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Mathematics

You might face barriers such as notation, or basic concepts that were not covered at high school, or perhaps you just need a refresher.
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This is not a comprehensive course in mathematics! All we need to do is provide a few key building blocks to make a foundation for Speech Processing.

  • Notation: sometimes, the notation is the biggest hurdle to overcome when (re)learning mathematics, so that’s where we will start.
  • Logarithms: by turning multiplication into addition, logarithms make computation simpler, and allow us to work with very large or very small numbers.
So that we can write general equations, we need to use variables to represent the quantities of interest.
A very important structure, especially in engineering and computer science, and something we need to understand properly before going any further.
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It's common for variables to occur in sequences, so we need notation for that. Then we can perform sum and product operations on them.
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To make notation simpler, we can write a complicated expression in the form of a function.
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The original purpose of logarithms was to convert multiplication into addition (and division into subtraction).
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Storing and computing with very large or small numbers presents difficulties with precision, but logarithms can be used to avoid such problems.
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A demonstration of logarithms in action should help our intuitions at this stage.
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Now we have an intuitive understanding, we can state the formal definition of logarithms.
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From that formal definition, we can state the relationships that enable us to convert multiplication into addition, amongst other things.
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Calculating the logarithm of a number is quite hard, so we use pre-calculated look-up tables.
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Reading

Sharon Goldwater: Vectors and their uses

A nice, self-contained introduction to vectors and why they are a useful mathematical concept. You should consider this reading ESSENTIAL if you haven't studied vectors before (or it's been a while).

Read about Napier’s Bones, a mechanical device for performing logarithmic computations. If you’re in Edinburgh, go to the National Museum of Scotland to see them for yourself.