MPO6002EDU Series Oscilloscope Guide

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FFT Aliasing

When using FFT, it is important to be aware of frequency aliasing. This requires that the operator have some

knowledge as to what the frequency domain should contain, and also consider the sampling rate, frequency

span, and oscilloscope vertical bandwidth when making FFT measurements.

Note Nyquist Frequency and Aliasing in the Frequency Domain

The Nyquist frequency is the highest frequency that any real-time digitizing oscilloscope can acquire without

aliasing. This frequency is half of the sample rate. Frequencies above the Nyquist frequency will be under

sampled, which causes aliasing. The Nyquist frequency is also called the folding frequency because aliased

frequency components fold back from that frequency when viewing the frequency domain.

Aliasing happens when there are frequency components in the signal higher than half the sample rate.

Because the FFT spectrum is limited by this frequency, any higher components are displayed at a lower

(aliased) frequency.

Because the frequency span goes from ≈ 0 to the Nyquist frequency, the best way to prevent aliasing is to make

sure that the frequency span is greater than the frequencies of significant energy present in the input signal.

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FFT DC Value

The FFT computation produces a DC value that is incorrect. It does not take the offset at center screen into

account. The DC value is not corrected in order to accurately represent frequency components near DC.

FFT Spectral Leakage

The FFT operation assumes that the time record repeats. Unless there is an integral number of cycles of the

sampled waveform in the record, a discontinuity is created at the end of the record. This is referred to as leakage.

In order to minimize spectral leakage, windows that approach zero smoothly at the beginning and end of the

signal are employed as filters to the FFT. The FFT Menu provides these windows: Rectangule, Hanning,

Hamming, Blackman-Harris, Bartlett, and Flat Top.

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Integrate

ò dt (integrate) calculates the integral of the selected source. It shows the accumulated amount of change.

You can use integrate to calculate the energy of a pulse in volt-seconds or measure the area under a waveform

by measuring the difference in the integrate function value across the pulse or waveform.

ò dt plots the integral of the source using the "Trapezoidal Rule". The equation is:

               n

In = co + Δ t ∑yi

i=0

Where:

? I = integrated waveform.

? Δt = point-to-point time difference.

? y = channel 1, 2, 3, 4, or Math (lower math function) data points.

? co = arbitrary constant.

? i = data point index.

The integrate operator provides an Offset softkey that lets you enter a DC offset correction factor for the input signal.

Small DC offset in the integrate function input (or even small oscilloscope calibration errors) can cause the integrate

function output to "ramp" up or down. This DC offset correction lets you level the integrate waveform.

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Differentiate

d/dt (differentiate) calculates the discrete time derivative of the selected source. You can use differentiate to

measure the instantaneous slope of a waveform. For example, the slew rate of an operational amplifier may

be measured using the differentiate function.

Because differentiation is very sensitive to noise, it is helpful to set acquisition mode to Averaging.

d/dt plots the derivative of the selected source using the "average slope estimate at 4 points" formula. The equation is:

di = yi+4 + 2yi+2 ? 2yi?2 ? yi?4

8 Δ t

Where:

? d = differential waveform.

? y = channel 1, 2, 3, 4, or Math (lower math function) data points.

? i = data point index.

? Δt = point-to-point time difference.

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Example of Differentiate Function

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Square Root

Square root (√) calculates the square root of the selected source.

Where the transform is undefined for a particular input, holes (zero values) appear in the function output.

Example of √ (Square Root)

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Advanced Math Expression

Advanced Math lets users create custom math waveform expressions that incorporate active waveforms,

measurements, and numeric constants.

1 Press the [Math] key. Then, press the Operator softkey and turn the V0 knob to select the expression.

2 Press the Settings softkey to enter the Expression Setting Menu.

3 Press Edit softkey to display the Expression Alpha-Numeric Keypad. Then use the V0 knob or touch screen

gesture to create an expression. When done, press Enter accept.

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Advanced Math Expression Alpha-Numeric Keypad

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· Operators include: +, -, *, /, >, >=, <, <=, ==, !=, &&, || , !

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· PI: π ≈ 3.14159

Math PI property represents the ratio of the circumference of a circle to its diameter.

· Functions include sine, cos, tan, asin, acos, atan, sinh, cosh, tanh, pow, sqrt, log, ln, abs, ceil, floor, intg, diff.