# Digital Signal Processing with F#

May 2019

## 2 - Writing Stateless Functions

Since we now know what a signal is (a value that changes over time), that DSP is easy (dealing with sequences of values), and that we are interested in functions that transform scalar inputs into scalar outputs, let us start directly by writing a processing function. Later on, you will see how to compose these small functions to a larger system.

### Amplifier

Amplifying signals is a science in itself. You could spend a lot of money buying analog gear that sounds just "right," but "right" is a subjective term based on a user's preferences. For us, a simple solution will be enough. Amplification of a signal in this context means scale values linearly. We can do that this way: Linear scaling of a value is mathematically just a multiplication, so that is indeed very simple. This function does the job:

``````// float -> float -> float
let amp amount input : float = input * amount
``````

### Another Example: Hard Limiter

Now that we have our amplifier, we want to have the ability to limit a signal to a certain boundary. Again, there are a lot of ways to do this in a "nice" sounding way, but we will use a very simple technique that leads to a very harsh sounding distortion when the input signal gets limited. The limiter looks like this:

``````// float -> float -> float
let limit threshold input : float =
if input > threshold then threshold
else if input < -threshold then -threshold
else input
``````
val amp : amount:float -> input:float -> float
val amount : float
val input : float
Multiple items
val float : value:'T -> float (requires member op_Explicit)

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type float = System.Double

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type float<'Measure> = float
val limit : threshold:float -> input:float -> float
val threshold : float