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

Question

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.

Answer 1

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
   .
   Note that this estimation is valid for an additive noise with the normal (Gaussian) distribution.
3. Determine the noise threshold as
   ,
   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.