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Harmonic Mean

Harmonic Mean

The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...

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Related Experiment Video

Updated: Jul 2, 2026

Preparing an Isotopically Pure 229Th Ion Beam for Studies of 229mTh

Preparing an Isotopically Pure ²²⁹Th Ion Beam for Studies of ^229mTh

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Microprocessor assisted real-time harmonic analysis by minicomputer.

T G Matheson¹, R J Higgins

¹Physics Department, University of Oregon, Eugene, OR 97403, USA.

The Review of Scientific Instruments

|December 1, 1978

Summary

This summary is machine-generated.

This study introduces a new real-time signal averaging technique for low audio frequencies. It overcomes previous limitations using parallel processing and a coherent Fourier transform for improved waveform analysis and display.

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Area of Science:

Electrical Engineering
Signal Processing
Instrumentation

Background:

Traditional lock-in detection instruments often face challenges with software emulations.
Earlier systems exhibited inherent problems that limited their effectiveness in low audio frequency analysis.

Purpose of the Study:

To develop an improved real-time signal averaging and harmonic analysis technique.
To overcome the limitations of previous software-based lock-in detection systems.
To enhance the analysis of low audio frequency waveforms.

Main Methods:

Employed parallel processing between a data acquisition minicomputer (HP-2116B) and a microcomputer (Z-80).
Replaced the chopper-type lock-in algorithm with a coherent Fourier transform.
Digitally generated a pure modulation sine wave with 0.01% total harmonic distortion (THD).

Main Results:

Eliminated problems associated with earlier lock-in detection systems.
Achieved simplified system tune-up procedures.
Produced a high-quality, flicker-free, real-time display of averaged waveforms.
Provided accurate harmonic content analysis.

Conclusions:

The new technique offers a significant advancement in real-time signal processing for low audio frequencies.
The system provides superior waveform averaging and harmonic analysis compared to previous methods.
The use of parallel processing and coherent Fourier transforms enhances accuracy and simplifies operation.