In my last article I talked about linear and non linear systems. These systems contain frequencies, such as harmonics and sidebands, that are not in the inputs. In this article I share a short video I made with my signal processing simulator that demonstrates the concepts. Watch the video with the sound on. Feel free to pause the video and take some time to understand what it is explaining.
A sine wave creates a single peak in the spectrum
In the first slide we see a vibration time waveform of a sine wave at the top and the corresponding spectrum at the bottom. A sine wave has a single frequency and a single amplitude and therefore results in a single peak in the vibration spectrum. I move the slider bar to change the frequency and you can see how the graphs update.
A repetitive but non sinusoidal wave creates harmonics in the spectrum
Next, I use another slider to distort or clip the top of the sine wave. As I do so, we start to see harmonics, or multiples of the base frequency, in the spectrum. You can pause the video if you want and see if you can calculate the frequency (number of cycles per second) of the time waveform. You should see 8 cycles per second or 8 Hz. What we see in the spectrum now are 8 Hz, 16 Hz, 24 Hz, 32 Hz etc. These are harmonics or multiples of 8 Hz.
Amplitude modulation creates sidebands in the spectrum
In the second slide I start with a sine wave at 25 Hz and a single peak in the spectrum. I then adjust a slider to “modulate” or to repetitively increase and decrease the amplitude of the original 25 Hz sine wave. This results in 2 new peaks in the spectrum on either side of the 25 Hz peak. These are called “sidebands.” They are 25 Hz plus and minus the modulating frequency. As I adjust the modulating frequency with the slider you can see the changes in the time waveform and in the spacing of the sidebands in the spectrum. Next I move the sliders to adjust the amplitude of the modulating frequency and then the amplitude of the frequency being modulated.
Harmonics and Sidebands
In the third slide, I combine the two effects. We begin with a sine wave being modulated by a sine wave. I then adjust the slider to distort the wave being modulated. This results in harmonics and the harmonics also have sidebands. This pattern is common in rolling element bearings, gears and AC motors.
This is just a tiny glimpse of one of my simulators and a tiny taste of what you will learn in one of my courses. Did someone say courses???? Click here for the schedule.