EMC Signal
In electromagnetic systems, it is often easy to measure the magnitude response but the phase response can be difficult to obtain. An engineer or scientist may have access to the magnitude response of a measurement in frequency space, and wish to obtain the phase or reconstruct the time domain signal.
Fortunately, there are theoretical tools that can be applied for just this problem. Without going deep into the underlying theory, the basic idea is that the symmetry properties of a Fourier transform provide certain constraints that can be exploited to obtain information that is not obviously available. This is particularly true when the associated time series data is ‘causal and stable’ – or goes to zero at early and late times.
Theorists refer to the ‘Cepstrum analysis’ as a way to relate the phase and magnitude of Fourier transformed data. In fact, one can obtain the ‘minimum phase’ as a function of frequency using the Hilbert transform. The complete Fourier transform can then be obtained from the minimum phase and then the original time series data can be reconstructed.
EMA provides a minimal phase time series reconstruction tool that is free for use. Simply run the executable in the same directory as your magnitude response data file, and follow the command line prompting. The input file must be of the form:
frequency1 magnitude1
frequency2 magnitude2
frequency3 magnitude3
…
See the Powerpoint below. Download the source, executable and a detailed ‘readme’.
References:
- Jie Yang, Jinhwan Koh, and Tapan K. Sarkar, Reconstructing a Nonminimum Phase Response From the Far-Field Power Pattern of an Electromagnetic System
- A.V. Oppenheim and R.W. Schafer, Discrete-Time Signal Processing
