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Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency.The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals.
The period and frequency are determined by the size of the mass m and the force constant k, while the amplitude and phase are determined by the starting position and velocity. The velocity and acceleration of a simple harmonic oscillator oscillate with the same frequency as the position, but with shifted phases. The velocity is maximal for zero ...
Crest and trough in a wave. A Crest point on a wave is the highest point of the wave. A crest is a point on a surface wave where the displacement of the medium is at a maximum. A trough is the opposite of a crest, so the minimum or lowest point of the wave.
which is the inverse transform formula. The complex number, (), conveys both amplitude and phase of frequency . See Fourier transform for much more information, including: conventions for amplitude normalization and frequency scaling/units; transform properties; tabulated transforms of specific functions
Peak-to-peak amplitude (abbreviated p–p or PtP or PtoP) is the change between peak (highest amplitude value) and trough (lowest amplitude value, which can be negative). With appropriate circuitry, peak-to-peak amplitudes of electric oscillations can be measured by meters or by viewing the waveform on an oscilloscope .
If the filter shows amplitude ripple within the passband, the x dB point refers to the point where the gain is x dB below the nominal passband gain rather than x dB below the maximum gain. In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops 3 dB below peak.
A modulated wave resulting from adding two sine waves of identical amplitude and nearly identical wavelength and frequency. A common situation resulting in an envelope function in both space x and time t is the superposition of two waves of almost the same wavelength and frequency: [2]
Increase of amplitude as damping decreases and frequency approaches resonant frequency of a driven damped simple harmonic oscillator. [ 1 ] [ 2 ] Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration that matches its natural frequency .