Just as with the energy spectral density, the definition of the power spectral density can be generalized to discrete time variables x n . As before, we can consider a window of − − N ≤ ≤ n ≤ ≤ N with the signal sampled at discrete times t n = t 0 + ( n Δ Δ t ) for a total measurement period T = ( 2 N + 1 ) Δ Δ t . S x x ( f ) = lim N → → ∞ ∞ ( Δ Δ t ) 2 T | ∑ ∑ n = − − N N x n e − − i 2 π π f n Δ Δ t | 2 Note that a single estimate of the PSD can be obtained through a finite number of samplings. As before, the actual PSD is achieved when N (and thus T ) approaches infinity and the expected value is formally applied. In a real-world application, one would typically average a finite-measurement PSD over many trials to obtain a more accurate estimate of the theoretical PSD of the physical process underlying the individual measurements. This computed PSD is sometimes called a periodogram. This periodogram converges to the true PSD as the number of estimates as well as the averaging time interval T approach infinity.