# Filter bank for complex spectrum

I'm using a complex-valued baseband signal as my input for subband adaptive filtering. Therefore i have a complex input spectrum.

• My problem is now, how to split my complex spectrum into $N$ equally spaced subbands?

I know i could use a DFT filter bank with impulse responses of

$$\displaystyle h_i(n) = p(n)e^{(j2\pi i/N)n} ,\quad i = 0,1,\ldots,N-1$$

where $p(n)$ is the impulse response of my lowpass prototype filter. But what bothers me is that $H_0(z)$ will be real valued and so $|H_0(e^{j\omega})| = |H_0(-e^{j\omega})|$ holds, and hence the complex spectrum isn't split right into $N$ subbands.

• Am I missing something there, or is it not possible to use DFT filter banks for complex-valued input signals?

• Are EMFBs (exponentially modulated filter bank) a workaround to solve this problem?