In Matlab, we can generate noise with zero-mean and unit variance by using "n = randn()". But in fact, the variance is not really equal to 1, but there is a slight error.
Assume that the length of the noise sequence is a constant of N. I generated the noise sequence many times, and calculated the variance of each noise sequence. Finally, I compared each variance with 1, and calculated the MSE (mean square error). For example, I have got the MSE which is around 1 * 10^-6.
Now, I generate narrow-band noise by using a low pass filter. The order of the filter is very high. After scaling, the variance of the filtered noise returns to around 1. But again, there is a slight error. I calculate the MSE as above, and I found that the MSE is around 5 * 10^-6.
Is the MSE getting larger due to the low pass filter? Is there any way to eliminate it? Thank you!