This is the first in a rapid-fire sequence of mini-blogs to get your brain cells warmed up for the Ask The Experts session on filter design on October 22. I want to get you thinking about three tradeoff-y conundra: Time or Frequency? Narrow or Broad? And… Analog or Digital. Here’s the first.
What information is hiding in your signal — and where? We’re taught the mathematical “interchangeability” of time and frequency through the work of Joseph Fourier. But don’t let that mislead you into thinking you can freely swap between them with eyes shut tight to the constraints and boundary conditions. We have to work with both domains. That’s because the vast majority of applications involve signals that vary in time. We have an inbuilt perception of time’s arrow, but frequency doesn’t really have an arrow.
Build a system that is open to a certain range of frequencies; capture a signal; analyze the time behaviour of the signal; and extract the info from it. You can run multiple instances of this over the same time interval but different frequency intervals. This requires prior knowledge of the frequency behaviour of your signal and gives you insight into what’s coded using time. Or…
Build a system that is “open” over a certain span of time; capture a signal; analyze the frequency/spectral content of the whole signal; and extract information from it. You can run multiple instances of this over the same frequency interval but different time intervals. This requires (some) prior knowledge of the time behavior of your signal and gives you insight into what’s coded using frequency.
Filters affect the behavior of these two approaches in differing ways. By filters, we really mean frequency-domain filters. They are designed to have differing gain responses to signal components of different frequencies. This allows them to discriminate between those frequency components. Due to M. Fourier’s time-frequency duality, they also have a characteristic impact on the time evolution of signals. But that’s a consequence of the frequency domain behaviour that you choose — and design for.
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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