This paper shows the general solution for the real‐number periodic sequence with an autocorrelation function with zero side lobe, aiming at the application to the spread‐spectrum communication. The general solution is derived by representing the autocorrelation function by a Fourier series and utilizing the components. The solution contains the phase constant. In other words, the sequence and the phase constant are related through the discrete Fourier transform Under the condition that the seqeunce is real, the phase constant is an odd function. However, when the phase constant takes only the value in {O, π}, the phase constant is an even (= odd) function, and the sequence is an even function. From the general solution, it is shown that N sequences obtained by shifting a sequence of order N are orthogonal. An example of the sequence is shown for the case where the phase constant is fixed as φ k E {0, φ }, φk = 2πk3/N (k = 0, 1, ‥, N ‐ l), and for the case where it is continuous as Phiv;1=‐ φ N‐1= θ. The general solution provides a basis for calculating various kinds of pseudonoise sequences.
In the pulse compression sonar, the code with a sharp autocorrelation function is used as in spread spectrum communication, and they share many common technologies. In this paper, the real-valued orthogonal pseudo-noise (PN) sequence that can be used in both over a broad frequency range including dc is applied to the pulse compression sonar. By adapting digital correlation processing, a high performance close to the theory has been obtained. The codes are generated from a binary orthogonal PN sequence with a length of 127 and a multivalue orthogonal PN sequence with a length of 256 and are sent into an acoustic transmission path at a frequency of about 40 kHz. The correlation operation of the received code and the transmitted code is carried out on a personal computer. The multiple echo is detected at a low noise while the Gaussian noise and the locked sinusoidal wave can be suppressed with a processing gain close to the one predicted by the theory.
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