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REVIEW 4 major objections 4 minor 34 references

Efficient Capon-Based Approach Exploiting Temporal Windowing For Electric Network Frequency Estimation

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Applying a non-rectangular temporal window before spectral estimation lets a fast Capon-based estimator recover the Electric Network Frequency from one-second power recordings with correlation 0.9990, and even plain STFT with a Parzen…

desk verdict The temporal-windowing observation is real and useful for ENF extraction, but the fast-Capon derivation has an unjustified Toeplitz assumption and a notation mismatch that sink the efficiency claim as written. read the letter →

arxiv 1908.08813 v2 pith:QZEHFXKW submitted 2019-08-22 eess.SP cs.CV

Georgios Karantaidis , Constantine Kotropoulos This is my paper · ORCID
classification eess.SPcs.CV
keywords ElectricNetworkFrequencyCaponspectralestimatortemporalwindowingGohberg-SemenculfactorizationKrylovmatricesParzenwindowmultimediaforensicsestimation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that temporal windowing, applied before spectral estimation, is a decisive and previously underused step in extracting the Electric Network Frequency (ENF) from audio and power recordings. It proposes a fast Capon-based spectral estimator that multiplies each frame by a non-rectangular temporal window—Parzen works best for power recordings—and speeds up covariance inversion through a Gohberg-Semencul factorization. On a 30-minute power recording, the method reaches a correlation of 0.9990 with the reference ENF even with a one-second frame, where competing methods fall below 0.99. The paper also reports that plain Short-Time Fourier Transform with a Parzen window reaches about 0.9990, outperforming recent state-of-the-art estimators. This matters because forensic authentication often must work on short recordings, and speed matters for large datasets.

What carries the argument

The load-bearing object is the filter-bank Capon spectral estimator combined with temporal windowing. Capon uses a data-dependent finite-impulse-response filter that passes frequency $\omega$ while minimizing output power from all other frequencies, giving the high-resolution spectral estimate $\hat{\varphi}(\omega) = (m+1)/(a^*(\omega)\hat{R}^{-1}a(\omega))$. The speed-up relies on writing $\hat{R}^{-1}$ via Krylov matrices and the Gohberg-Semencul factorization (Eq. 9), an exact expression of the inverse of a Toeplitz matrix as a difference of products of Krylov matrices, so the denominator at all frequency bins is evaluated with one zero-padded FFT instead of repeated matrix inversions. The temporal window—Parzen in the main power experiments—is the conceptual novelty: it is applied to the time series before covariance estimation, and the paper argues this choice, not the spectral estimator alone, controls estimation accuracy at short frame lengths.

What would settle it

Take a real one-second power-recording frame, build $\hat{R}$ exactly as in Eq. (5) with a Parzen window, and test whether $\hat{R}$ is Toeplitz or has the assumed displacement rank. Then compare the Gohberg-Semencul inverse from Eq. (9) with a direct inverse: if the matrices disagree materially, or if replacing the fast inversion with a direct inversion changes the reported 0.9990 correlation or runtime, the fast-implementation claim fails.

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Extended reading notes

Core claim

The authors claim that a filter-bank Capon spectral estimator, fed with temporally windowed frames, gives higher correlation with the ground-truth ENF than the state-of-the-art methods they compare against, while remaining computationally fast. The estimator forms the sample covariance $\hat{R}$ from windowed samples $\tilde{y}(t) = w(t-n)y(t)$, computes the data-dependent Capon filter $h = \hat{R}^{-1}a(\omega)/(a^*(\omega)\hat{R}^{-1}a(\omega))$, and evaluates the spectral denominator through a zero-padded FFT after expressing $\hat{R}^{-1}$ with Krylov matrices and the Gohberg-Semencul factorization, Eq. (9). With a Parzen window and a 1-second frame, the estimated ENF correlates at 0.9990 with the ground truth; at 5 and 10 seconds it reaches 0.9991. On the speech dataset, a rectangular window gives 0.9351 at 33 seconds, close to linear prediction but faster. The authors further show that window selection is decisive: Parzen or Hamming windows are needed for short power-record frames, while Kaiser and rectangular windows fail below 10 seconds, and the same window logic makes even STFT outperform recent specialized estimators.

Load-bearing premise

The speed-up assumes the covariance matrix built from windowed frames has a shift-invariant (Toeplitz) or low-displacement-rank structure; multiplying the frame by a non-rectangular window generally destroys that structure for the sample covariance in Eq. (5), and the paper provides no argument or approximation showing the Gohberg-Semencul factorization still applies.

Editorial extensions

If this is right

  • Forensic timestamping and authentication can work on power recordings as short as one second, since the estimated ENF matches the reference at 0.9990 correlation.
  • Window selection should become a standard control variable in ENF studies; the paper shows a Parzen-windowed STFT beating recent specialized estimators, so previous comparisons that used only rectangular windows may need revisiting.
  • The fast Capon implementation makes high-resolution spectral estimation practical for large speech datasets, where speed currently favors simpler methods.
  • For speech recordings, where the rectangular window wins, the proposed method yields 0.9351 correlation at 33 seconds, close to linear prediction but with lower time cost.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An extension the paper leaves implicit is jointly optimizing the window shape and frame length per harmonic's signal-to-noise ratio, which could push ENF accuracy further and could be tested on the same datasets.
  • The reported gap between windowed STFT and windowed Capon is small, raising the question of whether the Capon estimator's advantage persists once both methods use the same optimal window on a wider range of recordings.
  • A natural extension, which the conclusion gestures toward, is applying the windowed fast-Capon pipeline to single images with rolling-shutter or fluorescent-light ENF signatures, where short analysis windows are the norm.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper presents a fast Capon-based spectral estimator for Electric Network Frequency (ENF) extraction, combining temporal windowing with Gohberg–Semencul factorization and Krylov matrices to speed up matrix inversion. Experiments on power and speech recordings report high correlation with reference ENF signals and claim improvements over several state-of-the-art methods, especially at short frame lengths. The paper also investigates the effect of different temporal windows on both the proposed method and the STFT baseline.

Significance. If the algorithmic claims held, the method would be a practical contribution to ENF-based multimedia forensics, offering high accuracy with low computational cost at short frame lengths. The paper includes extensive comparisons with multiple baselines and attempts a statistical significance test. However, the central derivation is not sound: the fast inversion relies on a Toeplitz property that does not hold for the windowed sample covariance matrix, so the main claim of an efficient Capon-based method is unsupported as written.

major comments (4)
  1. [Section 3.2 and Eq. (5)] The fast implementation applies the Gohberg–Semencul (GS) factorization to the sample covariance matrix R-hat of Eq. (5), but after multiplication by a non-rectangular temporal window, R-hat is not Toeplitz. For windowed samples y-tilde(t) = w(t-n)y(t), the (i,j) entry of R-hat is proportional to sum_t w(t-i)w(t-j)y(t-i)y*(t-j), which depends on i and j through the window product, not only on i-j. The GS factorization requires Toeplitz or low-displacement-rank structure, and the paper supplies neither a proof nor an approximation showing that the windowed sample covariance satisfies this condition. This is the load-bearing step for the claimed computational efficiency and for the reported accuracy, so the central contribution is not established.
  2. [Section 3.2 vs. Section 3.1] There is a dimensional inconsistency between the covariance matrix used in the Capon formula and the one inverted by the GS algorithm. Eq. (5) defines an (m+1)x(m+1) matrix with m=10, and Eq. (6) only needs the inverse of this small matrix. In contrast, Eqs. (9)–(13) describe a fast inversion of an NxN matrix R_N, with N = LFs. The paper does not clarify how the N-dimensional matrix relates to the (m+1)-dimensional sample covariance, so either the fast algorithm is operating on a different matrix than the one used in Eq. (6), or the Capon formula is misstated. The claimed complexity reduction is therefore not backed by a coherent algorithmic description.
  3. [Section 4.1 and Tables 1–4] The harmonic index and temporal window are selected based on performance on the same test recordings (e.g., 'only the third harmonic was used, because it provides the best results' for Data 1, Section 4.1). This in-sample selection inflates the reported correlation coefficients and makes the comparisons to state-of-the-art methods optimistic. The authors should separate model selection from evaluation, for example by using a validation subset or cross-validation.
  4. [Section 4.2, Fisher transform] The significance test assumes n=1800 independent samples, but the ENF sequences being correlated are estimated from frames with a 1-second shift and frame lengths up to 20 seconds, so successive estimates are highly dependent. Moreover, the pairwise correlations are computed on the same recordings, so the samples are not independent across methods either. The statement that all pairwise differences are significant at the 95% level is therefore not statistically justified.
minor comments (4)
  1. [Table 2 and Table 4] 'Kaizer' is a typo for 'Kaiser'; please correct throughout the manuscript.
  2. [Section 4.2] The reference to 'Fig. 1' in the text does not appear to be accompanied by the actual figure or its data in the manuscript; include the figure or remove the reference.
  3. [Eq. (3)] The notation g-tilde(l) is used in the correlation formula but is not explicitly defined in the equation; define it for clarity.
  4. [Abstract and Section 2] The claim that this is the first use of a non-rectangular temporal window in ENF estimation should be verified against the broader ENF literature, which includes many windowing practices, or softened to avoid overstatement.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Capon/GS derivation is standard and the reported accuracy rests on external benchmarks, not on fitted inputs.

full rationale

The core Capon estimator is defined by Eqs. (4)-(6), with the sample covariance \hat R formed from the windowed data in Eq. (5); no parameter in these equations is fitted to the correlation coefficients reported in Tables 1-4. The fast inversion in Eqs. (7)-(14) is imported from the external references [19,21], and the paper's statement that R_N is Toeplitz (Sec. 3.2) is an assertion about the covariance model, not a restatement of the empirical result. The only self-citation is [8], used to justify the filtering/parametrization and to refer to datasets also used in prior work; it does not carry the central Capon/GS derivation or the accuracy claim. The reported accuracy is an empirical comparison against external baseline methods using the maximum-correlation metric applied to estimated versus ground-truth ENF (Eqs. (2)-(3)); this metric does not define the estimate in terms of the claimed outcome. The clear weakness of the paper -- applying Gohberg-Semencul inversion to a windowed sample covariance that is not obviously Toeplitz -- is an omitted justification/correctness gap, not a circular reduction; it does not make the predicted correlations equal to fitted inputs. Consequently, there is no step in the derivation chain that reduces by definition or by self-citation to its own inputs.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim depends on a handful of hand-chosen parameters (model order, frequency grid, filter lengths, window and harmonic choices per dataset) and on four assumptions, the most fragile being the Toeplitz structure of a windowed sample covariance matrix. No new physical entities are introduced.

free parameters (5)
  • Capon model order m = m=10
    Set to m=10 in Sec. 3.1; controls covariance matrix size and spectral resolution; no sensitivity analysis.
  • Frequency grid density Q = Q=4N
    Sec. 3.1 sets Q=4N; affects spectral sampling; chosen by hand.
  • Band-pass FIR filter lengths and passband width = C1=1001, C2=4801, 0.1 Hz band
    Sec. 2 chooses filter order and band around harmonics; dataset-specific and not justified.
  • Temporal window choice per dataset = Parzen (Data 1), Rectangular (Data 2)
    Sec. 4.2 selects the best window based on achieved correlation on the same recordings; this is in-sample selection.
  • Harmonic index used = 3rd harmonic (Data 1), 2nd harmonic (Data 2)
    Sec. 4.1 selects harmonic with best SNR; per-dataset choice.
assumptions (4)
  • ad hoc to paper The sample covariance matrix R-hat of Eq. (5) is Toeplitz after applying a temporal window.
    Needed for GS factorization Eq. (9); not established for non-rectangular windows.
  • domain assumption ENF is stationary within each analysis frame.
    Standard for spectral estimation; implicit in covariance estimation.
  • domain assumption The reference ground truth g (Frequency Disturbance Recorder) is exact and the maximum-correlation matching in Eq. (2) is a valid evaluation.
    Used to compute accuracy; no error model for g.
  • ad hoc to paper The Fisher z-test with n=1800 independent samples is valid for comparing correlation coefficients.
    ENF samples are autocorrelated, so the independence assumption is likely violated; the paper provides no justification.

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Cite this review

Pith. "Pith review of Efficient Capon-Based Approach Exploiting Temporal Windowing For Electric Network Frequency Estimation." pith.science (2026). https://pith.science/paper/QZEHFXKW

@misc{pith2026190808813,
  author       = {Pith},
  title        = {Pith review of: Efficient Capon-Based Approach Exploiting Temporal Windowing For Electric Network Frequency Estimation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QZEHFXKW}},
  note         = {Machine review of arXiv:1908.08813}
}
abstract

Electric Network Frequency (ENF) fluctuations constitute a powerful tool in multimedia forensics. An efficient approach for ENF estimation is introduced with temporal windowing based on the filter-bank Capon spectral estimator. A type of Gohberg-Semencul factorization of the model covariance matrix is used due to the Toeplitz structure of the covariance matrix. Moreover, this approach uses, for the first time in the field of ENF, a temporal window, not necessarily the rectangular one, at the stage preceding spectral estimation. Krylov matrices are employed for fast implementation of matrix inversions. The proposed approach outperforms the state-of-the-art methods in ENF estimation, when a short time window of $1$ second is employed in power recordings. In speech recordings, the proposed approach yields highly accurate results with respect to both time complexity and accuracy. Moreover, the impact of different temporal windows is studied. The results show that even the most trivial methods for ENF estimation, such as the Short-Time Fourier Transform, can provide better results than the most recent state-of-the-art methods, when a temporal window is employed. The correlation coefficient is used to measure the ENF estimation accuracy.

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Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

  1. [1]

    Efficient Capon-Based Approach Exploiting Temporal Windowing For Electric Network Frequency Estimation

    INTRODUCTION Multimedia content is present in all aspects of everyday life, containing citizens’ sensitive information. Audio, image, and video recordings are vulnerable to editings, alterations, and all kind of attacks trying to modify their content. It is evident that accurate methods in the field of multimedia forensics are necessary to confront such cr...

    work page Pith review arXiv 1908

  2. [2]

    The rectangular window has been used ex- clusively as a temporal window [3]

    WINDOW SELECTION AND ESTIMA TION PROCEDURE Window selection was not thoroughly investigated within ENF estimation. The rectangular window has been used ex- clusively as a temporal window [3]. Temporal windowing denotes the multiplication of the time-series with a window prior to spectral analysis. On the contrary, a lag window denotes the multiplication o...

    work page

  3. [3]

    PROPOSED APPROACH 3.1. The Capon method The periodogram can be interpreted as a filter bank ap- proach, which uses a band-pass filter whose impulse response vector is given by the standard Fourier transform vector[ 1,e −iω,...,e −i(N −1)ω]T . The Capon method, is another filter bank approach based on a data-dependent filter [21]: h = ˆR−1a(ω) a∗(ω) ˆR−1 a(ω) ...

    work page

  4. [4]

    Datasets Two datasets are employed in order to evaluate the proposed approach and compare it with other state-of-the-art methods

    EXPERIMENTAL EV ALUA TION 4.1. Datasets Two datasets are employed in order to evaluate the proposed approach and compare it with other state-of-the-art methods. The first dataset, namely Data 1, was recorded by connect- ing an electric outlet directly to the internal sound card of a desktop computer, while the second one, namely Data 2, com- prises of a sp...

    work page

  5. [5]

    CONCLUSION A novel approach for ENF estimation based on Capon method with temporal windowing has been discussed. Taking advan- tage of the Toeplitz structure of the covariance matrices and exploiting Krylov matrices, a fast and efficient approach has been developed, which yields higher accuracy compared to the state-of-the-art methods in power recordings. ...

    work page

  6. [6]

    Digital audio recording analysis: The electric network frequency (ENF) criterion,

    C. Grigoras, “Digital audio recording analysis: The electric network frequency (ENF) criterion,” Int. J. of Speech Language & the Law , vol. 12, no. 1, pp. 63–76, 2005

    work page 2005

  7. [7]

    Applications of ENF criterion in forensic audio, video, computer and telecommunication analy- sis,

    C. Grigoras, “Applications of ENF criterion in forensic audio, video, computer and telecommunication analy- sis,” F orensic Sci. Int., vol. 167, no. 2-3, pp. 136–145, 2007

    work page 2007

  8. [8]

    ENF extrac- tion from digital recordings using adaptive techniques and frequency tracking,

    O. Ojowu, J. Karlsson, J. Li, and Y . Liu, “ENF extrac- tion from digital recordings using adaptive techniques and frequency tracking,” IEEE Trans. Inf. F orensics and Security, vol. 7, no. 4, pp. 1330–1338, 2012

    work page 2012

Show all 34 references
  1. [9]

    Electrical network fre- quency (ENF) maximum-likelihood estimation via a multitone harmonic model,

    D. Bykhovsky and A. Cohen, “Electrical network fre- quency (ENF) maximum-likelihood estimation via a multitone harmonic model,” IEEE Trans. Inf. F orensics and Security, vol. 8, no. 5, pp. 774–753, 2013

    2013

  2. [10]

    Spectrum com- bining for ENF signal estimation,

    A. Hajj-Ahmad, R. Garg, and M. Wu, “Spectrum com- bining for ENF signal estimation,” IEEE Signal Proc. Letters, vol. 20, no. 9, pp. 885–888, 2013

    2013

  3. [11]

    An improved discrete Fourier transform-based algo- rithm for electric network frequency extraction,

    L. Fu, P. N. Markham, R. W. Conners, and Y . Liu, “An improved discrete Fourier transform-based algo- rithm for electric network frequency extraction,” IEEE Trans. Inf. F orensics and Security , vol. 8, no. 7, pp. 1173–1181, 2013

    2013

  4. [12]

    Robust electric network frequency estimation with rank reduction and linear prediction,

    X. Lin and X. Kang, “Robust electric network frequency estimation with rank reduction and linear prediction,” ACM Trans. Multimedia Com. Commun. and Appl. , vol. 14, no. 4, pp. 1–13, 2018

    2018

  5. [13]

    Assessing spectral estimation methods for electric network frequency ex- traction,

    G. Karantaidis and C. Kotropoulos, “Assessing spectral estimation methods for electric network frequency ex- traction,” in Proc. 22 nd Panhellenic Conf. Informatics , 2018, pp. 202–207

    2018

  6. [14]

    ”Seeing” ENF: Power-signature-based timestamp for digital multimedia via optical sensing and signal pro- cessing,

    R. Garg, A. L. Varna, A. Hajj-Ahmad, and M. Wu, “”Seeing” ENF: Power-signature-based timestamp for digital multimedia via optical sensing and signal pro- cessing,” IEEE Trans. Inf. F orensics and Security, vol. 8, no. 9, pp. 1417–1432, 2013

    2013

  7. [15]

    Ex- ploiting rolling shutter for ENF signal extraction from video,

    H. Su, A. Hajj-Ahmad, R. Garg, and M. Wu, “Ex- ploiting rolling shutter for ENF signal extraction from video,” in Proc. IEEE Int. Conf. Image Process. , 2014, pp. 5367–5371

    2014

  8. [16]

    Invisible geo-location signature in a single image,

    C. W. Wong, A. Hajj-Ahmad, and M. Wu, “Invisible geo-location signature in a single image,” inProc. IEEE Int. Conf. Acoustics, Speech and Signal Process. , 2018, pp. 1987–1991

    2018

  9. [17]

    Explor- ing the use of ENF for multimedia synchronization,

    M. Wu H. Su, A. Hajj-Ahmad and D. Oard, “Explor- ing the use of ENF for multimedia synchronization,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Pro- cess., 2014, pp. 4613–4617

    2014

  10. [18]

    ENF-based region-of-recording identification for media signals,

    R. Garg A. Hajj-Ahmad and M. Wu, “ENF-based region-of-recording identification for media signals,” IEEE Trans. Inf. F orensics and Security, vol. 10, no. 6, pp. 1125–1136, 2015

    2015

  11. [19]

    Edit detection in speech recordings via instantaneous electric network frequency variations,

    J. A. Apolinario P. A. A. Esquef and L. W. P. Biscainho, “Edit detection in speech recordings via instantaneous electric network frequency variations,” IEEE Trans. Inf. F orensics and Security, vol. 9, no. 12, pp. 2314–2326, 2014

    2014

  12. [20]

    Audio authenticity: Detecting ENF disconti- nuity with high precision phase analysis,

    J. A. Apolinario D. P. N. Rodriguez and L. W. P. Bis- cainho, “Audio authenticity: Detecting ENF disconti- nuity with high precision phase analysis,” IEEE Trans. Inf. F orensics and Security, vol. 5, no. 3, pp. 534–543, 2010

    2010

  13. [21]

    Au- dio authentication by exploring the absolute-error-map of ENF signals,

    G. Hua, Y . Zhang, J. Goh, and V . L. L. Thing, “Au- dio authentication by exploring the absolute-error-map of ENF signals,” IEEE Trans. Inf. F orensics and Secu- rity, vol. 11, no. 5, pp. 1003–1016, 2016

    2016

  14. [22]

    Audio authentication using the kurtosis of esprit based ENF estimates,

    P. M. J. I. Reis, J. P. C. L. Costa, R. K. Miranda, and G. D. Galdo, “Audio authentication using the kurtosis of esprit based ENF estimates,” in Proc. 10th Int. Conf. Signal Process. and Commun. Systems , 2016

    2016

  15. [23]

    Factors affecting ENF capture in audio,

    A. Hajj-Ahmad, C. Wong, S. Gambino, Q. Zhu, M. Yu, and M. Wu, “Factors affecting ENF capture in audio,” IEEE Trans. Inf. F orensics and Security, vol. 14, no. 2, pp. 277–288, 2019

    2019

  16. [24]

    IAA spectral estimation: Fast implementation using the Gohberg-Semencul factoriza- tion,

    M. Xue, L. Xu, and J. Li, “IAA spectral estimation: Fast implementation using the Gohberg-Semencul factoriza- tion,” IEEE Trans. Signal Process. , vol. 59, no. 7, pp. 3251–3261, 2011

    2011

  17. [25]

    Efficient implementation of iterative adaptive approach spectral estimation tech- niques,

    G. Glentis and A. Jakobsson, “Efficient implementation of iterative adaptive approach spectral estimation tech- niques,” IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4154–4167, 2011

    2011

  18. [26]

    Stoica and R

    P. Stoica and R. L. Moses, Spectral Analysis of Signals , Pearson Prentice Hall Upper Saddle River, NJ, 2005

    2005

  19. [27]

    Mathematical considerations in the estima- tion of spectra,

    E. Parzen, “Mathematical considerations in the estima- tion of spectra,” Technometrics, vol. 3, no. 2, pp. 167– 190, 1961

    1961

  20. [28]

    On the use of windows for harmonic anal- ysis with the discrete Fourier transform,

    F. J. Harris, “On the use of windows for harmonic anal- ysis with the discrete Fourier transform,” Proc. of the IEEE, vol. 66, no. 1, pp. 51–83, 1978

    1978

  21. [29]

    A. V . Oppenheim and R. W. Schafer,Discrete-Time Sig- nal Processing, Prentice Hall Press, Upper Saddle River, NJ, USA, 3rd edition, 2009

    2009

  22. [30]

    An automated approach to the electric network frequency (ENF) criterion - theory and prac- tice,

    A. J. Cooper, “An automated approach to the electric network frequency (ENF) criterion - theory and prac- tice,” Int. J. of Speech Language and the Law , vol. 16, no. 2, 2009

    2009

  23. [31]

    PARSHL: An analy- sis/synthesis program for non-harmonic sounds based on a sinusoidal representation,

    J. O. Smith and X. Serra, “PARSHL: An analy- sis/synthesis program for non-harmonic sounds based on a sinusoidal representation,” in Proc. Int. Computer Music Conf., 1987, pp. 290–297

    1987

  24. [32]

    Using the ENF crite- rion for determining the time of recording of short digi- tal audio recordings,

    M. Huijbregtse and Z. Geradts, “Using the ENF crite- rion for determining the time of recording of short digi- tal audio recordings,” in Proc. Int. Workshop Computa- tional F orensics, 2009, pp. 116–124

    2009

  25. [33]

    An efficient algorithm for a large Toeplitz set of linear equations,

    J. Jain, “An efficient algorithm for a large Toeplitz set of linear equations,” IEEE Trans. Acoustics, Speech, and Signal Process., vol. 27, no. 6, pp. 612–615, 1979

    1979

  26. [34]

    Papoulis, Probability and Statistics , Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1990

    A. Papoulis, Probability and Statistics , Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1990

    1990

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