Doubt about behavior of `dft`

Great thing that you guys have added inverse ffts! However, I can’t figure out how to exactly preserve the original coordinates of the data though. I was able to do that with ffts so I’m guessing there should be also a way to do this with xrft. Here’s a MWE:

In [105]: import xarray as xr

In [106]: import xrft

In [107]: T = xr.tutorial.open_dataset("air_temperature").air.isel(time=[0, 1])

In [108]: T_f = xrft.dft(T, dim="lat", true_phase=True, true_amplitude=True)

In [109]: T2 = xrft.idft(T_f, dim="freq_lat", true_phase=True, true_amplitude=True,)

In [110]: T.lat
Out[110]: 
<xarray.DataArray 'lat' (lat: 25)>
array([75. , 72.5, 70. , 67.5, 65. , 62.5, 60. , 57.5, 55. , 52.5, 50. , 47.5,
       45. , 42.5, 40. , 37.5, 35. , 32.5, 30. , 27.5, 25. , 22.5, 20. , 17.5,
       15. ], dtype=float32)
Coordinates:
  * lat      (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0
Attributes:
    standard_name:  latitude
    long_name:      Latitude
    units:          degrees_north
    axis:           Y

In [111]: T2.lat
Out[111]: 
<xarray.DataArray 'lat' (lat: 25)>
array([-30. , -27.5, -25. , -22.5, -20. , -17.5, -15. , -12.5, -10. ,  -7.5,
        -5. ,  -2.5,   0. ,   2.5,   5. ,   7.5,  10. ,  12.5,  15. ,  17.5,
        20. ,  22.5,  25. ,  27.5,  30. ])
Coordinates:
  * lat      (lat) float64 -30.0 -27.5 -25.0 -22.5 -20.0 ... 22.5 25.0 27.5 30.0
Attributes:
    spacing:  2.4999999999999964

Using the xrft.fft option also doesn’t produce what I expected:

In [112]: T_f = xrft.fft(T, dim="lat",)

In [113]: T2 = xrft.ifft(T_f, dim="freq_lat")

In [114]: T.lat
Out[114]: 
<xarray.DataArray 'lat' (lat: 25)>
array([75. , 72.5, 70. , 67.5, 65. , 62.5, 60. , 57.5, 55. , 52.5, 50. , 47.5,
       45. , 42.5, 40. , 37.5, 35. , 32.5, 30. , 27.5, 25. , 22.5, 20. , 17.5,
       15. ], dtype=float32)
Coordinates:
  * lat      (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0
Attributes:
    standard_name:  latitude
    long_name:      Latitude
    units:          degrees_north
    axis:           Y

In [115]: T2.lat
Out[115]: 
<xarray.DataArray 'lat' (lat: 25)>
array([-30. , -27.5, -25. , -22.5, -20. , -17.5, -15. , -12.5, -10. ,  -7.5,
        -5. ,  -2.5,   0. ,   2.5,   5. ,   7.5,  10. ,  12.5,  15. ,  17.5,
        20. ,  22.5,  25. ,  27.5,  30. ])
Coordinates:
  * lat      (lat) float64 -30.0 -27.5 -25.0 -22.5 -20.0 ... 22.5 25.0 27.5 30.0
Attributes:
    spacing:  2.4999999999999964

I feel like I’m missing something obvious but can’t quite figure it out…

How can I preserve coords so that I get the same result going to fourier space and back?

[lanougue]

Hi @tomchor, @roxyboy ,

When T_f(…,true_phase=True) is evaluated, the phase is preserved but the coordinates of T are lost in the transformation. T_f is in the Fourier domain and is not associated to any direct (lat) coordinates. Thus, when idft() is called on T_f, idft has no idea on which range of coordinates you need the result. The default is on centered coordinates with the same range of your inital coordinates ([-30,30] in your example). If you want your data back in the good range of coordiantes, you need to shift the centered standard output coordinates. As your initial coordinates are around 45 degree, you have to call idft with the lag argument: T2 = xrft.idft(T_f, dim=“freq_lat”, true_phase=True, true_amplitude=True, lag=45)

However, looking to you example, I see that the returned result is the same as the orignal T but reversed. This is because signal is on decreasing “lat” axis. This is a xrft bug ! For now, as a workaround, use: T = T.sortby(‘lat’) just after loading T to get the expected behaviour.

[lanougue]

Yes, it should resolve this.