Discrete Fourier transform system using the dual chirp-Z transform

Abstract

A transform system provides a real-time implementation of the discrete Foer transform (DFT) of length N, the system being useful in sonar and radar signal processing. The input signal g.sub.n, 0.ltoreq.n.ltoreq.N-1, comprises a discrete signal, generally complex, of N samples. The system comprises an input for receiving the input signal g.sub.n and convolving in a first, input, convolver with a signal represented by the function e.sup.i.pi.n.spsp.2.sup./N , to result in a first modified signal at the output of the first convolver. Means are provided for generating the signal e.sup.-i.pi.n.spsp.2.sup./N. A multiplier receives the first modified signal and the signal e.sup.-i.pi.n.spsp.2.sup./N and multiplies these two signals its output being a second modified signal. A second, output, convolver, whose input is connected to the output of the multiplier, convolves the output signal from the multiplier with a signal represented by the function e.sup.i.pi.n.spsp.2.sup./N, to result in a discrete Fourier transformed (DFT) signal at the output. The output signal is generally a complex signal, having a real part and an imaginary part. One of the three chirps, represented by the two signals e.sup.i.pi.n.spsp.2.sup./N and the signal e.sup.-i.pi.n.spsp.2.sup./N, is multiplied by a factor of (1-i) either explicitly or in a summer for the corresponding complex operation in order to obtain the correct output phase.

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