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audioimage-processingdwt

How to gain hard and soft threshold in discrete wavelet transform by integer samples

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.

Solution

  • 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.