Logic Blog

Ana.logue Signal Processing
Supplemental Note - Notation

As we progress onwards, it's becoming clear to me that I need a set of terms and shorthands that I can use to concisely and unambiguously convey what I'm talking about. So much like when I did for digital systems, I've distilled out some concepts from real-world techy-type stuff into a kind of notation to use for the analogue aspects of the Logic Blog. These will likely be the standards as I move forwards, which is why this note is published separately.

I will likely have to come back and extend this at some point, but I'll inform you in the main thread if / when I do.

Thanks to Aya for enabling the [sub][/sub] and [sup][/sup] BBCode tags to make this all possible.



1. Generic Signals

For the sake of keeping text down (an futile exercise if ever I saw one), and removing ambiguity, generic signals will be described as follows (though specific diagrams may use other labels for special cases, or if I forget or get distracted):

Inputs: i_n
Outputs: o_n
Internals: S_n

Internals will most likely be labelled on a diagram in some way or another and the subscripts are optional. So if there is only one output, it'll probably be named simply "o" rather than "o₁". I'll also probably be using 1-indexed for most of the analogue stuff, as it feels nicer, though this might turn round and bite me once we look at binary number representations (because I'm obliged to 0-index bitnumbers).

Anyway, as an example, we may describe the function of an AND gate on N analogue signals as:

o = min ( i₁, i₂, i₃, ..., i_N )

2. Signed and Unsigned Numbers

Last time I talked about the fact that some analogue signals can take negative values and some can't. For easy differentiation between the two scenarios, I'll start using the terms "signed", for values that can take negative values, and "unsigned", for those that can't, remembering the limit of 100 on the magnitudes:

Unsigned: 0 ≤ s ≤ 100
Signed: -100 ≤ s ≤ 100

Note that many of our systems will only work with unsigned values. However, you will be able to use them with inputs that are technically signed as long as you can guarantee that the input values will never drop below 0. Alternatively you can choose to ignore the value of the signal if it is negative (forcing it to 0) but using the positive component (see section 3 below).

We also covered the concept of some devices taking the magnitude only of the inputs. Typically this is known as "absolute" value and for this I will be using the standard notations:

Absolute value of Signal "s" : |s|

Where :

|s| = |-s|
0 ≤ |s|

3. Positive and Negative Components

Splitting signed signals is going to be a big part of how we get around the limitations of calculations taking absolute values only, to obtain the positive and negative components. These are the positive and negative outputs of the splitter device and will be annotated as follows:

Positive output: o⁺
Negative output: o^-

Note that in these cases, only one of s⁺ and s^- can ever be non-zero at the same time and in both cases the signal is unsigned. This splitting is therefore very similar to taking the absolute value, in the sense that one of the two ouptuts of the splitter will be the absolute value and the other will be 0, so the following is true:

max ( s⁺, s^– ) = |s|

Spoiler - geekNotes: On obtaining the Absolute Value

As a random side note, I generally find the requirement for absolute values to be an annoyance, but there may be times when you actually want the absolute values. If this is the case, my preferred method is to us a combiner and wire your signed signal into the positive input:

o = |i| - 0 = |i|

Alternatively you can pass the signal through two NOT gates to give:

o = 100 - ( 100 - |i| ) = |i|

Note, both of these work for obtaining the absolutes of both analogue and digital (ternary) signals. Nice huh?

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