# Fourier Analysis: Inspect Waveforms in FIGURE 1

• casper12
In summary, the conversation is about analyzing periodic waveforms in terms of their Fourier series. The question asks for a state by inspection of the waveforms and their coefficients, specifically looking at their even/odd symmetry, period, and simplifying characteristics. The conversation also includes some advice and hints on how to approach the problem.
casper12

## Homework Statement

b) state by inspection (i.e. without performing any formal analysis) all you can about each of the periodic waveforms shown in FIGURE 1 in terms of their Fourier series when analysed about t = 0

## Homework Equations

3. The Attempt at a Solution

Hi could someone please be able to give me some advice on what the question is asking for.

thank you

It sounds like it might be asking about even/odd ... which coefficients will be non-zero in your Fourier expansion.
Maybe even the period, like the argument of your sines and cosines, etc.

Does anybody have any updates regarding this post, I am not even sure where to begin. The lessons from uni do not give any suggestion on what the question is after.

rob1985 said:
Does anybody have any updates regarding this post, I am not even sure where to begin. The lessons from uni do not give any suggestion on what the question is after.
Hi Rob 1985, currently doing this question myself and have got as far as basically stating if the waveform is Odd or Even and which coefficients relate to it. Also stating the F.S for the waveforms from the appendix in lesson 4. but yes the lessons don't really give much help.

There are simplifications one can make regarding a periodic waveform. You need to distinguish among possible kinds of symmetry:
• odd vs. even functions
• shifting of x and/or y axes
• half-wave symmetry
Each of these imply certain simplifying characteristics of the waveform. As a starter hint, an odd function has only sine terms (assuming you're using sine - cosine expansion. There are parallel simplifications for the exponential version etc.)

BTW don't confuse even vs. odd harmonics with even vs. odd functions. They have nothing to do with each other. Just an unfortunate nomenclature.

## 1. What is Fourier analysis?

Fourier analysis is a mathematical technique used to decompose a complex waveform into its individual sinusoidal components. It is named after the French mathematician and physicist Joseph Fourier.

## 2. Why is Fourier analysis important?

Fourier analysis is important because it allows us to understand and analyze complex waveforms, such as sound waves and electrical signals. It is widely used in many fields, including physics, engineering, and signal processing.

## 3. How does Fourier analysis work?

Fourier analysis works by representing a complex waveform as a sum of sine and cosine functions of different frequencies and amplitudes. This is done using a mathematical tool called the Fourier transform.

## 4. What can we learn from Fourier analysis?

From Fourier analysis, we can learn about the different frequencies present in a waveform, their amplitudes, and how they contribute to the overall shape of the waveform. This information can help us understand and manipulate the waveform for various applications.

## 5. What are some applications of Fourier analysis?

Fourier analysis has many applications, including signal processing, image processing, data compression, and solving differential equations. It is also used in fields such as music and speech recognition, astronomy, and medical imaging.

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