What is Spectrum
Some measurements require that we preserve complete information about the
signal -frequency, amplitude and phase. This type of signal analysis is called
vector signal analysis , which is discussed in Application Note 150-15, Vector
Signal Analysis Basics . Modern spectrum analyzers are capable of performing
a wide variety of vector signal measurements. However, another large group of
measurements can be made without knowing the phase relationships among
the sinusoidal components. This type of signal analysis is called spectrum
analysis . Because spectrum analysis is simpler to understand, yet extremely
useful, w will begin this application note by looking first at how spectrum
analyzers perform spectrum analysis measurements, starting in Chapter 2.
Theoretically, to make the transformation from the time domain to the frequency
domain, the signal must be valuated over all time, that is, over ± infinity.
How v r, in practice, we always use a finit time period when making a
measurement. Fourier transformations can also be made from the frequency
to the time domain. This case also theoretically requires the valuation of
all spectral components over frequencies to ± infinity. In reality, making
measurements in a finite bandwidth that captures most of the signal energy
produces acceptable results. When performing a Fourier transformation on
frequency domain data, the phase of the individual components is indeed
critical. For example, a square wav transformed to the frequency domain
and back again could turn into a sawtooth wav if phase were not preserved.
What is a spectrum?
So what is a spectrum in the context of this discussion? A spectrum is a
collection of sine waves that, when combined properly, produce the
time-domain signal under examination. Figure 1-1 shows the wav form of a
complex signal. Suppose that we w re hoping to see a sine wav . Although
the wav form certainly shows us that the signal is not a pure sinusoid, it
does not give us a definitive indication of the reason why. Figure 1-2 shows
our complex signal in both the time and frequency domains. The frequency-
domain display plots the amplitude v rsus the frequency of each sine wav
in the spectrum. As shown, the spectrum in this case comprises just two sine
waves. We now know why our original waveform was not a pure sine wav .
It contained a second sine wav , the second harmonic in this case. Does this
mean w have no need to perform time-domain measurements? Not at all.
The time domain is bett r for many measurements, and some can be made
only in the time domain. For example, pure time-domain measurements
include pulse rise and fall times, overshoot, and ringing.
Time domain measurements Frequency domain measurements
Figure 1-2. Relationship between time and frequency domain
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