Many of today's digital oscilloscopes include a fast Fourier
transform (FFT) function that can let you perform frequency-domain analysis. It's a feature that's especially valuable
if you have limited or no access to a spectrum analyzer, and yet occasionally require a frequency-domain analysis
capability.
Although a spectrum analyzer does exhibit better dynamic range and less distortion, a digital oscilloscope FFT can
provide a cost-effective, space-saving alternative. A typical digital oscilloscope with FFT can compute both magnitude
and phase.
Moreover, a number of useful features are usually provided to assist in spectral analysis. You may find controls for
adjusting memory depth, for example, or for setting the sampling rate, as well as setting the vertical and horizontal
scales of the FFT. Automatic measurements and markers may be included for measuring spectral peak frequencies and
magnitudes, as well as deltas between peaks.
Other features, although designed primarily for time-domain analysis, can also be useful for an FFT. For example, in
some oscilloscopes, display traces can be annotated and saved to a disk file, or an oscilloscope's configuration can be
saved and recalled as a setup file.
Functions may also be able to be chained together to perform complex tasks such as computing the average, maximum, or
minimum of several FFT spectra. Also, measurement statistics may be available for computing the mean and standard deviation
of a measurement over several acquisitions.
The Role of Deep Memory
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Many members of the newest generation of oscilloscopes that can do an FFT also provide what we're calling deep memory.
This feature increases the record length of an FFT and that, in turn, can improve the estimate of a frequency spectrum.
Longer record lengths also provide finer frequency resolution and better dynamic range. By upgrading the processor speed
and improving the efficiency of the FFT algorithm, new-generation oscilloscopes can perform FFTs on long records very quickly.
With all this capability, the oscilloscope FFT provides a convenient tool for spectral analysis. For a further discussion
of FFT fundamentals and highlights of characteristics that are important in FFT, see the reference
at the end of this article.
Characterizing an AM Signal
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Here's a real-world application for a deep-memory oscilloscope FFT. The application is to measure the characteristics of
an amplitude-modulated (AM) signal.
The parameters of interest are the carrier frequency, fo, the modulation
frequency, fm, and the modulation index, a.
The spectrum of an AM signal contains all the information necessary to compute these parameters.
The figure below shows the spectrum of a typical AM signal with sinusoidal modulation. The center spectral line represents
the carrier; the sidebands are due to the modulation. The modulation frequency is the difference between the carrier frequency
and one of the sidebands.
Figure 1 - The spectrum of a typical AM signal modulated
with sinusoidal modulation.
The modulation index is a measure of the amplitude difference between the carrier signal and the modulation signal. It can
be computed from the magnitude delta, AdB, between the carrier and the
modulation sidebands, and is given by Equation 1.
 |
(1) |
When the modulation frequency is a small percentage of the carrier frequency,
a high-resolution FFT spectrum is necessary to distinguish the sidebands from the carrier. In this example, a function generator
(an Agilent Model 33250A) was used to generate an AM signal with a carrier frequency of 77 MHz, a modulation frequency of 1 kHz,
and an AM depth of 2% with a sine wave shape (where the AM depth is equal to the modulation index).
Notice that the modulation frequency is 0.0013% of the carrier frequency. This means that differentiating the modulation from
the carrier will require a high-resolution frequency spectrum.
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