Very often in Engineering we come across the need to employ the use of Fourier Transforms and subsequently most students fail to understand the underlying structure and nature of transforms of this kind.
According to the entry regarding Fourier transforms found in Wikipedia, “the Fourier transform decomposes a function into a continuous spectrum of its frequency components, and the inverse transform synthesizes a function from its spectrum of frequency components“.
Imagine this;
You’re dining at a lounge,there’s a guitarist on the stage and he is strumming his guitar. Each strum he makes is a chord played. A chord is a combination of two or more notes hence, it can be likened to a function.
Now here’s the proposed problem, with a given chord (comprising of a series of different vibrations/frequency) how is one going to decide which notes also known as frequency components are ),being played to form that chord? That’s exactly why mathematicians say, “Fourier Transforms have come to save the day!”For more information on Fourier Transforms and Series’ please visit Eric Weinstein’s Math World http://mathworld.wolfram.com/FourierTransform.html the web’s most extensive site in relation to mathematics.
Steps in Solving Fourier Series Problems
Before we proceed with solving the problem we must make certain the rule involved in Fourier series and any problem relating to fourier series will exceed the rule unless stated. The rule is as follows:
Step 1: Determine if the given function f(t) is an even or odd function using the following properties,
f(t) = f(-t) [even function]
f(t) = -f(t) [odd function]
Step 2: If f(t) is an even function the term bn (as seen in the formula) will result in bn=0
Step 3: Find the components that must be sought before proceeding, the Period, T0 = period from start of signal to end of signal before repetition , f0 = T0-1 , a0 , ω0= 2πf.
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