Skip to main content
SpringerLink
Log in

Robust DFT-based filtering of pulse-like FM signals corrupted by impulsive noise

  • Original paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

Filtering of pulse-like FM signals with varying amplitude corrupted by impulse noise is considered. The robust DFT calculated for overlapped intervals is used for this aim. This technique is proposed in order to decrease amplitude distortion of output signals that can be introduced by the robust DFT calculated within a wide interval including possible zero-output. The proposed algorithm is realized through the following steps. In the first stage, the robust DFT is calculated for the intervals. Filtered signals from the intervals are obtained by applying the standard inverse DFT for the robust DFTs applied to input data. In the second stage, results for different overlapped intervals are combined using the appropriate order statistics. In addition, an algorithm inspired by the intersection of the confidence intervals rule is used for adaptive selection of the interval width in the robust DFT. Algorithm accuracy is tested on numerical examples. Computational complexity analysis is also provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

x(n):

signal

A(n):

signal amplitude

\({\phi (n)}\) :

signal phase

X(k):

standard DFT

X α(k):

robust L-DFT

r k (i),i k (i):

sorted real and imaginary parts of modulated signal sequence

a :

parameter of the L-filter

a i :

coefficients of the L-filter

\({\hat{f}(n)}\) :

filtered signal

N :

signal duration

W N :

exp (−j2π /N)

Δt :

sampling rate

Q :

number of subintervals

x i (n):

signal within interval i

δ:

overlapping coefficient

IDFT{}:

standard inverse DFT

F(ξ):

loss function

p ν(ξ):

pdf of noise

MAE, MAE l :

mean absolute value and its

 :

locally calculated version

RMSE, RMSE l :

root mean squared error and its locally calculated version

R :

number of trial in the Monte Carlo simulation

N l :

number of instants within “high” amplitude interval

κ:

parameter of the ICI procedure

Γ:

parameter of the CV procedure

ξ i :

ξ i  = N/Q i interval width

p(n;ξ i ), \({\hat{f}_{\xi _{i}}(n)}\) :

estimates produced by interval width ξ i

σ (n;ξ i ):

standard deviation of estimate \({\hat{f}_{\xi_{i}}(n) }\)

ρ:

parameter of noise

\({\Gamma _{{\rm opt}},\hat{f}_{\Gamma _{{\rm opt}}}(n)}\) :

optimal value of Γ and corresponding estimate

\({\hat{f}_{\Gamma _{l}}(n),\xi _{\Gamma _{l}}(n)}\) :

estimate and optimal interval width for Γ l

References

  1. Lombardi M.J. and Godsill S.J. (2006). On-line Bayesian estimation of signals in symmetric α-stable noise. IEEE Trans. Sig. Proc. 54(2): 775–779

    Article  Google Scholar 

  2. Radford, D., Kurekin, A., Marshall, D., Lever, K., Lukin, V.: Robust processing of SAR hologram data to mitigate impulse noise impairments. Proc. Fusion (2005)

  3. Arce G.R. (2005). Nonlinear Signal Processing—A Statistical Approach. Wiley, New York

    Google Scholar 

  4. Astola J.T. and Kuosmanen P. (1997). Fundamentals of Nonlinear Digital Filtering. CRC Press, Boca Raton

    Google Scholar 

  5. Wang Z. and Zhang D. (1999). Progressive switching median filter for the removal of impulse noise from highly corrupted images. IEEE Trans. Circ. Syst. II, 46(1): 78–80

    Article  Google Scholar 

  6. Besdok E. (2004). Impulsive noise suppresion from images with a modified two-step iterative median filter. J. El. Imag. 13(4): 714–719

    Article  Google Scholar 

  7. Djurović I. and Stanković L.J. (2002). Realization of the robust filters in the frequency domain. IEEE Sig. Proc. Lett. 9(10): 333–335

    Article  Google Scholar 

  8. Arce G.R. (1998). A general weighted median filter structure admitting negative weights. IEEE Trans. Sig. Proc. 46(12): 3195–3205

    Article  Google Scholar 

  9. Kalluri S. and Arce G.R. (2001). Robust frequency-selective filtering using weighted myriad filters admitting real-valued weights. IEEE Trans. Sig. Proc. 49(11): 2721–2733

    Article  Google Scholar 

  10. Shmulevich, I., Arce, G.R.: Spectral design of weighted median filters admitting negative weights. IEEE Sig. Proc. Lett. 8(12) 313–316

  11. Arce G.R. and Paredes J.L. (2000). Recursive weighted median filters admitting negative weights and their optimization. IEEE Trans. Sig. Proc. 48(3): 768–779

    Article  Google Scholar 

  12. Katkovnik V. (1998). Robust M-periodogram. IEEE Trans. Sig. Proc. 46(11): 3104–3109

    Article  Google Scholar 

  13. Katkovnik V. (1999). Robust M-estimates of the frequency and amplitude of a complex-valued harmonic. Sig. Process. 77(1): 71–84

    Article  MATH  Google Scholar 

  14. Huber P.J. (1973). Robust regression: asymptotics, conjectures and Monte Carlo. Ann. Math. Stati. 1(5): 799–821

    MATH  MathSciNet  Google Scholar 

  15. Huber P.J. (1981). Robust Statistics. Wiley, New York

    Book  MATH  Google Scholar 

  16. David H.A. and Nagaraja H.N. (2003). Order Statistics. Wiley, New York

    Book  MATH  Google Scholar 

  17. Katkovnik V. and Stanković L.J. (1998). The instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length. IEEE Trans. Sig. Process. 46(9): 2315–2326

    Article  Google Scholar 

  18. Stanković L.J. and Katkovnik V. (1998). Algorithm for the instantaneous frequency estimation using time-frequency distributions with variable window width. IEEE Sig. Proc. Lett. 5(9): 224–227

    Article  Google Scholar 

  19. Stanković L.J. and Katkovnik V. (2000). Instantaneous frequency estimation using higher order distributions with adaptive order and window length. IEEE Trans. Inf. Th. 46(1): 302–311

    Article  Google Scholar 

  20. Djurović, I., Stanković, L.J., Böhme, J.F.: Myriad filter based form of the DFT. EUSIPCO’2002, Vol. III. Toulouse, France, 433–436

  21. Djurović I., Katkovnik V. and Stanković L.J. (2001). Median filter based realizations of the robust time-frequency distributions. Sig. Process. 81(7): 1771–1776

    Article  Google Scholar 

  22. Djurović I., Stanković L.J. and Böhme J.F. Robust (2003). L-estimation based forms of signal transforms and time-frequency representations. IEEE Trans. Sig. Proc 51(7): 1753–1761

    Article  Google Scholar 

  23. Djurović I., Lukin V.V. and Roenko A.A. (2004). Removal of α-stable noise in frequency modulated signals using robust DFT forms. Telecommun. Radioeng. 61(7): 574–590

    Article  Google Scholar 

  24. Stoica P. and Moses R.L. (1997). Introduction to Spectral Analysis. Englewood Chiffs, Prentice-Hall

    MATH  Google Scholar 

  25. Welch, P.: The use of fast Fourier transform for the estimation of power spectra: a method based on time-averaging over short, modified periodograms. IEEE Trans. Aud. Electroacust. 15(2) (1967)

  26. Oktem, R.: Transform domain algorithms for image compression and denoising. PhD Thesis, Tampere University of Technology (Tampere, Finland), 142 p. (2000) http://www.cs. tut.fi/~karen/project_site

  27. Nikias C.L. and Shao M. (1995). Signal Processing with Alpha Stable Distributions and Applications. Wiley, New York

    Google Scholar 

  28. Tsihrintzis G.A. and Nikias C.L. (2005). Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process. IEEE Trans. Commun. 43(2–4): 904–914

    Google Scholar 

  29. Goldenshluger A. and Nemirovski A. (1997). On spatial adaptive estimation of nonparametric regression. Math. Meth. Stat. 6: 135–170

    MATH  MathSciNet  Google Scholar 

  30. Katkovnik, V., Egiazarian, K., Astola, J.: Adaptive varying window methods in image processing Part I: denoising and deblurring. TICSP Series Report #13 (2003)

  31. Fan J. and Gijbels I. (1996). Local Polynomial Modeling and Its Applications. Chapman & Hall, London

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electrical Engineering Department, University of Montenegro, 81000, Podgorica, Montenegro

    Igor Djurović

  2. Department of Receivers, Transmitters and Signal Processing, National Aerospace University, 17 Chkalova Street, 61070, Kharkov, Ukraine

    Vladimir V. Lukin

Authors
  1. Igor Djurović
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir V. Lukin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Igor Djurović.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Djurović, I., Lukin, V.V. Robust DFT-based filtering of pulse-like FM signals corrupted by impulsive noise. SIViP 1, 39–51 (2007). https://doi.org/10.1007/s11760-007-0005-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-007-0005-8

Keywords

Search

Navigation