithm, the M frequencies are estimated from the I sets of M remainders. The configuration essentially resolves the 2.pi. or aliasing ambiguity problem for multiple frequencies in a parallel, highly efficient manner. In its current configuration, the system is designed for complex signal inputs.

Frequency measurement receiver with means to resolve an ambiguity in

The receiver through an improved Prony method provides a measure of the frequencies, the angle of arrival (AOA) and the phase of signals at the receiver. The device comprises two antennas spaced a known distance apart. These antennas receive signals at different angles. Signals from the antennas are sent to delay lines. Each delay line experiences a different delay period. Signals are then sent to four correlator circuits whose outputs are analog signals which contain all the information required to solve for the frequencies and the angles of arrival of signals at the receiver. The signals are supplied to a digital processor where a mathematical method is used to solve for the frequencies, the phases and the angles of arrival of signals at the receiver.

Instantaneous frequency measurement (IFM) receiver to measure frequency

The IFM receiver employs only two delay lines, thereby simplifying the IFM receiver design. The basic principle is to use two delay lines to provide fine frequency resolution, and at the same time cover a wide input bandwidth. The two delay line lengths must be relatively prime. The algorithm for achieving frequency resolution is based on the Chinese remainder theorem. That theorem states that if an unknown number X is divided by a with a remainder r.sub.1 and also divided by b with a remainder r.sub.2, where a and b are relatively prime numbers, the number X can be determined from a, b, r.sub.1, and r.sub.2 is X&lt;ab.

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Centerville, OH, United States of America

William S McCormick