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ℒ_{p}-Norm-like Affine Projection Sign Algorithm for Sparse System to Ensure Robustness against Impulsive Noise

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## Abstract

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## 1. Introduction

## 2. Original APSA

## 3. Proposed ${\mathcal{L}}_{p}$-Norm-like APSA

## 4. Simulation Results

#### 4.1. System Identification for Sparse System in Presence of Impulsive Noises

#### 4.2. Speech Input Test Including a Double-Talk Situation

#### 4.3. Practical Considerations for the p Parameter

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**NMSD learning curves for the white input in a sparse system with impulsive noises (Pr = 0.01).

**Figure 4.**NMSD learning curves for the correlated input generated using ${G}_{1}\left(z\right)$ in a sparse system with impulsive noises (Pr = 0.01).

**Figure 5.**NMSD learning curves for the correlated input generated using ${G}_{2}\left(z\right)$ in a sparse system with impulsive noises (Pr = 0.01).

**Figure 6.**NMSD learning curves for the white input in a sparse system with impulsive noises (Pr = 0.01). The system suddenly changes (${\mathbf{w}}_{o}\to -{\mathbf{w}}_{o}$) at iteration $3.8\times {10}^{3}$).

**Figure 7.**NMSD learning curves for the correlated input generated using ${G}_{1}\left(z\right)$ in a sparse system with impulsive noises (Pr = 0.01). The system suddenly changes (${\mathbf{w}}_{o}\to -{\mathbf{w}}_{o}$) at iteration $3.8\times {10}^{3}$.

**Figure 8.**NMSD learning curves for the correlated input generated using ${G}_{2}\left(z\right)$ in a sparse system with impulsive noises (Pr = 0.01). The system suddenly changes ${\mathbf{w}}_{o}\to -{\mathbf{w}}_{o}$) at iteration $3.8\times {10}^{3}$.

**Figure 12.**NMSD learning curves with several values of p to decide the p value to ensure the best filter performance for the white input in a sparse system with impulsive noises (Pr = 0.01).

**Figure 13.**NMSD learning curves with several values of p to decide the p value to ensure the best filter performance for the correlated input generated using ${G}_{1}\left(z\right)$ in a sparse system with impulsive noises (Pr = 0.01).

**Figure 14.**NMSD learning curves with several values of p to decide the p value to ensure the best filter performance for the correlated input generated using ${G}_{2}\left(z\right)$ in a sparse system with impulsive noises (Pr = 0.01).

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**MDPI and ACS Style**

Shin, J.; Kim, J.; Kim, T.-K.; Yoo, J.
*ℒ*_{p}-Norm-like Affine Projection Sign Algorithm for Sparse System to Ensure Robustness against Impulsive Noise. *Symmetry* **2021**, *13*, 1916.
https://doi.org/10.3390/sym13101916

**AMA Style**

Shin J, Kim J, Kim T-K, Yoo J.
*ℒ*_{p}-Norm-like Affine Projection Sign Algorithm for Sparse System to Ensure Robustness against Impulsive Noise. *Symmetry*. 2021; 13(10):1916.
https://doi.org/10.3390/sym13101916

**Chicago/Turabian Style**

Shin, Jaewook, Jeesu Kim, Tae-Kyoung Kim, and Jinwoo Yoo.
2021. "*ℒ*_{p}-Norm-like Affine Projection Sign Algorithm for Sparse System to Ensure Robustness against Impulsive Noise" *Symmetry* 13, no. 10: 1916.
https://doi.org/10.3390/sym13101916