The DWT is motivated by the ability to see signal in time and frequency at the same time, if I understood that correctly.
I am using the following Matlab commands for some signal x:
[A,D] = dwt(x,'db4');
Then I plot A vs some vector t, representing 'time'. I do know the algorithm behind A and D: low (high) pass filter, then downsample by 2.
My questions: Where is the time axis and where is the frequency axis if I all what I have are the coefficients A (approximation) and D (detail)?
Second question: If all of this is a simple filtering and downsampling, I don't see what is new in DWT...