def getVarsDFT(x,t): """Uses the discrete fast fouier transform to calculate the analytic signal (which is the hilbert transform of the FS) this is diffrent as it uses the numpy solvers to calculate the DFT, which is not robust and designed for uniform sampling, and does not account for the dampening. Then the instantnious phase is calculated (and amp). The instantanious Freq is estimated by finite difference. x 1d np array of data t 1d np array of time corrisponding to x t will be used to sort the x value, redundant data at a time point will be combine via median. returns x new x value (if redundent or unordered it will be diffrent) t new corrisponding time th instantanious phase dth instantanious freq r inst... amp... """ t,x = dataUtil.aveUnqTime(t,x,method='median') z = signal.hilbert(x) th = np.unwrap(np.arctan2(z.imag,z.real)) r = np.abs(z) dth,t = dataUtil.FD(th,t) return(x,t,th,dth,r)
def crossCorr(traj1,traj2,tstep=0,taumax=0): """Performs corss correlation between two dynamic trajectories with non uniform time spacing, and possibally diffrent time courses. will only use the overlaping time interval. will use a step size for tau equal to the smallest step size in the data and will apply linear interpolation to compute a uniform time course. A preprocessing step is used to get a unique time seris for each trajectory, meaidan value is used. """ # get unique time courses t1,x1_tmp = du.aveUnqTime(traj1[0],traj1[1],'median') t2,x2_tmp = du.aveUnqTime(traj2[0],traj2[1],'median') # find common range tmin = np.max(np.array([t1[0],t2[0]])) tmax = np.min(np.array([t1[-1],t2[-1]])) # we could use any step, but no reason to go lower # then smallest interval if tstep==0: tstep = np.min(np.array([np.min(t1[1:]-t1[:-1]),np.min(t2[1:]-t2[:-1])])) # the range to do linear interp t = np.arange(tmin,tmax,tstep) x1 = np.zeros(len(t)) x2 = np.zeros(len(t)) # do linear interp for i in range(len(t)): x1[i] = du.getOrInterp(t1,x1_tmp,t[i]) x2[i] = du.getOrInterp(t2,x2_tmp,t[i]) # calculate the number of tau steps if a max is specified if taumax>0: # how many steps to get to max? tausteps = int(taumax/tstep)+1 else: tausteps = 0 # now we have an evenly spaced time seris for two varriables # run the corss corelation cc,_ = crossCorrUniform(x1,x2,tstop=tausteps) tau = np.arange(float(len(cc))) tau = tau*tstep return(cc,tau)
