I'm trying to calculate the power of a signal and my tutor has given me this formula to do it

photo of the handwritten formula

I've spent the past while building a program and now the foundations are there it's time to implement the maths side of it. The problem is I can't actually read it. Would someone be able to transcribe it and explain it to me?

  • 2
    $\begingroup$ $P_x=\dfrac{1}{T}\sum_{t=1}^{T}x^2(t)$ $\endgroup$ – jojek Feb 13 '15 at 17:23

As @jojek has already said in the comments, the formula reads $$ P_\mathrm{x} = \dfrac{1}{T}\sum_{t=1}^{T}x^2(t) $$ As $t$ usually denotes continous time I find this formulation a little bit odd. What your tutor probably actually meant is $$ P_\mathrm{x} = \dfrac{1}{T}\int_{t=0}^{T}x^2(t) \mathrm{d}t $$ It calculates the average power of the (continous-time) signal $x(t)$ of length $T$. In computer programs we're dealing with discrete-time (and discrete valued) signals, of course and the average power of the digital signal $x_n$ is given by $$ \tilde P_\mathrm{x} = \dfrac{1}{N}\sum_{n=1}^{N}x_n^2, $$ where $N$ is the length of $x_n$ in samples.

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