# Getting frequency content at different times from discrete wavelet transform coeffs

After being away from DSP for a long time, I am trying to familiarize myself with wavelet transform. Here is what I (think) have understood so far:

• Wavelet transform provides you high time resolution at higher frequencies and high frequency resolution at lower frequencies.
• DWT can be calculated by using QMF pair and subsampling. When used recursively, filter pair increases frequency resolution and subsampling decreases time resolution.
• Result of level 1 DWT [cA, cD] = dwt(signal, Lo_D, Hi_D) essentially gives low frequency and high frequency splits of the signal called approximation and details.

If my understanding is correct, in this algorithm, the end result is essentially in time domain. If I want to know what frequencies are present, I have to take an fft of the coefficients. Is that correct? If so, is there a way I can get the frequency domain representation without extra step of taking fft?

Question 2: If scalogram is the answer to question 1, how is it generated using results of repeated use of dwt? I want to avoid using ready MATLAB functions for better understanding except maybe dwt

Thanks