Daqarta
Data AcQuisition And Real-Time Analysis
Scope - Spectrum - Spectrogram - Signal Generator
Software for Windows
Science with your Sound Card!
The following is from the Daqarta Help system:

Features:

Oscilloscope

Spectrum Analyzer

8-Channel
Signal Generator

(Absolutely FREE!)

Spectrogram

Pitch Tracker

Pitch-to-MIDI

DaqMusiq Generator
(Free Music... Forever!)

Engine Simulator

LCR Meter

Remote Operation

DC Measurements

True RMS Voltmeter

Sound Level Meter

Frequency Counter
    Period
    Event
    Spectral Event

    Temperature
    Pressure
    MHz Frequencies

Data Logger

Waveform Averager

Histogram

Post-Stimulus Time
Histogram (PSTH)

THD Meter

IMD Meter

Precision Phase Meter

Pulse Meter

Macro System

Multi-Trace Arrays

Trigger Controls

Auto-Calibration

Spectral Peak Track

Spectrum Limit Testing

Direct-to-Disk Recording

Accessibility

Applications:

Frequency response

Distortion measurement

Speech and music

Microphone calibration

Loudspeaker test

Auditory phenomena

Musical instrument tuning

Animal sound

Evoked potentials

Rotating machinery

Automotive

Product test

Contact us about
your application!

Magnitude via Vector Sum

It often happens that we can't directly measure the amplitude and phase angle of a sinusoid, but instead we measure its sine and cosine "component" amplitudes. In the sine wave clock example we measured the sine component of the clock face (the height of the hand's pointer) to get our sine waveform. The cosine component is measured similarly, as the length of the "shadow" of the hand on the horizontal axis:

We can thus find the true amplitude or "magnitude" as the hypotenuse of this right triangle by taking the square root of the sum of the squares of the sine and cosine components. This is called the "vector sum" of the components. Similarly, we can find the phase as the angle whose tangent is equal to the sine component divided by the cosine component.

The sine and cosine components are often referred to as the "in-phase" and "quadrature" components, especially in discussions of older analog methods. Engineering math types prefer to use "real" for the cosine component and "imaginary" for the sine component, corresponding to a wonderfully intimidating exponential expression called "complex notation", perfect for casual dining conversation and impressing uninitiated audiences.


See also Sine Wave Basics, Sine Wave Phase, Making Waves via Sine Wave Synthesis

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