Appendix D Computer Programs ApD
517
D.2.9 Program D.47: Spectral Analysis of Time Series (FFT Method)
• Theoretical background: see Section 4.3.3.
• Input data: the name and path of the file containing the values of time
series in the format:
t
f(t)
For example, your file should be in the format:
!::"t
f(L~t)
2!::,.t
f(2!::"t)
f(3!::"t)
N!::"t
f(N !::"t)
As the procedure with overlapping segments is used, the number of points,
N, has to be divisible by 128. In the areas provided, enter the sampling interval !::"t and segment length N DB. The N D B value should be equal to
128 or 256. As an example, file D47.dat is given (CD drive\data\d47.dat)
with N = 3072 and !::"t = 0.3906 s.
• Output: graph of frequency spectrum. On the vertical axis, values of
normalized spectrum S(w)/ S(wmax ) are given, where W max is the peak frequency at which the spectrum reaches its maximum. The peak frequency,
as well as the variance (calculated as an integral over the spectrum), are
also provided.
D.2.10 Program D.81: Instantaneous Release of Substance in Uniform Flow (One-Dimensional Case)
• Theoretical background: see Section 8.3.4.
• Input data:
- mass m of released substance [kg/m], in the form of a Gaussian
curve,
- variance of initial distribution (J [m],
- coefficient of horizontal diffusion Kx [m 2 /s],
- current velocity U [m/s],
- time t [s] after which a final distribution is required.
• Output: graphs of initial (blue line) and final (red line) concentrations
c(x,t). On the vertical axis, concentrations are normalized against initial
concentration at x = O. The value of this concentration c(O, 0) is indicated. The horizontal distance, x, from the centre of release is normalized
by distance Xmax = 3(J.