Symmetry and periodicity of frequency-shifted discrete Fourier transform
One version that's useful is $b=\frac{1}{2}$ 

If you have an input sequence of N real numbers, the output sequence can also be represented as N real numbers: Two for DC and Nyquist and 2*(N/2-1) for N/2-1 complex values. Mixing real and complex numbers makes real time processing a bit more awkward.

Using the transform you suggest with $b=\frac{1}{2}$ results in exactly N/2 complex numbers which allows for more efficient code on SIMD real time processors. $b=\frac{1}{2}$  maintains complex conjugate symmetry. Instead of, say, sampling -10,0,10,20,30, .. you sample at -150,50,50,150,250,... avoiding DC and Nyquist.