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I gained samples of audio signal that have integer representation. I want to take dwt from samples and destroy them, by selected threshold. My problem is threshold choice.

samsam114
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ali
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  • What about a hard and soft thresholding by D. Donoho? The threshold can be estimated from the finest wavelet coefficients. Take a look at his papers: Ideal spatial adaptation via wavelet shrinkage, Nonlinear Wavelet Methods for Recovering Signals, Images, and Densities from indirect and noisy data, Wavelet Shrinkage: Asymptopia. – DaBler Jan 13 '17 at 15:29

1 Answers1

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You must perform the following steps:

  1. Calculate the forward DWT, with any reasonable wavelet (say, CDF 5/3 or CDF 9/7) and either with real numbers or integers.
  2. Estimate the noise variance σ2 from the finest wavelet coefficients d1 using
    sigma = med(|d1|)/0.6745.
    Note that this estimation is valid for an additive noise with the normal (Gaussian) distribution.
  3. Determine the noise threshold as
    lambda = sigma sqrt(2 ln N),
    where the N is the length of the signal.
  4. Perform the hard or soft thresholding using the estimated threshold.
  5. Calculate the inverse DWT using the thresholded coefficients.

References

  • Donoho, D. L.; Johnstone, I. M.: Ideal Spatial Adaptation by Wavelet Shrinkage. Biometrika, vol. 81, no. 3, 1994, pp. 425–455.
DaBler
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