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1.3. Units and dimensional analysis — Digital Signals Theory

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For many new-comers (and not-so-new-comers) this string of letters can be difficult to remember and reassemble when necessary. What I want to stress in this function is that this becomes much easier when you can reason about what the pieces mean. To do that properly, we’ll need to think about the units of measurement involved. Once we have each variable with its corresponding units, it’s easier to see the right way to arrange them, and then you won’t have to memorize so much. In the form above, our signal 𝑥 ( 𝑡 ) has three fundamental properties: 𝐴 , the amplitude; 𝑓 , the frequency; and 𝜙 , the phase offset. Now, imagine that we’ve temporarily forgotten the exact form of (1.6), but we know it involves amplitude, frequency, and phase. How could we reconstruct (1.6)? Remember from the previous section: cosines (and sines) take angles as their input, and produce a distance measurement (positive or negative) as output. However we combine 𝐴 , 𝑓 , and 𝜙 , we know that whatever

1.3. Units and dimensional analysis — Digital Signals Theory Toggle navigation sidebar Toggle in-page Table of Contents Digital Signals Theory Theme by the Executable Book Project Contents Units and dimensional analysis Contents 1.3. Units and dimensional analysis # Now would be a good time to pause and solidify some concepts. In the previous section, we learned about sinusoidal waves, which have a standard form (1.6) # \[x(t) = A \cdot \cos(2\pi \cdot f\cdot t + \phi).\] In code, this would look something like: import numpy as np def x ( t , amplitude , frequency , phase ): '''Compute t

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