using Plots

, FFTW

, PlutoUI

3.4 s

This notebook explores the effect of sampling frequency on the DFT spectrum. The radio buttons below allow you to set the frequency for the basic sinusoid.

md"""This notebook explores the effect of sampling frequency on the DFT spectrum.

The radio buttons below allow you to set the frequency for the basic sinusoid."""

192 μs

Set base frequency

md"""##### Set base frequency"""

182 μs

@bind f Radio(["2" => "2 Hz", "4" => "4 Hz"], default="2")

78.1 ms

Parameter set up

begin

fs1 = 100

ts1 = 0:(1/fs1):π

fs2 = 2

ts2 = 0:(1/FS):π

md"""`Parameter set up`"""

end

5.8 ms

The plot below shows the original sinusoid at the frequency shown above along with a sampled version of it. The sampling rate can be set with the slider below

md""" The plot below shows the original sinusoid at the frequency shown above along with a sampled version of it. The sampling rate can be set with the slider below"""

186 μs

begin

fi = parse(Int32, f)

o_signal = sin.(2π*fi*ts2)

p11 = plot(ts1, sin.(2π*fi*ts1), label="Original", title="Original = $fi Hz, Dots sampling at $FS Hz")

p12 = scatter!(p11, ts2, o_signal, marker=:o, line=:false, label="Sampled")

end

137 ms

Set the sampling frequency using the slider below

md""" Set the sampling frequency using the slider below"""

175 μs

@bind FS Slider(100:-1:2)

38.1 ms

The plot below shows the magnitude spectrum of the signal. As you can see increasing the sampling frequency results in a sharper magnitude spectrum and cleaner peaks.

md""" The plot below shows the magnitude spectrum of the signal. As you can see increasing the sampling frequency results in a sharper magnitude spectrum and cleaner peaks."""

188 μs

begin

sF = fftshift(fft(o_signal))

freqs = fftfreq(length(o_signal), FS)

local mag = plot(fftshift(freqs), abs.(sF), title="Symmetric magnitude spectrum", label=false, xlim=(-8,8), ylim=(0, 120))

end

46.9 ms