The outputs of the DWT as shown on your figure are in the time domain. The DWT decomposes your signal into "sub-bands". The division into sub-bands depends on the levels of your filter bank. I find the example on the Wikipedia page (https://en.wikipedia.org/wiki/Discrete_wavelet_transform) for a three-level filter bank very instructive and corresponds well to the example you show.

Depending on the number of levels in your filter bank, your input signal is split into bands covering different frequency ranges. So each level simultaneously splits the signal into high and low frequency components. That's why DWT can be used e.g. for noise filtering.

Thank you, Yannick Suter

you are saying, if we gave time domain signal to DWT, outputs at low pass filter and high pass filter are also in time domain signal.

Means which type domain signal we are giving as input to the DWT same type domain signal will come as output with a range accordingly decomposition levels.

Is it correct? please clarify

It is a very interesting question.

Wavelet transformation is not like a Fourier transform, which convert time domain to frequency domain. It is more than that.

In some applications, we need to analyse a signal in both time as well as frequency domain. It can be performed by wavelet transform.

Wavelet transform uses shift and scaling version of original signal. Here shifting used for time domain analyses and scaling for frequency domain.

Just go through the basics of wavelet. Fourier transform converts original signal into different frequencies on the basis of sinusoidal.

Let me know if you require further clarification.

For signal processing you typically do:

Signal (time domain) -> DWT -> Processing -> inverse DWT -> Output Signal (time domain)

Where the processing step is doing whatever you would like with the DWT output. In the image you posted, you only show the Signal->DWT part, which gives you the DWT coefficients.

Referring to your image, the "A" (e.g. cA1) and "D" are the approximate and detailed coefficients from the transform. A simplified explanation would be, that "A" are the low-pass outputs, and the "D"s the high-pass outputs, but down-sampled by a factor of 2 at each stage (see wiki article).

What do you want to do with the DWT of the signal? Denoising?

I highly recommend you have a look at http://zone.ni.com/reference/en-XX/help/371419D-01/lvasptconcepts/wa_dwt/ where the whole signal processing with DWT is outlined. The image you show, is "only" for computing the decomposition coefficients, without processing the signal and reconstruction.

Because at every stage, a sub-sampling by a factor of 2 is performed, you need to put the outputs of the different stages together after up-sampling again for the inverse DWT and get the filtered version of your original signal in the time domain.

Let's look at a denoising example. To get rid of some noise in your signal, you may want to filter out some high-frequency components of your signal. At the end of the image you show, we have the DWT coefficients. At this point, we could reconstruct the original signal with these coefficients, no processing is done. But now, you can e.g. throw away some high frequency coefficients to reduce the noise. So now you are left with a reduced number of coefficients / subbands. If you want to get the processed signal again in the time domain, you need to apply an inverse DWT:

The link I provided above shows this nicely.

So long story short, in the image you posted, you only show the Signal->DWT part, giving you the DWT coefficients, and not yet a filtered version of your input. From these coefficients, you can reconstruct the original signal using the inverse DWT. If you want to process, do something with the coefficients before applying the inverse DWT to get the signal in the time-domain.

Here's some example code for C++ if you want to play around a bit:

http://wavelet2d.sourceforge.net/#toc-Section-3.1

I hope that clarifies it a bit.

The DWT is time domain decomposition. It's out put is in time domain. It is based on correlation of mother wavelet with signal by dilation and translation of mother wavelet.

Hi. Sandeep Singh Sengar

Thank you so much for your prompt response to my request.

You are saying, Wavelet transform uses shift and scaling version of the original signal.

Shifting used for time domain analyses and

Scaling for frequency domain.

please clarify my doubts how time domain possible with shifting and how frequency domain possible with scaling?

For example:

[C,L] = wavedec(sig_new, 6, waveletFunction);

cD1 = detcoef(C,L,1);

cA1 = appcoef(C,L,waveletFunction,1);

The outputs of cD1 and cA1 are in time domain or in frequency domain.

If I want outputs in frequency domain what to do.

Please clarify doubts.

I am looking forward to a positive response from you.

THANK YOU SO MUCH FOR YOUR TIME AND CONSIDERATION

Venkata Phanikrishna Balam Did it clarify you ? If yes, would you like to state this here according to your understanding?

any idea, how can we convert signal from time domain to frequency domain using wavelet particularly in python