Introduction To Spectrum Analysis; Analysis Amplitude Vs. Time; Analysis Amplitude Vs. Frequency - Hameg Instruments HM5510 Manuel

I n t r o d u c t i o n t o S p e c t r u m A n a l y s i s
Intrduction to Spectrum Analysis
Analysis of electrical signals is a fundamental task for most
engineers and scientists. Also, many non-electrical signals are
converted into electrical signals in order to render them fi t for
analysis with electric measurement instruments. There are
transducers for mechanical signals like pressure or accelera-
tion as well as such for chemical and biological processes.

Analysis amplitude vs. time

The traditional route for signal analysis is the representation
amplitude vs. time on an oscilloscope.
However, oscilloscope display has its shortcomings: in the
fi rst place the dynamic range is limited to in general 8 cm of
display, details with less than about 1 % of full scale are hardly
discernible. With an ordinary scope increasing the sensitivity
leads to overdriving the vertical amplifi er which mostly creates
distortions. Unless they are fairly strong and visible individual
frequencies are not detectable.
The simplest signal is the sine wave as described by:
Y(t) = Y × sin (2π × ––)
y(t)
Y
T
The same signal, represented in the frequency domain will
look like this:
y(f) = F
0
y(f)
Y

Analysis amplitude vs. frequency

The representation of a signal in the frequency domain is given
by amplitude vs. frequency, it is important to note that only
the amplitudes of the frequencies contained in a signal are
preserved, the phase or time relationship between them is
30
Subject to change without notice
t
T
t
= 1 / f
f
F
0
lost forever. This implies that due to this loss it is impossible
to reconstruct the signal again from the frequency spectrum.
(It is possible to derive two spectra from the original signal, in
this case reconstruction would be possible.)
As an example the following signal is fi rst shown in the am-
plitude vs. time domain:
The next picture shows the individual components of the signal
separately :
f
0
f
1
f
2
Now the components are shown in the frequency domain:
f 0 f 1
FFT (Fast Fourier Transform) analysis
The frequency range over which FFT is possible depends on the
properties of available A/D- and D/A converters. FFT analysis
requires the fulfi llment of these preconditions:
– The signal must be periodic
– Only multiples of the signal period may be used for the
calculations
A period (or multiples thereof) is sampled, then the spectrum
will be calculated from the samples. As the sampling will yield
discrete amplitude values the method is also called Discrete
Fourier Transform (DFT). The result is a discrete frequency
spectrum.
Time
e
T i m
e
T i m
F r e q
u e n
c y
f 2
Frequency