Fourier Result on Time Series explained python
Matthew Harrington 
I have passed my time series data,which is essentially measurements from a sensor about pressure, through a Fourier transformation, similar to what is described in . The file used can be found here: The code related is this :
import pandas as pd
import numpy as np
file='test.xlsx'
df=pd.read_excel(file,header=0)
#df=pd.read_csv(file,header=0)
df.head()
df.tail()
# drop ID
df=df[['JSON_TIMESTAMP','ADH_DEL_CURTAIN_DELIVERY~ADH_DEL_AVERAGE_ADH_WEIGHT_FB','ADH_DEL_CURTAIN_DELIVERY~ADH_DEL_ADH_COATWEIGHT_SP']]
# extract year month
df["year"] = df["JSON_TIMESTAMP"].str[:4]
df["month"] = df["JSON_TIMESTAMP"].str[5:7]
df["day"] = df["JSON_TIMESTAMP"].str[8:10]
df= df.sort_values( ['year', 'month','day'], ascending = [True, True,True])
df['JSON_TIMESTAMP'] = df['JSON_TIMESTAMP'].astype('datetime64[ns]')
df.sort_values(by='JSON_TIMESTAMP', ascending=True)
df1=df.copy()
df1 = df1.set_index('JSON_TIMESTAMP')
df1 = df1[["ADH_DEL_CURTAIN_DELIVERY~ADH_DEL_AVERAGE_ADH_WEIGHT_FB"]]
import matplotlib.pyplot as plt
#plt.figure(figsize=(15,7))
plt.rcParams["figure.figsize"] = (25,8)
df1.plot()
#df.plot(style='k. ')
plt.show()
df1.hist(bins=20) from scipy.fft import rfft,rfftfreq
##
# convert into x and y
x = list(range(len(df1.index)))
y = df1['ADH_DEL_CURTAIN_DELIVERY~ADH_DEL_AVERAGE_ADH_WEIGHT_FB']
# apply fast fourier transform and take absolute values
f=abs(np.fft.fft(df1))
# get the list of frequencies
num=np.size(x)
freq = [i / num for i in list(range(num))]
# get the list of spectrums
spectrum=f.real*f.real+f.imag*f.imag
nspectrum=spectrum/spectrum[0]
# plot nspectrum per frequency, with a semilog scale on nspectrum
plt.semilogy(freq,nspectrum)
nspectrum
type(freq)
freq= np.array(freq)
freq
type(nspectrum)
nspectrum = nspectrum.flatten()
# improve the plot by adding periods in number of days rather than frequency
import pandas as pd
results = pd.DataFrame({'freq': freq, 'nspectrum': nspectrum})
results['period'] = results['freq'] / (1/365)
plt.semilogy(results['period'], results['nspectrum'])
# improve the plot by convertint the data into grouped per day to avoid peaks
results['period_round'] = results['period'].round()
grouped_day = results.groupby('period_round')['nspectrum'].sum()
plt.semilogy(grouped_day.index, grouped_day)
#plt.xticks([1, 13, 26, 39, 52])My end result is this :Result of Fourier Trasformation for Data
My question is, what does this eventually show for our data, and intuitively what does the spike at the last section mean?What can I do with such result? Thanks in advance all!
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