Sample InSAR test

README

In the attached data table, you have a set of 12 differential InSAR observations ("obs" in units of millimetres) 
for a single pixel observed over a patch of ground undergoing a periodic surface movement signal.

The InSAR observations are formed from 11 SAR images collected by the Sentinel-1A satellite at regular 12 day intervals.
First and second epochs for each InSAR observation are given in the attached table ("epoch1" and "epoch2").

Write and submit some code (in the language of your choice) to re-construct the periodic ground surface movement signal
from the InSAR observations.

Answer the following questions:

1) What is your estimate of the absolute amplitude of the ground surface movement signal?

2) What is your estimate of the period of the ground surface movement signal?

data.csv

sample_insar_test.py

"""
A sample test from the InSAR team.

You have a set of 12 differential InSAR observations ("obs" in units of millimetres)
for a single pixel observed over a patch of ground undergoing a periodic surface
movement signal.

The InSAR observations are formed from 11 SAR images collected by the Sentinel-1A
satellite at regular 12 day intervals.
First and second epochs for each InSAR observation are given in the attached table
("epoch1" and "epoch2").

Write and submit some code (in the language of your choice) to re-construct the
periodic ground surface movement signal from the InSAR observations.

Answer the following questions:

    1) What is your estimate of the absolute amplitude of the ground surface movement signal?
    2) What is your estimate of the period of the ground surface movement signal?
"""
import numpy
import pandas
import structlog


PATHNAME = "data.csv"
SAMPLE_SPACING = 12  # we've been told the sample spacing is 12 days
_LOG = structlog.get_logger()


def main():
    """
    Sample script that attempts to answer Matt's test.

    Keywords I picked up on are:
        periodic/period
        signal
        amplitude
        regular
        intervals
    """
    # loading the data; TABLE schema: obs  epoch1  epoch2
    dataframe = pandas.read_csv(PATHNAME)

    frequencies = numpy.fft.fftfreq(dataframe.shape[0], SAMPLE_SPACING)

    # need to estimate the period of the signal and will do so using Fourier

    # need to normalise the transformation to get the correct amplitudes
    fwd_transform = numpy.fft.fft(dataframe.obs) / numpy.sqrt(dataframe.shape[0])

    # only interested in the positive frequencies above the fundamental frequency
    offset = 1
    pos_freq = frequencies > 0
    magnitude = numpy.abs(fwd_transform[pos_freq])  # amplitudes
    second_harmonic = numpy.max(magnitude[offset:])  # max amplitude
    harmonic_idx = numpy.argmax(magnitude[offset:])

    signal_period = 1 / frequencies[pos_freq][offset:][harmonic_idx]

    _LOG.info("my answers", signal_period=signal_period, max_amplitude=second_harmonic)


if __name__ == "__main__":
    main()

My (unconfident) answer:

2021-06-18 11:45.23 my answers                     max_amplitude=8.411596348840888 signal_period=72.0