I don't understand what is a first order sequence. For more context: I am reading a paper where the author extracts different sequences (in the STFT domain) and then "The resulting sequences are differentiated (via first-order difference)".

What is the meaning of first order difference here?


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The first-order difference operation is a technique for numerical differentiation. It is the simplest method that I know of, and consists of just treating a discrete-time signal as piecewise linear between each pair of points and calculating the slope between them. The idea is that this time series of slopes should approximate the time derivative of the underlying signal.

$$ x_d[n] = \frac{x[n] - x[n-1]}{T} $$

where $T$ is the sampling period of the signal $x[n]$.


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