# Spectrum Analyzer basics

My aluminum spectrum analyzer frame post generated more interest than I had expected (thanks Lady Ada!). I've been planning a series of posts going into more detail. I'm not by any means an expert, I'm certainly no where as skilled as Scotty, who designed this model. Hopefully my relative naiveté means that I can explain things in an approachable way without leading you too far astray.

To get started, I should probably start with the concept of spectrum analysis.The idea is that we're trying to interrogate the frequency content of the electrical signals. This is in contrast to something like an oscilloscope, which analyzes the amplitude of signals over time.

There are several methods for performing frequency, or spectral, analysis.One, relatively simple, way is to collect samples and to do a DiscreteFourier Transform (probably a Fast Fourier Transform, or FFT). Many digital oscilloscopes have an FFT function, including the venerable Rigol. There are significant limitations to the FFT, however. The most significant is the Nyquist limit. This limit states that to reproduce a digitized signal, you require twice the sample rate as the highest frequency component. Similarly, to interrogate a given frequency with an FFT, you also must sample at twice that frequency.There are nuances to this, the most important being the need to attenuate signal of a higher frequency, otherwise you'll introduce aliasing (the appearance of signals that aren't really there). Hopefully, it's clear that the Nyquist limit severely constrains the span of frequencies that the FFT is appropriate. Even if you're able to afford a digital oscilloscope that can sample at high enough rates, the computational expense involved with all these DFTs limits its usefullness.

The alternative to the DFT is the heterodyne. The core idea of a heterodyne is the modification of the frequencies in a system through non-linear mixing. Essentially, if you add two signals you get the sum of the power of each for every frequency component in each signal. I know that's a mouthful, but hopefully the

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