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Why Sinusoids?

• They are a clear example of a digital audio signal.

• Very sensitive. A general rule of thumb is:

  If it sounds good on a sinusoid, it will probably sound good on another type of signal.

• Think of sinusoids as a single, isolated "harmonic", so:

  If you modify a complex spectrum, you modify each and every one of its harmonics. It is simpler to start with just one.

• Fourier series uses sinusoids:

  Summing sinusoids can represent any periodic wave, i.e. sound

Digital Representation of Signals

Digital signals are sequences that are indexed by n, which is called the sample number n

Sequence of indices

The indices of the sequence can be represented like this:

Sequence of values

To obtain the actual values of for these indices, we need a function, call it f, of the sample number.

A function is a mathematical term that defines a relationship between two sets, in this case, a sample number n and its output value, denoted f(n).

So, our Sequence of indices above becomes an indexed sequence of values, like this:

The sine function

Given that the sinewave is an example of an audio signal, we need to find a function we can use. Luckily for us, we can make use of our trigonometry chops to use the sine function.

We can use the sin function in place of the f function above and it will give us the sine wave:

Here's a nice visual representation by Jack Schaedler

Formally, we still need a few tweaks to the sin function above. So, the actual sinusoid needs to have all the following parameters:

f(n) = a • sen(ωn + ø)

Where:

• n sample number
• a amplitude
• ω angular frequency
• ø phase (we can ignore this one for now)

How to make a sinweave in Pd

This patch is real, open it with Pd here.

Go to Using Pd for a recipe.