A periodic function f(t) with time period T repeats itself after half time period T/2. The Fourier series of f(t) would containa.sine terms onlyb.even harmonic terms onlyc.odd harmonic terms onlyd.cosine terms only
Question
A periodic function f(t) with time period T repeats itself after half time period T/2. The Fourier series of f(t) would containa.sine terms onlyb.even harmonic terms onlyc.odd harmonic terms onlyd.cosine terms only
Solution
The answer is (d) cosine terms only.
Here's why:
A function that repeats itself after half its period is known as a half-wave symmetric function. In the Fourier series, such functions are represented only by cosine terms.
The Fourier series of a function is a way to represent the function as an infinite sum of sine and cosine waves. For a function that is half-wave symmetric, the sine terms will all cancel out, leaving only the cosine terms.
So, for a periodic function f(t) with time period T that repeats itself after half time period T/2, the Fourier series of f(t) would contain cosine terms only.
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