Periodic signals repeat after a period T; others do not.
A signal is periodic if x(t+T)=x(t) for all t; the smallest T is the fundamental period and f₀=1/T. Sums of sinusoids are periodic only if frequency ratios are rational. Aperiodic signals, such as a single pulse, have continuous spectra.
cos(2πt) has period 1 s and cos(3πt) has 2/3 s, so their sum repeats every 2 s.
Periodic signals are common in power systems and machines, and their period defines the frequency content you must handle.
Periodic signals repeat after a period T; others do not.
Periodic signals are common in power systems and machines, and their period defines the frequency content you must handle.
Find the period of each term, then the sum is periodic with the least common multiple of those periods if the ratio is rational.
Yes, a pure sinusoid repeats forever. A decaying exponential, for example, is not periodic.
Typical applications include identifying the period of mains voltage at 50 Hz, checking that a motor vibration repeats every shaft turn and determining the period of a sum of two sinusoids.
Study "Continuous and discrete signals" first (topic 2 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
Fundamental frequency. Harmonics. Period of sum = LCM of periods.
cos(2πt) has period 1 s and cos(3πt) has 2/3 s, so their sum repeats every 2 s.
The next topic is "Even and odd signals", which builds directly on this one.
It is classed as Beginner in Signals, Control & Comms (topic 3 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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