Getting frequency content at different times from discrete wavelet transform coeffs
Question 1: I think you want to investigate centfreq &amp;  scal2freq (Scale to frequency):


  FREQ = centfrq('wname') returns the center frequency in hertz of the
  wavelet function
  
  F = scal2frq(A,'wname',DELTA) returns the pseudo-frequencies
  corresponding to the scales given by A and the wavelet function
  'wname' (see wavefun for more information) and the sampling period
  DELTA.


The intuition that I use is to think about your question is: The wavelet transform is a hierarchical (tree-like) decomposition of an input signal. I would not say it is in the "time-domain" as is commonly understood. I think of the DWT output via the duality: Wavelets &lt;---> Filterbanks.

Imagine a set of 8 bandpass filters tuned to filter different ranges from low to high on the frequency spectrum. You know which frequency ranges correspond to which filters, so you know how much signal lives in each of the 8 frequency ranges based on the bandpass filter output. That's a basic frequency analysis. You wouldn't need to compute an FFT at this point. And with the successive QMF filtering, then decimation of your signal at each level, your DWT coefficients may only be one-sample (or have a very coarse resolution), so an FFT wouldn't make any sense.  

There's a good explanation @ https://math.stackexchange.com/questions/28581/which-time-frequency-coefficients-does-the-wavelet-transform-compute

Question 2: A scalogram (Scalogram (and related nomenclatures) for DWT? ) is good for visualizing your transformed signal, but I think it would be overkill just to compute which frequency range your wavelet coefficients correspond to.