Spectral Analysis
The Fourier Transform is used to convert time domain signals
into the frequency domain.
Using SystemView
To
perform spectral analysis:
 Set the number of samples
in the System Time Specification window
to a power of 2
 Set the sampling rate
at least 4 times the highest frequency in the model (exactly 4
times higher will place the spectrum in the middle of the display
window)
 Make certain to capture
one or more complete cycles of the signal of interest (It may
be necessary to adjust the stop time to do this, however this
will affect the sampling rate if the number of samples remains
fixed.)
Sinewave
A sinewave has only one
spectral component.

Although the amplitude
of the sinewave in the time domain is 1, its magnitude in
the frequency domain is ½. This difference is a natural result
of the FFT. The calculated value will vary as a function of
the sampling rate and number of samples.
In this case the sampling rate is 64 and the number of samples
is 64.
Notice that the power spectrum in 50 W
is 10 dBm.


This model is identical except the number of samples is increased
to 128.
The sinewave magnitude
in the frequency domain is now 1 and the power spectrum
in 50 W remains at 10 dBm.

If it
is necessary to calculate the (voltage) magnitude of a spectrum,
in order to compare the magnitude with a standard waveform in a
math handbook, add a globally linked gain token of 2/(dt*ns).
Square Wave

A square wave is
composed of many sine waves (the odd harmonics of the fundamental).
The spectrum of
any signal represents the value of all sine waves which when
added duplicate the signal being analyzed

Pulse
Wave

A
pulse wave is composed of many harmonics (even and odd) of
the fundamental.
The
amplitude of some harmonics may equal zero. This phenomenon
is a function of the pulse duty cycle.
The
overall shape of the harmonic envelope is known as the sinc
or _{ } function.

Ramp
Wave

A ramp waveform has
fewer spectral components than a pulse. From this we observe
that the number and amplitude of spectral components are directly
related to the number of rapid transitions in the signal. 
Triangle
Wave

This txt file
is needed to run this model. 
Arbitrary
Wave

This txt file
is needed to run this model. 
Product of Sine Waves

Multiplying two sine
waves in the time domain creates sum and difference frequencies
in the frequency domain. 
Spectral Amplitude Coefficients
The amplitudes
of spectral components in SystemView are generally different from
those seen on a spectrum analyzer. This is because the computer
is analyzing only a small time portion of the signal, whereas the
spectrum analyzer sees a continuous signal.
If it
is necessary to see the same values as a spectrum analyzer, place
a gain token of 2/(dt*ns) at the measuring point. This distorts
the amplitude in the time domain, but compensates for the time scale
in the Time Specification Window.
Student Tasks
 Modify each of the
above models by changing the input signal frequency to 1 KHz and
perform the FFT on 1cycle.
 Perform the FFT on
2.5 cycles of the pulse model and explain the change in the calculated
spectrum.
 Perform the FFT on
1 cycle of the pulse model, but set the number of samples to something
other than a power of 2. Explain the change in the calculated
spectrum.
 Create a SystemView
model of a triangle wave.
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