Many researchers used DWT for denoising of the signal. Using wavelet we can suppress noise which are out of frequency band of the signal. Although, we can also do the same thing using conventional filters (butterworth, Chebyshev). So, my query is what are the advantages of wavelet for filtering, apart form automatic threshold?
The main advantage of wavelet basis is that they despite having irregular shape are able to perfectly reconstruct functions with linear and higher order polynomial shapes, such as, rect, triangle, 2nd order polynomials, etc. Note that Fourier basis fail to do so, as in case of famous example of rect function at the edges. As a result, wavelets are able to denoise the particular signals far better than conventional filters that are based on Fourier transform design and that do not follow the algebraic rules obeyed by the wavelets.
You'll do a lot of injustice to wavelets if you treat them merely as filters. To appreciate their power I'd suggest to read the underlying theory used to develop wavelets.
wavelet is best for non stationary signal analysis, here original signal attach with mother wavelet signal and then makes analysis, means Mother wavelet signal make Zoom of basic signal, then analysis, so result is coming bast in comparison to other technique.
The main advantage of wavelet basis is that they despite having irregular shape are able to perfectly reconstruct functions with linear and higher order polynomial shapes, such as, rect, triangle, 2nd order polynomials, etc. Note that Fourier basis fail to do so, as in case of famous example of rect function at the edges. As a result, wavelets are able to denoise the particular signals far better than conventional filters that are based on Fourier transform design and that do not follow the algebraic rules obeyed by the wavelets.
You'll do a lot of injustice to wavelets if you treat them merely as filters. To appreciate their power I'd suggest to read the underlying theory used to develop wavelets.
Wavelet analysis: for periods and phase identification
Spectrum analysis: for stationary signal spectrum
As Mohammed Mobien mentioned, the wavelet approach to signal processing is more of a "decomposition" rather than a filter. The reason wavelets are being used more and more is because they are (again, as Mohammed says) capable of deconstructing complex signals into basis signals of finite bandwith, and then reconstructing them again with very little loss of information. Practically, this means that there is little-to-no signal leakage or phase-shifting of the original signal when you decompose it. Conventional filters generally have problems with signal leakage or phase-shifting that have to be dealt with, or at least acknowleged in the output.
Hope that helps.
Unless you use adaptive filters, then conventional fixed-coefficient filters are efficient in removing out of band signals. If applied to in-band signals, then conventional filters will also remove the signal of interest. De-noising works well in conjunction with wavelet filters for removing noise where the noise and signal spectra overlap. The scheme employs a threshold in order to de-noise the signal, but without removing the signal of interest. Donoho's sigma*root(two-log-N) is a universal threshold which works well, but there are others. De-noising works more effectively when using the translation invariant wavelet transform, rather than the dwt.
Hope that helps
Hello
I can suggest you to view this publications
https://www.researchgate.net/publication/235933497_Noise_cancellation_in_Doppler_moment_estimation_of_array_weather_radar_signals_using_lifted_biorthogonal_wavelets
https://www.researchgate.net/publication/233966030_De-noised_estimation_of_theweather_Doppler_spectrum_by_the_wavelet_method
Cordially
Article Noise cancellation in Doppler moment estimation of array wea...
Article De-noised estimation of theweather Doppler spectrum by the w...
Some good replies above for you Puneet from various contributors, just to add a bit more on the DWT. The DWT decomposes by decimating in powers of 2 and filtering, two essentially different operations, which taken together form a very good way of decomposing the signal into low and high frequency sub-bands and then de-noising. De-noising does not necessarily mean 'filtering' in the strict sense of the term. The wavelet 'filters' perform a different operation to that attributed to conventional filters, the latter usually remove noise or other unwanted signals above or below specified cut-off frequencies. De-noising in wavelet operations can be performed by an additional operation namely that of applying a threshold to the signal, based on some statistical threshold criterion, below which samples will be removed in a particular sub-band, whereas samples above the threshold will be retained. It means for example that the user has more discretion and control and can essentially pin-point transients in low- and high- frequency sub-bands, which would otherwise be removed by conventional filtering, or can de-noise within sub-bands but leave other sub-bands alone. Of course the signal can then be reconstructed using the inverse DWT once the de-noising is completed. There is also the un-decimated transform (or stationary wavelet transform) , which works by adding zeros dyadically in between the filter coefficients, it means therefore that the data is not decimated. The de-noising criterion however work in the same manner as does the reconstruction.
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