Docs: add example (#96)

docs/make.jl

@@ -7,6 +7,7 @@ makedocs(
     pages = Any[
         "Home" => "index.md",
         "API" => "fft.md",
+        "Examples" => "examples.md",
     ],
 )
 

docs/src/examples.md

@@ -0,0 +1,49 @@
+# Examples
+
+Here you can find some basic examples of how to use this package.
+
+
+## Spectrum of a 1D Signal
+
+This example shows how to obtain and plot the spectrum of a simple, real-valued signal with a second-order harmonic using FFTW and [Plots](https://github.com/JuliaPlots/Plots.jl).
+
+```julia
+using Plots
+using FFTW
+
+# Number of points
+N = 2^12 - 1
+# Sample spacing
+Ts = 1 / (1.1 * N)
+# Sample rate
+fs = 1 / Ts
+# Start time
+t0 = 0
+tmax = t0 + N * Ts
+
+# time coordinate
+t = t0:Ts:tmax
+
+# The underlying signal here is the sum of a sine wave at 60 cycles per second
+# and its second harmonic (120 cycles per second) at half amplitude. We have
+# discrete observations (samples) of this signal at each time `t`, with `fs`
+# samples per second.
+
+signal = sin.(2π * 60 * t) + .5 * sin.(2π * 120 * t)
+
+# The `fft` function calculates the (discrete) Fourier transform of its input.
+# The first half of the returned array contains the positive frequencies, while
+# the second half contains the negative ones. For visualization purposes, we
+# rearrange the array to have the zero-frequency at the center.
+
+F = fftshift(fft(signal))
+freqs =  fftshift(fftfreq(length(t), fs))
+
+# Plot
+time_domain = plot(t, signal, title="Signal", xlims=(0, 4 / 60), xlabel="time (s)", label="")
+freq_domain = plot(freqs, abs.(F), title="Spectrum", xlims=(0, 200), xlabel="frequency (Hz)", label="")
+plot(time_domain, freq_domain, layout = 2)
+savefig("Wave.pdf")
+```
+
+![](img/1D60Hz.png)