# Expectation of terms in double summation

1. May 10, 2010

### singhofmpl

Does any body help me how to find the average (expectation) of terms involving double summation? Here is the equation which I'm trying solve.

[\tex]E\Big[2\sum_{k=0}^{N-2}\sum_{j=k+1}^{N-1}f(k,j)\cos[2\pi(j-k)t-\theta_{k,j}]\Big][\tex]
where f(k,j) and [\tex]\theta_{k,j}[\tex] are some function of k and j.

2. May 10, 2010

### Xitami

[ latex ] expresion [ /latex ]

3. May 10, 2010

### Redbelly98

Staff Emeritus
Are you wanting to take the time-average? Have you been given the equation for doing that -- it involves doing an integral with respect to time...

4. May 10, 2010

### singhofmpl

Yes I want to take the time average of the said expression. Its not part of any assignment. I came accross this equation while deriving PAPR for the QAM OFDM signal. It does not involve any integral.

5. May 10, 2010

### Redbelly98

Staff Emeritus
The cosine terms all have a time-average of 0, except when j=k. As long as the f's and θ's are time-independent, this simplifies things greatly.

When j=k, the time-average of cos[2π(j-k)t - θk,j]=cos(θk,j). However, it appears that j is never equal to k in this summation, so we are left with 0 for the average.

Last edited: May 10, 2010
6. May 10, 2010

### singhofmpl

Dear Sir
Thanks a lot for your prompt response. After your comment now I've got the confirmation of my answer. Thanks a lot once again.