Cerne Page-Fourier Analysis and the Lockin Amplifier

Using a lockin amplifier to gain insight into Fourier analysis- a conceptual approach

Fourier analysis is a powerful mathematical tool that is extremely useful in a wide range of fields. When I first learned about Fourier analysis I had trouble understanding why and how it works. Typically students learn about Fourier analysis before using lockin amplifiers, but one could argue that understanding how a lockin amplifier works is very helpful in gaining a deeper understanding of Fourier analysis. The following links are intended to show and explain lockin detection and Fourier analysis in a more conceptual way.

We start by demonstrating the power of lockin detection to find a small signal that is buried in large background noise. Click here for a video of my lockin amplifier demonstration

Now let's take a closer look at how the lockin amplifier works. How a lockin amplifier works

In this computer simulation we will look at how a lockin amplifier can extract the desired frequency component from a noisy background simply by multiplying the noisy signal by a sinusoidal wave and averaging. Click here for a video of a Labview simulation on lockins

Now that we are more familiar with how a lockin amplifier works, we're ready to take a new look at Fourier analysis. This video guides you through the graphical interactive simulations for Fourier analysis on CLAW

Since particles behave like waves in quantum mechanics, the concepts that we learned in Fourier analysis also apply to quantum mechanical particles. Here's a simple cartoon to explain the Heisenberg momentum(wavelength)-position(distance) uncertainty principle, which is not as mysterious as people tend to think once you accept that small particles have wave-like properties. A simple picture of Heisenberg's uncertainty principle

We gratefully acknowledge support from the National Science Foundation (NSF-DMR1006078).