# How to apply the Fourier or Wavelet transformed data to LSTM model

I am dealing with a PHM RUL problem, a time series problem of machine signal. I consider to apply Fourier transform or Wavelet Transform to my sensor feature and train the LSTM model. But I have some problems when I using these transformed sensor data. my data looks like:

sensor 1    sensor 2   sensor 3    RUL
1           1.5         3        5
2           2.5         2        4
3           3.5         1        3
4           4.5         0        2
...          ...        ...      ...


First 3 column is my features(x), the last column is my RUL(y). The data have n rows which are time sequential. Every x mapping to one y.

I have some ideal to employ the transformed sensor data to my training model.

1. Simply treat the transformed sensor data as a new feature.
2. Concat the transformed sensor data after original time series data.
3. Only feed the transformed sensor data to my training model.
4. Create two LSTM model. The original data and transformed sensor data feed in their own model respectively, then combine the result by something like ensemble.

I can't make sure which one is more reasonable. Actually, all these ways will face a problem when I mapping my transformed sensor data(x) to my original RUL(y). That is, the transformed sensor data often have difference length(rows) from the original data. I can not mapping x to y if their length is different.

Any advise about how to apply the transformed data to LSTM model will be appreciated !