sixy6e · June 18, 2021 01:51 · sixy6e · Jun 18, 2021
diff --git a/README b/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?
diff --git a/data.csv b/data.csv
diff --git a/sample_insar_test.py b/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()
	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?
obs	epoch1	epoch2
10.3921	1	2
9.6647	1	6
-8.1724	2	3
-13.6400	2	5
-10.0686	3	4
-3.6267	3	5
1.5047	4	8
5.1846	5	7
4.8141	7	10
5.1083	8	9
11.7095	9	11
-2.6498	10	11
	"""
	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()