SUMMARY
Computes amplitude and unwrapped phase.
SYNTAX
UNWRAP {FILL {ON|OFF|n}},{INTTHR v},{PVTHR v}
INPUT
FILL {ON}: Turn zero fill option on. FILL OFF: Turn zero fill option off. FILL n: Turn zero fill option on and change fill value to n. INTTHR v: Change the integration threshold constant to v. PVTHR v: Change the principal value threshold constant to v.
DEFAULT VALUES
UNWRAP FILL OFF INTTHR 1.5 PVTHR 0.5
DESCRIPTION
This command transforms time-series data in memory to spectral data containing amplitude and "unwrapped" phase components. This procedure works for data with a "smoothly varying phase." The data is filled with zeros to the next power of two before being transformed. You may specify a larger number of zeros by using the FILL option.
This is an implementation of the algorithm due to Tribolet. Two methods are used to estimate the unwrapped phase at each frequency. One is to numerically integrate the phase derivative through the use of the fast Fourier transform. The step size used in this trapezoidal integration is halved at each frequency if necessary to obtain a consistent estimate. You can control the threshold value on this check using the INTTHR option. This value is in radians. Decreasing INTTHR will improve the phase estimate. Too small a value, however, will not allow the solution to converge.
The second method used in this algorithm is to first compute the principle value of the phase using the inverse tangent function. The unwrapped phase is estimated by adding multiples of 2*PI to the principal value until the discontinuities are reduced to values less than a threshold value. You control the threshold value on this check using the PVTHR option. Again, decreasing this threshold value will improved the phase estimate, but will also increase the chance that no solution may be found. Initial trial values for these two thresholds are usually such that:
PI/4 < PVTHR < INTTHR < 2*PI
ERROR MESSAGES
- 1301: No data files read in.
- 1306: Illegal operation on unevenly spaced file
- 1606: Maximum allowable DFT is
- Too many data points in file.
WARNING MESSAGES
- 1610: Unwrap failed at data point for file
- Adjust threshold constants and retry.
HEADER CHANGES
B, E, and DELTA are changed to the beginning, ending and sampling frequencies of the transform respectively. The original values of B, E, and DELTA are saved as SB, SE, and SDELTA and are restored when an inverse transform is performed.
REFERENCES
Tribolet, Jose M.; "A New Phase Unwrapping Algorithm"; IEEE Transactions on Acoustics, Speech, and Signal Processing; Vol. ASSP-25, No 2, April 1977; page 170.
LATEST REVISION
January 8, 1983 (Version 8.0)