# will always periodogram produce correct frequencies?

let say we have some data,some signal written in this form

$x(t)=s(t)+\epsilon(t)$

where $s(t)$ is pure signal and $\epsilon(t)$ is white noise with mean zero and some variance ,question is that if we have enough sample data,should periodogram always estimate frequencies correctly?let say we have following sinusoidal data

$y[t]=A_1(sin(\omega_1*t+\phi_1)+A_2*sin(\omega_2*t+\phi_2)+....+A_p*sin(\omega_p*t+\phi_p)$+$z(t)$

i know that there is problem of variance increasing related to periodogram,but will it affect on frequency estimation?also i know that resolution of periodogram is $1/N$,but let us suppose that two frequency are not so close to each other,then will periodogram produce correct frequency estimation?variance is not important for me know

• Why use a periodogram and not discrete Fourier series? – user2718 Apr 16 '14 at 21:17
• You should write a little more about your application and ask for a suggested analysis technique to accomplish your goal rather than suggest an analysis technique and ask if it will work. – user2718 Apr 16 '14 at 21:31