I want to add a White Gaussian noise to noise-free signal given desired SNR value. To do that, I am looking for a way to estimate the power of the signal. The noise-free signal looks like the following:

enter image description here

Do you have any clue about how to estimate the power of the signal ( mean of the signal, the integral of the difference between the decreasing linear line and the concave down decreasing line, ....)?

Many thanks in advance!!!


1 Answer 1


The plot has the power already measured for each sample. If the raw data samples (and not the power results shown here, then the average power can be direclty measured (given by the variance of the waveform). We may think that simply averaging the power measurements in the plot would give us the average signal power--- This would be the average of the squares which is not the same as a true power measurement given by the square of the average. It will be close but such an approach is highly dependent on the statistics of the waveform. For example, if the waveform was a complex Gaussian signal, the average of the squares would under-estimate the true power by -1.05 dB. This is detailed nicely in the app note by Agilent (formerly HP) # 1303 available at this link http://hpmemoryproject.org/an/pdf/an_1303.pdf .

Typically SNR would be determined from the noise power within the occupied bandwidth of the signal while a white noise contribution is spread evenly over the sampling bandwidth. If the signal is oversampled, then you would want to increase the white noise source accordingly to maintain a target spectral density within the bandwidth of the signal.

  • $\begingroup$ Thanks a lot Dan for your answer! $\endgroup$
    – akho
    Aug 25, 2020 at 20:26
  • $\begingroup$ I generated synthetically the noise-free signal and I did not do any experiment. To generate the signal, I used mathematical formula ( the formula used to measure the power of each sample point ) and I did the convolution with input pulse modeled by hyperbolic secant function. I used this paper ieeexplore.ieee.org/document/6837432 to model the signal . $\endgroup$
    – akho
    Aug 25, 2020 at 20:40
  • 1
    $\begingroup$ @akho then if you have the waveform you can compute the power directly (the variance). $\endgroup$ Aug 25, 2020 at 21:20
  • $\begingroup$ I am sorry. I did not get it. To estimate the power, shall I measure the average of the power of each sample and I add then the variance of the waveform ? Thank you. $\endgroup$
    – akho
    Aug 25, 2020 at 21:34
  • 1
    $\begingroup$ No given the waveform as a set of samples, compute the variance of those samples. $\endgroup$ Aug 25, 2020 at 21:36

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