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A Zadoff–Chu (ZC) sequence, also referred to as Chu sequence or Frank–Zadoff–Chu (FCZ) sequence, is a complex-valued mathematical sequence which, when applied to radio signals, gives rise to an electromagnetic signal of constant amplitude, whereby cyclically shifted versions of the sequence imposed on a signal result in zero correlation with one another at the receiver. A generated Zadoff–Chu sequence that has not been shifted is known as a "root sequence". These sequences exhibits the useful property that cyclically shifted versions of itself are orthogonal to one another, provided, that is, that each cyclic shift, when viewed within the time domain of the signal, is greater than the combined propagation delay and multi-path delay-spread of that signal between the transmitter and receiver. The complex value at each position ''n'' of each root Zadoff–Chu sequence parametrised by ''u'' is given by : where : : : : Zadoff–Chu sequences are CAZAC sequences (constant amplitude zero autocorrelation waveform). They are named after Solomon A. Zadoff and D. C. Chu. Note that the special case results in a Chu sequence. == Properties of Zadoff-Chu sequences == 1. They are periodic with period if is odd. : is prime, Discrete Fourier Transform of Zadoff–Chu sequence is another Zadoff–Chu sequence conjugated, scaled and time scaled. : where is the multiplicative inverse of u modulo . 3. The auto correlation of a Zadoff–Chu sequence with a cyclically shifted version of itself is zero, i.e., it is non-zero only at one instant which corresponds to the cyclic shift. 4. The cross-correlation between two prime length Zadoff–Chu sequences, i.e. different values of , is constant 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Zadoff–Chu sequence」の詳細全文を読む スポンサード リンク
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