# Create sine wave with noise within 10-20 Hz

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Eric on 3 Feb 2018
Answered: Walter Roberson on 3 Feb 2018
Hi everyone,
I would like to create a sine wave with noise within a narrow spectrum (10-20 Hz). Is it possible to create a sine wave with random frequencies between 10-20 Hz?
Eric

Walter Roberson on 3 Feb 2018
Construct a vector of coefficients in complex conjugate pairs, in an arrangement similar to
[0, zeros(1,N), A B C D, zeros(1,M), zeros(1,M), D' C' B' A' zeros(1,N)]
here the A B C D are the coefficients that will be used for the random noise in 10-20 Hz range. Use an appropriate number of coefficients according to your desired frequency resolution. Notice that the exact same coefficients must appear at the end but in reverse order and in their complex conjugate (random complex values for these are fine as long as the end of the vector has them in reverse order and complex conjugate of the originals.)
Now when you ifft() that vector, it will be the noise signal to add to your sine wave.