The conventional signal power calculation can be:
$$ P(n) = \frac{1}{N}\sum_{i=0}^{N-1}x^2(n-i) $$
$x(n)$ is the signal. However, I have seen another method:
$$ P(n) = \lambda P(n-1) + (1-\lambda) x^2(n) $$ Here, $\lambda$ is the forgetting factor. So what is the difference between these two methods? Which one is widely used in real-time process? Which one is more computationally efficient?
So what is the difference between these two methods?
They are different types of lowpass filters. There are many other choices as well.
Which one is widely used in real-time process?
You'll probably find the IIR lowpass more frequently than a moving average filters. Moving average isn't a great lowpass filter since it has a lot of side lobes in the frequency domain.
In general, people use a lowpass filter that's the best choice for the requirements of their specific application. For example, if you calculate the power for a sound pressure level meter, there are standards for different time constants, which in turn determines the choice of lowpass filter.
Which one is more computationally efficient?
In almost all cases the IIR version will be more efficient.
They both square the input going in, $x^2[n]$.
They both filter $x^2[n]$ with a low-pass filter having gain at DC equal to 1 (or 0 dB). So the intent is to get the DC value of $x^2[n]$ and to not scale that DC value.
The impulse response of the two low-pass filters are different.
