Periodic signals expressed as harmonics of the fundamental.
A periodic signal is a sum of harmonics: x(t)=Σc_n e^{jnω₀t}, c_n=(1/T)∫x e^{-jnω₀t}dt. Square wave has odd harmonics decaying as 1/n; triangle as 1/n². Dirichlet conditions guarantee convergence; Gibbs phenomenon at jumps.
Ripple in a rectified waveform is analysed through its Fourier series.
Fourier series separates a periodic signal into harmonics, so it reveals what frequencies are present and how a filter or system will change them.
Periodic signals expressed as harmonics of the fundamental.
Fourier series separates a periodic signal into harmonics, so it reveals what frequencies are present and how a filter or system will change them.
The lowest frequency in a periodic signal, and all harmonics are integer multiples of it.
Each coefficient gives the amplitude and phase of one harmonic, so the coefficients describe the whole spectrum.
Typical applications include finding the harmonic content of a rectifier output, designing a filter to remove the third harmonic from a motor drive and analysing the vibration of a rotating machine by harmonic order.
Study "Differential equation models" first (topic 13 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
Trigonometric, exponential forms. Harmonic distortion. Power in harmonics.
Ripple in a rectified waveform is analysed through its Fourier series.
The next topic is "Fourier transform properties", which builds directly on this one.
It is classed as Beginner in Signals, Control & Comms (topic 14 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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