The second in our Wake Up! Time to Filter! mini-blog sequence.
What’s getting in the way? Are you trying to filter something out, or filter something in? Both the wanted signal and the uninvited guest information can be either narrowband (spectral components over a small span of frequencies) or broadband (that’ll be a large span of frequencies). That gives us four cases to consider, but the two common ones for driving filtering decisions are:
- You’ve got a narrowband signal, but it’s being smothered by some broadband noise.
- You’ve got a broadband signal, but it’s being drowned out by a narrow-band interferer.
A narrow-band signal tends to “contain” its useful information in the frequency domain and is usually reasonably insensitive to the time-domain behavior of a filter applied to it. So, it’s common to use fairly aggressive filtering practices that squeeze down the passband in order to provide as much stopband as possible.
A broadband signal is spread out in the frequency domain and so can express some fairly complex time domain behavior. (The more broadband a signal is, the less it looks like a sinewave — which is the ultimate low-information signal.) This can present a tough filtering challenge when a big narrow-band interloper needs to be suppressed. It’s the stopband that needs to be concentrated, with as wide a passband as possible. The filter design challenge then revolves around providing as much attenuation as you need (but no more — it’s wasteful), together with the most benign — or at least “compensatable” — behavior in the time domain. Always a challenge, simulation of the signals, the processing, and the detector are pretty essential in this case.
Untangling the behavior of two broadband signals is a challenge for “conventional” filtering, because their spectra are likely to overlap significantly. The solution in this case is not to use frequency-domain filtering at all, but process signals entirely in the time domain, encoding a symbol as a uniquely identifiable sequence of time domain events. A correlation process is then used to assess the likelihood that an incoming signal “contains” that sequence. This code-spreading method underpins most modern forms of digital communication. Filtering is still heavily involved, but only to define the boundary conditions for the frequency band in which all this time-domain activity happens.
The case of two narrowband signals is the easiest, so we solved it a long time ago. Good old-fashioned radio relies on this.
Please join us on Wednesday, October 22, at 1:00 p.m. ET (10:00 a.m. PT) for a chat session in which we will discuss “Filter Design.”
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