I may not be able to help you fully but this may be of some help.

In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer.

Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term Fourier analysis often refers to the study of both operations.

The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends on the domain and other properties of the function being transformed. Moreover, the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, and the general field is often known as harmonic analysis. Each transform used for analysis has a corresponding inverse transform that can be used for synthesis.

*The first three successive partial Fourier series (shown in red) for a square wave (shown in blue). The second half of the course is devoted to Fourier series and Fourier integrals.*

2. sawtooth wave where 50% of the period is at a height of 1 and other 50% of the period is at a height of 0.7. now i have to calculate the Fourier transform of both waves and no matter how many times i tried i always end up with the same formula used for regular sawtooth wave on both occasions. If anyone can help me anyhow i would appreciate it since if i don't get this by February i will fail so i'm kind of desperate.]]>