Frontmatter

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using Plots, PlutoUI, WAV
2.2 s

Chirp wave/function
md"""### Chirp wave/function"""
176 μs

Chirp wave of function is a waveform that sweeps frequencies. It is a commonly employed waveform in audiology, radar/sonar and laser applications to perform rapid testing of equipment (in order to ascertain it works across all frequencies)

You can read more about it here.

MATLAB provides a command called chirp but it is part of the Signal Processing Toolbox. So we are going to write our own.

md""" Chirp wave of function is a waveform that _sweeps_ frequencies. It is a commonly employed waveform in audiology, radar/sonar and laser applications to perform rapid testing of equipment (in order to ascertain it works across all frequencies)

You can read more about it [here](https://en.wikipedia.org/wiki/Chirp).

MATLAB provides a command called [`chirp`](https://www.mathworks.com/help/signal/ref/chirp.html) but it is part of the Signal Processing Toolbox. So we are going to write our own.
"""
417 μs

Defining equations.

Based on the Wikipedia page we write a function that takes as input a starting frequency f0, an ending frequency f1 and a time vector t at whose beginning and ending these frequencies should be available.

Since we need to sweep across frequency range $[f_0, f_1]$ and have the rate of change of frequency be a linear function, we have to first determine the chirp rate c, based on the values in the time vector provided.

$$c = \dfrac{f_1 - f_0}{t_f - t_0}$$

so that

$$f(t) = f_0 + ct$$

Next, we chose the sine wave to do our sweeping and followind the derivation in Wikipedia we get:

$$f(t) = \sin\left(2\pi(ct^2/2 + f_0t)\right)$$
md""" ### Defining equations.

Based on the Wikipedia page we write a function that takes as input a starting frequency `f0`, an ending frequency `f1` and a time vector `t` at whose beginning and ending these frequencies should be available.

Since we need to _sweep_ across frequency range $[f_0, f_1]$ and have the rate of change of frequency be a linear function, we have to first determine the chirp rate `c`, based on the values in the time vector provided.

```math
c = \dfrac{f_1 - f_0}{t_f - t_0}
```

so that
```math
f(t) = f_0 + ct
```

Next, we chose the sine wave to do our sweeping and followind the derivation in [Wikipedia](https://en.wikipedia.org/wiki/Chirp#Linear) we get:

$$f(t) = \sin\left(2\pi(ct^2/2 + f_0t)\right)$$
"""
492 μs

We implement the function in a straightforward fashion
md""" We implement the function in a straightforward fashion"""
176 μs
chirp (generic function with 1 method)
function chirp(f0, f1, t)
c = (f1 - f0)./(t[end]- t[1])
return sin.(2π*(c.*t.^2/2 + f0.*t))
end
882 μs

Let us examine a plot of it
md""" Let us examine a plot of it"""
171 μs
begin
local t = 0:0.001:10
plot(t, chirp(2, 30, t), label=false, title = "Chirp function")
end
74.4 ms

What does a chirp sound like?
md"""## What does a chirp sound like?"""
170 μs
begin
local t = 0:0.0005:10
filename = "files/chirp.wav"
wavwrite(chirp(100, 1100, t), filename)
end
12.2 ms
chirp.wav
DownloadButton(read(filename), basename(filename))

111 μs