Periodicity of peaks within a signal

Question

I have a signal, in which i want to detect the period of the peaks, that exist within this signal: for example : After each 5mm or (5 seconds depending on the sampling rate and speed of my motor) i have a peak in my motor current.
I though of using the FFT, but then i had some problems with the sampling rate which lead me to look for the ununiform fft, but i wasnt very successfull.
I also tried using the Savitzky golay filter to smooth the data, since i read that it actually helps finding peaks within the signal, but not the period.
I tried appliying the FFT to the smoothed data, but I wasn't able to find any frequence.
So i was wondering is there is an algorithm that detects the periodicity of peaks within a signal.
this is the Normal Signal plot .

The signal in display(20mm/s) has been smoothed using the Savitzky golay filter, with a window of 51.

Answer 1

Before applying the algorithm below, you should first apply a DC blocking filter. That should remove the DC offset (and partially the step at the beginning), which will allow more usual periodicity techniques to be used.

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You can try using the average square difference function. There is a nice write up on this answer and a way to implement it in an efficient manner here.

Here's an example plot. The $\color{red}{\bf red}$ circle shows the selected minimum. Note how the "octave" problem shows up: if the signal is periodic with period $P$, it's also periodic with period $N P$ where $N$ is an integer.

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R Code Below

#30511

pulse <- 16 - seq(-4,4)^2
len <- length(pulse)

T <- 1000
P <- 49

ix <- seq(1,T - len, P)

data <- rep(0,T)

for (this_one in ix)
{
  data[this_one + seq(0,len-1)] <- pulse
}

data <- data #+ rnorm(T,0,1)

plot(data, type="l")

asdf <- function(data, Pmax)
{
  N <- length(data)
  asdf <- rep(0,Pmax)
  for (p in seq(1,Pmax))
  {    
    ix <- seq(p+1,N)
    asdf[p] <- sum((data[1:length(ix)] - data[ix])^2)
  }

  return(asdf)
}

calc <- asdf(data, 5*P)

par(mfrow=c(2,1))
plot(data, type="l")
title('Repeating pulses')

plot(1:(5*P), calc, type="l")
period <- which.min(calc)
points(P, calc[P], col="grey", lwd = 12)
points(period, calc[period], col="red", lwd = 5)
title('ASDF')