Beating wave frequency detecting

Hi all, I know that two sine waves with different frequencies superimposed to create beating patterns, but how to detect the frequency of such beating pattern??

code:

clear;
clc; close

t = linspace(0,10, 1000);
Fs = 100;

f1 = 8;
f2 = 9;
y = sin(2*pi*f1*t) + sin(2*pi*f2*t); %+ randn(size(t));

plot(t, y)

direct fft can only find two peaks at 8-Hz and 9-Hz, but where is the 1-Hz??

I just figure out that fft to abs(y) shows the beating frequency. but is there a way that I can show 1, 8, 9-Hz together in one spectrum?

Thank you for any help Kyle

Answer 1

[Wayne King]

Hi Kyle, the beat is an amplitude modulation at 1 Hz.

You can visualize this by looking at the oscillation in the envelope, which you can isolate with the Hilbert transform

ya = hilbert(y);
plot(t(1:500),abs(ya(1:500)));
grid on;

You can see that the envelope oscillates at 1 Hz, which is your beat frequency.

[Wayne King]

There is no 1-Hz component in the spectrum of y by the way.