If you refer to the documentation for
wavedec, a signal $x$ is decomposed on one level into two sets of coefficients: $cA_1$ and $cD_1$. They correspond to a low-pass and a high-pass filter applied to $x$, following by a downsampling. As a result, if you reconstruct $x_1$ with
waverec from $cA_1$ only (setting $cD_1$ to zero), and $x_2$ from $cD_1$ only (setting $cA_1$ to zero), $x_1$ will mostly correspond to the lower half of $x$ spectrum, and $x_2$ the upper half.
The same reasoning works on several levels: if your signal has a range of frequency in $[0\,,f]$, $cD_1$ gathers coefficients mostly from $[f/2\,,f]$, $cD_2$ gathers coefficients mostly from $[f/4\,,f/2]$, etc.
So for a sampling frequency of $44100$ Hertz, the bands would be:
- $cD_1$: $11025 \to 22050$
- $cD_2$: $5512.5\to 11025 $
- $cD_3$: $2756.25 \to 5512.5$
- $cD_4$: $1378.125 \to 2756.25$
- $cD_5$: $689.0625 \to 1378.125 $
If you want to filter out a frequency band, you can zero wavelet coefficient whose spectrum intersect that frequency band, and reconstruct the data. This is a form of thresholding in the wavelet domain. As you guessed, it can work in a way similar to Fourier.
Indeed, thresholding and shrinkage are very effective with wavelets, possibly more than with a Fourier transform, for denoising. In the wavelet domain, you can design the shrinkage to preserve specific time intervals, allow smooth transitions, etc.
But the wavelet filters are imperfect filters. And downsampling cause aliasing, causing a not-so-clean filtering. To perfect a pure band-pass filter, I would not recommend the DWT (discrete wavelet transform), unless the wavelet is of quite high order.