The Gabor representation uses the same temporal resolution
in each frequency band 
.
However, a 
that is a good resolution at a low
frequency may not be a good resolution at a high frequency.
Therefore, in a multiresolution representation higher
frequency bands may have a smaller (finer) 
than
lower frequency bands.
Of course, the Gabor relationship 
still holds, so the frequency resolution 
must increase (i.e. become coarser) at higher frequencies.
This is often acceptable, however, since the ratio of 
to the frequency remains constant
(so this is also called a ``constant Q'' representation,
since 
).
In the most common arrangement, the central frequencies of
the frequency bands increase by powers of 2, 
.
Therefore, the widths of the frequency bands also increase by
powers of 2, 
, but the time
resolutions decrease (become finer) by powers of 2, 
.
In this case the elementary functions are generated by
contracting and translating a single mother wavelet:
[ W_jk(t) =
W_00[
2^k ( t - j;t_0) ] ,
]
for 
and 
.
The Gabor elementary function, or a slight variant of it
called the Morlet wavelet, can be used as a mother wavelet.
The signal then is represented by a linear superposition of
wavelets:
[ (t) =
_k=0^N _j=0^2^k T;/;t_0
c_jk W_jk(t) .
]
The generation of the signal is controlled by the triangular
array of coefficients 
.
Like the continuous Gabor transform, there is also a
continuous wavelet transform that represents the
coefficients in a continuous field.
Also like the Gabor transform, the wavelet transform allows independent
control of frequency content and time-evolution. However, because of
the essentially exponential measurement of frequency ( 
in the
wavelet vs. k in the Gabor), translation along the frequency axis
causes dilation or compression of the signal's spectrum.
A shift of 
changes the instantaneous spectrum from 
to
.
Much more could be said about the information processing affordances of
these representations, but it is beyond the scope of this paper.