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Time or Frequency?

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.

You can:

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.

Log in now by clicking here to join or to leave an early message! Just click “Reply” or “Post Message” when you get to the site.

4 comments on “Time or Frequency?

  1. Davidled
    October 16, 2014

    As two elements are available, engineer will looks at both to review the signal characteristics. In the time domain, signal amplitude and pattern could be easily glanced. Typically, signal pattern provides the output of system. Signal and noise ratio of each filtering method and amplitude of each frequency might be estimated via the frequency domain in the engineering tool.   

  2. samicksha
    October 23, 2014

    Thank You @daej for these two elements in your comment, infact i would say Time& Frequency are two key elements which help us go for required synchronisation solutions.

  3. geek
    October 31, 2014

    @DaeJ: I agree. It really does depend on the signal characteristics. Some applications may require high frequency transmissions while others may only with low frequency. Naturally, the time component flows in the opposite direction of frequency so there isn't really a trade-off involved in this case.

  4. yalanand
    October 31, 2014

    In the time domain, signal amplitude and pattern could be easily glanced.

    @Daej, true. For a beginner Time domain concepts are pretty easy to understand but same cannot be said about the frequency domain. Understanding the frequency domain concept is  pretty tricky.

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