I’m currently writing and trying to program about shfs and shms and cant get any results.

Trying to repruduce with psds some stochastic harmonic functions (SHFs) /methods (SHMs)

The psd is clear, just a function about earthquakes.
SHM is also clear but the function in pic 1:pic1 gives me problems.
What is N?
Is N the sum of t const. and omega_i itterating between all the steps before?
like list1[i] = “function1” + list1[i-1] ?

• the second thing:
  SHF shf formula
  omega_dash is differently described as omega omega_dash
  and i’m not sure if the difference is ment or not.

I already got the psd, looking like that:
psd
saved in a list.

My shm looks in code like this:

def SHM(psd,t, ele):
    i = 1
    y = [0]
    phi = random.uniform(0, 2 * 3.14)
    while i != ele:
        y.append((A(i, psd) * math.cos(i*t+phi)) + y[i-1)
        i = i+1
    return y

with A beeing:

def A(i, S_0):
    dw = 1
    s = (2*(S_0[i]*dw)**0.5)
    return s

and my inputs are:

while z != 5000:
    while i != 80:
        psd.append(RuPe(S0,omega,omega*0.1,i,daem,daem))
        i = i+1
    #plt.plot(SHF(psd,80,10))
    z = z+1

RuPe is the PSD Formula
with z,i starting as 0

SHM Results

and i have no idea how to get SHF to work, so i got results like this:

def SHF(psd, t, ele):
    i = 1
    y = [0,]
    phi = random.uniform(0, 2 * 3.14)
    while i != ele:
        if i == 0:
            a = A(i,psd)
        else:
            a = abs(A(i,psd) - A(i-1,psd))
        y.append(a * math.cos((i) * t + phi))  #'''y[i-1])'''
        i = i + 1

    return y

SHF results

maybe there is another guy with experience in stochastics and could help me :/