Remember that according to Fourier, a square wave or triangular wave is
made up of a series of sine waves and contains frequencies higher than the
fundamental. If you sample a square wave at a rate equal to four times the
fundamental frequency, then reconstruct the samples as a sine wave, you
have all the information about the square wave, up to that frequency. This is
no different than viewing the same square wave on an oscilloscope with
insufficient bandwidth to reproduce the higher-frequency components. To
accurately reproduce the square wave, you must sample it at a rate at least
twice the highest frequency in its Fourier expansion.
Aliasing
The effect of sampling rate is the same as bandwidth: loss of high frequency
information in the signal. However, there is an additional complication
associated with sampling a signal. If the signal contains frequencies higher
than half the sampling rate, then there will be errors due to aliasing.
Consider sampling a sine wave at a rate less than twice the frequency of the
sine wave as shown in figure 13-25. Notice that the set of resulting samples
is indistinguishable from samples of a lower-frequency sine wave.
Sine Wave Having Frequency f and Sampled at Frequency <2f
Figure 13–25
Measurements
Time-interval measurements
13–52
Summary of Contents for 54710A
Page 7: ...vi ...
Page 9: ...viii ...
Page 16: ...Glossary Index Contents Contents 7 ...
Page 17: ...Contents 8 ...
Page 65: ...2 16 ...
Page 86: ...4 Applications ...
Page 96: ...6 Display 6 4 Scale 6 5 Offset 6 6 Input 6 6 Probe 6 7 Calibrate 6 10 Channel Menu ...
Page 98: ...Channel menu and menu map for the HP 54712A plug in Figure 6 1 Channel Menu 6 3 ...
Page 110: ...7 Thresholds 7 4 Top Base 7 6 Define time 7 8 Statistics 7 9 Define Measure Menu ...
Page 112: ...Define measure menu and menu map Figure 7 2 Define Measure Menu 7 3 ...
Page 143: ...8 22 ...
Page 163: ...9 20 ...
Page 164: ...10 Messages ...
Page 178: ...12 Function 12 3 Define Function 12 4 Display 12 7 Math Menu ...
Page 186: ...13 Measurements ...
Page 245: ...13 60 ...
Page 246: ...14 Setup Memory 14 3 Save 14 3 Recall 14 4 Default Setups 14 4 Setup Menu ...
Page 261: ...15 10 ...
Page 274: ...17 Scale 17 3 Position 17 3 Reference 17 4 Windowing 17 5 Time Base Menu ...
Page 282: ...Trigger menu and menu map Figure 18 1 Trigger Menu 18 3 ...
Page 319: ...19 18 ...
Page 322: ...20 Waveform 20 3 Pixel 20 6 Waveform Menu ...
Page 346: ...Limit test menu and menu map Figure 22 2 Limit Test Menu 22 3 ...
Page 357: ...22 14 ...
Page 360: ...Mask menu map Figure 23 1 Mask Menu 23 3 ...
Page 370: ...Figure 23 3 Figure 23 4 Mask Menu Edit Mask 23 13 ...
Page 407: ...Index 10 ...
Page 409: ......