Complex band pass filter

I'm trying to find some mathematical docs about the complex (analytic signal) band pass filtering in discrete time. I've read some text already but most of them describes the problem in real time only.

I would really appreciate some equations.

[EDIT:]

I found this coefficients' computation equation for real signals:

$$ w_{bp}(n) = \begin{cases} \displaystyle\frac{\sin\left[2\pi f_{t2}\left(n-\frac M2\right)\right]}{\pi\left(n-\frac M2\right)}-\frac{\sin\left[2\pi f_{t1}\left(n-\frac M2\right)\right]}{\pi\left(n-\frac M2\right)}, & \text{if } n \ne \frac M2 \\[2ex] 2\left(f_{t2} - f_{t1}\right), & \text{if } n = \frac M2 \end{cases} $$

I know I have to specify the FIR filter order ($M$) which is approximately 4 / Normalised width of transition band. The application of the filer is a simple convolution of the coefficients computed by the equation above and real signal samples.

Now what I need to know is how to achieve this in complex plain. I also found a similar thread here, which describes the low pass filter design.

PS: I already have my complex $f_c = 5 \textrm{ kHz}$ signal sampled at $f_s = 32\textrm{ kHz}$ and I'm familiar with the complex plain problematics.