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1. Jean Baptiste Joseph Fourier, 1768-1830.

A French mathematician and physicist who

discovered that periodic functions can be expanded

into a series of sines and cosines.

2. If the time signal occurs only once, then T is infinite,

and the frequency representation is a continuum of

sine waves.

This application note is intended to explain the fundamentals of swept-tuned,

superheterodyne spectrum analyzers and discuss the latest advances in

spectrum analyzer capabilities.

At the most basic level, the spectrum analyzer can be described as a

frequency-selective, peak-responding voltmeter calibrated to display the

rms value of a sine wave. It is important to understand that the spectrum

analyzer is not a power meter, even though it can be used to display power

directly. As long as we know some value of a sine wave (for example, peak

or average) and know the resistance across which we measure this value,

we can calibrate our voltmeter to indicate power. With the advent of digital

technology, modern spectrum analyzers have been given many more

capabilities. In this note, we shall describe the basic spectrum analyzer

as well as the many additional capabilities made possible using digital

technology and digital signal processing.

Frequency domain versus time domain

Before we get into the details of describing a spectrum analyzer, we might

first ask ourselves: “Just what is a spectrum and why would we want to

analyze it?” Our normal frame of reference is time. We note when certain

events occur. This includes electrical events. We can use an oscilloscope to

view the instantaneous value of a particular electrical event (or some other

event converted to volts through an appropriate transducer) as a function

of time. In other words, we use the oscilloscope to view the waveform of a

signal in the time domain.

Fourier

theory tells us any time-domain electrical phenomenon is made

up of one or more sine waves of appropriate frequency, amplitude, and phase.

In other words, we can transform a time-domain signal into its frequency-

domain equivalent. Measurements in the frequency domain tell us how

much energy is present at each particular frequency. With proper filtering,

a waveform such as in Figure 1-1 can be decomposed into separate sinusoidal

waves, or spectral components, which we can then evaluate independently.

Each sine wave is characterized by its amplitude and phase. If the signal

that we wish to analyze is periodic, as in our case here, Fourier says that the

constituent sine waves are separated in the frequency domain by 1/T, where

T is the period of the signal

Chapter 1

Introduction

Figure 1-1. Complex time-domain signal

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