Usage of complex filters in communication

digital filterdigital-communications

In the last stage of a communication transmitter, at the front end a filter is used to eliminate unwanted signals from other frequencies. As far as I read in literature, are these filters "real" filters? Why can't we use a complex filter in communications?

If the answer is no, can you give me an application where complex filters are used ? (In signal processing).

Best Answer

Any electromagnetic signal is real-valued, and hardware filters thus have real inputs and outputs, so their transfer function must be real-valued as well.

In principle it would be possible to build a complex-valued hardware filter, by creating two filters and using one of the outputs as I and the other as Q signal, however this is useful only with a complex input, requiring you to build four filters (I->I, I->Q, Q->I, Q->Q), one adder (for the Q outputs) and one subtractor (for the I outputs), which is difficult to do in hardware.

Thus, you can see complex-valued filters in digital signal processing mostly.

Complex filters are useful if you need an asymmetric frequency response.

In digital communication, many transceivers are built using the direct conversion paradigm for cost reasons, which leaves the (complex-valued) signal centered around 0 Hz.

Filtering that signal does not require an asymmetric transfer function, so the complex signal is passed through a real-valued filter, using two separate filters with the same transfer function.

There are a few use cases for complex-valued filters on complex-valued signals, but these are usually few and far between, so you stumble over them seldom.