Circuits, Systems, and Signal Processing

, Volume 37, Issue 8, pp 3351–3352

# Correction to: Improved Eigenvalue Decomposition-Based Approach for Reducing Cross-Terms in Wigner–Ville Distribution

Correction

## 1 Correction to: Circuits Syst Signal Process  https://doi.org/10.1007/s00034-018-0846-0

The original version of the article unfortunately contained few errors in reference citations and equations. This has been corrected with this erratum.
• In Sect. 1, the sentence “The time–frequency representation (TFR) finds applications in many areas like as communication [14], seismology [41], speech signal analysis and synthesis [6], biomedical engineering [24], and mechanical vibrational signal analysis [17,71].” should read as follows:

“The time–frequency representation (TFR) finds applications in many areas such as communication [3], seismology [41], acoustic signal analysis [6], biomedical engineering [24], and induction motor and rotating machinery fault diagnosis [17,71].”

• In Sect. 1, the sentence “The short-time Fourier transform (STFT) computes the Fourier transform (FT) of windowed signal, which leads to fixed resolution in time–frequency domain [13,35].” should read as follows:

“The short-time Fourier transform (STFT) computes the Fourier transform (FT) of windowed signal, which leads to fixed resolution in time–frequency domain [14,35].”

• In Sect. 2, the sentence “If FT of s(t) is represented by $$S(\varOmega )$$, the representation of WVD in frequency domain can be given as follows [16]:” should read as follows:

“If FT of s(t) is represented by $$S(\varOmega )$$, the representation of WVD in frequency domain can be given as follows [16,35]:”

• Equation (2) should read as follows:
\begin{aligned} \hbox {WVD}_S \left( {t,\varOmega } \right) =\frac{1}{2\pi }\mathop \int \nolimits _{-\infty }^{+\infty } S\,\left( {\varOmega +\frac{\varOmega '}{2}} \right) S^{*}\left( {\varOmega -\frac{\varOmega '}{2}} \right) e^{+j\varOmega 't}d\varOmega ' \end{aligned}
• Equation (6) should read as follows:
\begin{aligned} X_m \left[ l \right] =\varLambda _{{y}_{\left( m \right) } } \hbox {Fn}\left( {{V}_{{y}_{\left( m \right) }}} \right) +\varLambda _{{y}_{\left( {L-m+1} \right) }} \hbox {Fn}\left( {{V}_{{y}_{\left( {L-m+1} \right) }}} \right) \end{aligned}