Frequency resolution and timestep in DFT
The "timestep" $dt$ (using your nomenclature) between DFT windows can really be anything you choose. There are a few different cases to consider:


$dt &lt; N$: In this case, there is overlap between successive windows of samples that you input to the DFT. This can be used if you would like to get answers more frequently than every $N$ samples. It's quite common to see something like 50% overlap between windows being used.
$dt = N$: In this case, there is no overlap; you just take successive blocks of $N$ samples and use those as inputs to the DFT. This would give you the minimum processing load while not skipping any input data.
$dt &gt; N$: As you noted, in this case, you're skipping data between windows (sometimes called "underlap"). This can reduce your processing load further, but since you're skipping data, you run the risk of missing the analysis of some feature in that portion of data that was discarded.


The frequency spacing of the DFT is related to the sample rate and the DFT length. Specifically:

$$
df = \frac{f_s}{N}
$$

where $f_s$ is the sample rate of the input data. $df$ in the equation above corresponds to the frequency spacing between each output (i.e. with $f_s$ measured in Hz, the outputs will have a spacing of $df$ Hz).