The basics of DSP for use in intelligent sensor applications: Part 2

July 06, 2010

We’re all familiar with the general idea of a filter: it removes something that we don’t want from something we do want. Coffee filters that pass the liquid coffee but retain the grounds or air filters that pass clean air but trap the dust and other pollutants are two common examples of mechanical filters in everyday life.

That same concept can be applied to noisy electrical signals to pass through the “true” signal of interest while blocking the undesirable noise signal.

Looking at Figure 2.5c below, imagine for a moment that the signal of interest is in the lower-frequency region and that the noise signal is in the higher-frequency region. Ideally, we’d like to be able to get rid of that high-frequency noise, leaving just the signal component that we want.

 Figure 2.5c. Combination of Low- and High-frequency Content Signal in the Frequency Domain

We can picture the process that we’d like to perform as one in which we apply a mask in the frequency domain that passes all of the low-frequency signal components without affecting them at all but that zeros out all of the high-frequency noise components.

Graphically, such a mask might look like the frequency spectrum shown in Figure 2.6a below.

If we multiply each point in the graph of Figure 2.5c by the corresponding point in the graph of the mask in Figure 2.6a, we get the resulting frequency spectrum shown in Figure 2.6b, which is precisely what we want.

 Figure 2.6b. Result of Multiplying Mask in 2.6a with Spectrum in 2.5c

Thought experiments like these are helpful, but is it possible to implement this in the real world? The answer is “yes,” albeit with some important qualifications that arise from deviations between real-world and idealized system behavior.

Before we get into those qualifications, though, let’s take a look at an important foundational concept: sampling.

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