玉质先生：

抱歉，因为旅行，回复晚了。

这个题目我不熟悉，下面的回答也许是答非所问，但我尽力了。

Question 1:  Non-integer sampling ratios: The sampling period is rarely an integer divisor of the signal period. In practice, an ideal integer N of samples per cycle does not exist. 

Answer:   Assume we have N arbitrary sampling points, x_1, x₂ ……..x_N.   There is a unique polynomial p(x) of degree N-1 which interpolates these N points. The integral is then approximated by 

Question 2: Zero-crossing misalignment: Sampled data points generally do not align precisely with the signal's zero-crossing points.

Answer: I do not understand your question well.  If you mean x₁ and x_N above do not agree with a and b, which are zero crossing points of the function, then you can use the zeros of p(x) to determine a and b and 

then use  

  to  approximate the integral.

Question 3: Dynamic signal periods: The actual signal period T fluctuates over time and must be measured continuously in real time. 

Answer:  Again, I do not understand your question well.  If you are talking about what I indicated in question #2 above, then you can choose x_1, x₂ ……..x_N  to completely cover a cycle, that is, the point before x₁ is of opposite sign as x₁ and the point after x_N is of opposite sign as x_N , then compute the integral as indicated above.  Two such cycles of opposite signs would then be a signal period.

Together, issues 1, 2, and 3 severely degrade integration accuracy.

4. The current solutions, such as FFT windowing, are highly CPU-intensive and impractical for real-time AC power monitoring.

Questions:

• Is there an existing time-domain solution available today?

Answer:  Are my answers above a time-domain solution ?

• If it not exist, would you be interested in reviewing and improving a proposed real time solution?

Answer:  I am not familiar with this topic enough.