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:

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

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.
Take a (real-valued) low pass filter with impulse response $h_{LP}[n]$ and with cut-off frequency $(f_2-f_1)/2$, where $f_1$ and $f_2$ are the lower and upper band edges of the desired band pass filter. Define a center frequency $f_0=(f_1+f_2)/2$. Then a real-valued band pass filter is obtained by

$$h_{BP}[n]=2h_{LP}[n]\cos(2\pi f_0n)\tag{1}$$

Depending on the design of the low pass filter, the filter in $(1)$ can be identical to the one in your question.

If you want a complex-valued band pass filter with a pass band at positive frequencies (but not at negative frequencies), you simply have to modulate the low pass impulse response $h_{LP}[n]$ by a complex exponential instead of by a cosine:

$$h^c_{BP}=h_{LP}[n]e^{j2\pi f_0n}\tag{2}$$