# scipy.signal.correlation_lags

scipy.signal.correlation_lags(in1_len, in2_len, mode='full')

  Calculates the lag / displacement indices array for 1D cross-correlation.

  Parameters:
    in1_len int

      First input size.

    in2_len int

      Second input size.

    mode str {‘full’, ‘valid’, ‘same’}, optional

      A string indicating the size of the output. See the documentation `correlate` for more information.

  Returns:
    lags array

      Returns an array containing cross-correlation lag/displacement indices. Indices can be indexed with the np.argmax of the correlation to return the lag/displacement.

  See also

  `correlate`

    Compute the N-dimensional cross-correlation.

  Notes

  Cross-correlation for continuous functions \(f\) and \(g\) is defined as:

  \[\left ( f\star g \right )\left ( \tau \right ) \triangleq \int_{t_0}^{t_0 +T} \overline{f\left ( t \right )}g\left ( t+\tau \right )dt\]

  Where \(\tau\) is defined as the displacement, also known as the lag.

  Cross correlation for discrete functions \(f\) and \(g\) is defined as:

  \[\left ( f\star g \right )\left [ n \right ] \triangleq \sum_{-\infty}^{\infty} \overline{f\left [ m \right ]}g\left [ m+n \right ]\]

  Where \(n\) is the lag.

  Examples

  Cross-correlation of a signal with its time-delayed self.

      >>> import numpy as np
      >>> from scipy import signal
      >>> rng = np.random.default_rng()
      >>> x = rng.standard_normal(1000)
      >>> y = np.concatenate([rng.standard_normal(100), x])
      >>> correlation = signal.correlate(x, y, mode="full")
      >>> lags = signal.correlation_lags(x.size, y.size, mode="full")
      >>> lag = lags[np.argmax(correlation)]