A Signal Complexity-Based Approach for AM–FM Signal Modes Counting
Abstract
:1. Introduction
2. Materials and Methods
2.1. AM–FM Signals and Spectrogram Representation
2.2. Signal Complexity
2.2.1. Shannon Entropy
2.2.2. Kolmogorov Complexity
2.2.3. Minimum Description Length
2.2.4. Run Length Encoding
2.2.5. Asymptotic Equipartition Property
- (i)
- has probability nearly 1;
- (ii)
- elements in are nearly equiprobable;
- (iii)
- cardinality is nearly .
2.3. The Proposed Method
- Step 1.
- spectrogram thresholding and binary map derivation;
- Step 2.
- binary map encoding by RLE;
- Step 3.
- selection of typical columns for modes counting.
2.3.1. Thresholding by MDL
- , the total energy of ;
- , the energy of the thresholded ;
- , the discarded energy during the thresholding process;
2.3.2. Encoding by RLE and Modes Counting
2.3.3. The Algorithm
- Step 1.
- Binary map derivation
- (1)
- Compute signal STFT and spectrogram.
- (2)
- Threshold spectrogram at the of its absolute maximum (this is a pre-processing step, justified by the assumption that noise is equally distributed over the whole domain).
- (3)
- For each u in the signal time support
- (4)
- Set B as the overall columns obtained in step 3.3.
- (5)
- Zero-pad B.
- (6)
- Remove black holes.
- Step 2.
- 2D RLE encoding and modes counting
- (1)
- Code the first binary column, i.e., by RLE and compute according to Equation (21).
- (2)
- For i ranging from 2 to n
- (2.1)
- apply RLE to column , resulting in the coded sequence ;
- (2.2)
- compute as the difference between the number of couples in and the one in , as in Equation (22); if and IsIsolated() (see Algorithm 1) define = IsIsolated(); set ; otherwise, set .
Algorithm 1: Function to check if a detected contribution is isolated. |
|
3. Results and Discussion
3.1. Experimental Results
3.2. Some Observations
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
AEP | Asymptotic Equipartition Property |
AM | Amplitude Modulated |
FM | Frequency Modulated |
IF | Instantaneous Frequency |
MCS | Multicomponent Signal(s) |
MDL | Minimum Description Length |
RLE | Run Length Encoding |
RT | Radon Transform |
STFT | Short-Time Fourier Transform |
TF | Time-Frequency |
TFD | Time-Frequency Distribution |
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Bruni, V.; Tartaglione, M.; Vitulano, D. A Signal Complexity-Based Approach for AM–FM Signal Modes Counting. Mathematics 2020, 8, 2170. https://doi.org/10.3390/math8122170
Bruni V, Tartaglione M, Vitulano D. A Signal Complexity-Based Approach for AM–FM Signal Modes Counting. Mathematics. 2020; 8(12):2170. https://doi.org/10.3390/math8122170
Chicago/Turabian StyleBruni, Vittoria, Michela Tartaglione, and Domenico Vitulano. 2020. "A Signal Complexity-Based Approach for AM–FM Signal Modes Counting" Mathematics 8, no. 12: 2170. https://doi.org/10.3390/math8122170