# Documentation

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Generate root Zadoff-Chu sequence of complex symbols

## Description

example

SEQ = lteZadoffChuSeq(R,N) generates the Rth root Zadoff-Chu sequence with length N, as defined in the LTE specifications [1]. The output SEQ is an N-length column vector of complex symbols.

The function generates the actual sequence using the following algorithm:

$seq\left(m+1\right)=\mathrm{exp}\left(-j\cdot \pi \cdot R\cdot m\cdot \left(m+1\right)/N\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}for\text{\hspace{0.17em}}\text{\hspace{0.17em}}m=0,...,N-1$

This function uses a negative polarity on the argument of the exponent or a clockwise sequence of phases.

## Examples

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Generate the 25th root length-139 Zadoff-Chu sequence.

Use lteZadoffChuSeq to generate the sequence and then plot its absolute values.

plot(abs(xcorr(seq)./length(seq)))

## Input Arguments

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Example: 25

Data Types: single | double
Complex Number Support: Yes

Example: 139

Data Types: single | double
Complex Number Support: Yes

## Output Arguments

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The output sequence is a complex-valued column vector that contains the Rth root Zadoff-Chu sequence of length N.

## References

[1] 3rd Generation Partnership Project: Technical Specification Group Radio Access Network. "Evolved Universal Terrestrial Radio Access (E-UTRA)," Physical Channels and Modulation, Release 10, 2010–2012, TS 36.211, Vol. 10.0.0.