# Terminology for instantaneous phase of magnitude component of complex signal

Signal Processing Asked on November 4, 2020

In my field, we deal with data that are originally complex-valued. Typically, researchers convert their data from real + imaginary to magnitude + phase, and then discard the phase data (i.e., we generally only deal with the magnitude portion of a complex signal).

There are a number of papers on phase synchrony, in which the Hilbert transform is applied to this magnitude-only data to estimate the analytic signal, from which instantaneous phase is extracted. I am very much a novice in signal processing, so I found this a little confusing. The papers refer to the instantaneous phase signal estimated from magnitude-only data just as "phase signal". These folks might not be aware of the complex-valued nature of the raw signal, which is reasonable given how these data are generally handled, but I think there should be a more appropriate term for "phase estimated from magnitude signal using the Hilbert transform", given that there’s very little similarity between the real phase signal and this estimated phase signal.

Is this an established concept and, if so, is there a term that would differentiate the two kinds of phase signal?

and then discard the phase data

What's gone is gone. You can't reconstruct the phase of the original data unless you have some additional information.

in which the Hilbert transform is applied to this magnitude-only data to estimate the analytic signal, from which instantaneous phase is extracted.

That's a just mathematical process. You shove data in, and data comes out. Whether the result is useful or not depends on what you want to do with it and why you chose this mathematical process in the first place. If you want to associate any physical meaning with the result you need to justify this with some physical property or law.

To clarify, the Hilbert transform applied to the real component of a complex signal is not a good estimate of the original complex signal?

Correct. In general most signals are NOT analytic unless there is a strong reason why they should. If there is a reason to interpret the results that way, it should be stated in the paper. In order to "estimate" a discarded phase, you need have some additional information or (justified) assumptions about your original signal otherwise you might as well just toss the dice. If there is a additional information, it should be stated AND the phase estimation method should be properly derived from it.

Correct answer by Hilmar on November 4, 2020

## Related Questions

### Implementation of modulation/demodulation models

1  Asked on November 8, 2021

### What’s the relation between frequency band of $X(jomega)$ and $Phi_{xx}(jomega)$?

1  Asked on November 5, 2021

### How to get an interpolation weight from a mathematical definition

1  Asked on November 5, 2021

### Transposed convolutional layer

1  Asked on November 5, 2021 by shepplogan

### Average image over $N$ frames with one frame buffer

2  Asked on November 5, 2021 by user674907

### Understanding rho and theta in hough

1  Asked on November 5, 2021

### Encoding sequence of unfair coin flips

3  Asked on November 5, 2021 by certusic

### How to calculate sine wave SNR from oscilloscope

2  Asked on November 5, 2021 by dcrown

### How do decibels scale with wave amplitude?

1  Asked on November 5, 2021

### Moving Average Filter’s Magnitude Response

1  Asked on November 5, 2021 by varungupta

### DFT exercise in the book Understanding digital signal processing 3 Ed

2  Asked on October 24, 2021 by henrique-luna

### Sparse Inverse Fourier Transforms

1  Asked on October 24, 2021 by tobi-akinyemi

### Save computational burden by calculating the output of decimate filter at output rate?

1  Asked on October 24, 2021

### Find signal power in a band by integrating the PSD in a frequency band (and zeroing the out-of-band DFT bins)

1  Asked on October 24, 2021 by ecook

### Speech recognition algorithm in GNU Octave to convert speech to text (and vice versa)

1  Asked on October 24, 2021

### Find camera pose by knowing triangle coordinates

1  Asked on October 24, 2021 by duloren

### Comparing similarity of two simultaneously recorded EEGs in freq domain

2  Asked on October 24, 2021 by thejohn

### Convolution : Anechoic Speech signal and Impulse response

1  Asked on October 24, 2021 by tanmayee-pathre

### Are there any advantages oversampling?

2  Asked on October 24, 2021

### Calculation of gain at certain frequency in case of nth order IIR filter

1  Asked on October 24, 2021