white noise generation and filtering some band
I want to generate a white nose with unite amplitude 0.3 and frequency range from 0 -2.687.(all these values are non-dimensional). I integrated the following to get the signal of time domain: The maximum frequency is 2.687, its fundamental period is 0.3721.So I set the time interval is 0.3721/10 to ensure it can capture the maximum frequency sufficiently. I set the minimum frequency is 2.687/320 which means j=1,2..320 in the above integration. In order to capture the minimum frequency, I set the signal time length as 2560*0.3721 which is much larger the period of minimum frequency. Then by using matlab, I generated the white noise signal and its amplitude spectra. But its amplitude had a relatively large fluctuation from the desired 0.3. I tried to increased time domain and frequency integration number I an J , but I cannot get improved results.
Besides, for my simulation case, I eventually need to get a filtered white noise from which a narrow band low frequency 0.04-0.08 will be removed. Based on above parameters, I failed to generate it. Is it due to that the band is narrow or low? Whats my problem? Any advice would be greatly appreciated.