Tutorial Question 3.6:
There are two aspects of the Fourier theory; analysis and synthesis. Major components of Fourier
analysis and synthesis are shown below. Write a short essay (half a page to one page) explaining the
process of “Fourier Analysis” and its reverse, the process of “Fourier Synthesis”. Your easy should
contain explanations about the interrelation between the original periodic signal, x(t), its spectrum,
and its synthesized version.
Answer:
Fourier Analysis:
The process of decomposing any periodic function into its constituent sine or cosine waves is called
Fourier analysis. We start from x(t) and then calculate {a
k
}.
Fourier Synthesis:
It is a method of expressing an arbitrary periodic function as a sum of cosine terms, or it can be used
to express a function in terms of the frequencies (harmonics) it is composed of. Once the harmonic
content of a sustained wave from Fourier analysis are known, the capability of synthesizing that wave
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 Three '10
 Pd
 Fourier Series, Mathematical analysis

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