4 FOURIER SERIES(latest) part1

# 4 FOURIER SERIES(latest) part1 - Excellent does not an...

• Notes
• 68

This preview shows pages 1–10. Sign up to view the full content.

Excellent does not an accident, but it comes through a hard work!!

This preview has intentionally blurred sections. Sign up to view the full version.

Excellent does not an accident, but it comes through a hard work!! Introduction on Fourier Series Introduction on Fourier Series The ability to analyze waveforms of various types is an important engineering skill. Fourier analysis provides a set of mathematical tools which enable the engineer to break down a wave into its various frequency components. It is then possible to predict the effect of a particular waveform may have from knowledge of the effects of its individual frequency components. Often an engineer finds it useful to think of a signal in terms of its frequency components rather than in terms of its time domain representation.
Excellent does not an accident, but it comes through a hard work!! LESSON OUTCOMES LESSON OUTCOMES 2 T The oscillation of an undamped spring-mass system around the equilibrium is a sine wave .

This preview has intentionally blurred sections. Sign up to view the full version.

Excellent does not an accident, but it comes through a hard work!! 4.1 Periodic functions
Excellent does not an accident, but it comes through a hard work!! PERIODIC FUNCTIONS PERIODIC FUNCTIONS A function is said to be periodic if its image values are repeated at regular intervals in its domain. Thus the graph of a periodic function can be divided into ‘vertical strips’ that are replicas of each other. The interval between two successive replicas is called the period of the function. A function is periodic with period T if, for all its domain values , f t f t t ( ) ( ) f t T f t For example, The function has periods since t t f sin ..., , 6 , 4 , 2 sin( 2 ), sin( 4 ), sin( 6 ), ..., all equal to sin . t t t t + + + Illustrating the cosine wave's fundamental relationship to the circle.

This preview has intentionally blurred sections. Sign up to view the full version.

Excellent does not an accident, but it comes through a hard work!! PERIODIC FUNCTIONS PERIODIC FUNCTIONS A periodic function has a basic shape which is repeated over and over again. The fundamental range is the time (or sometimes distance) over which the basic shape is defined. The length of the fundamental range is called the period . Example: Periodic function Note: Throughout this chapter, we will use/ express general periodic function as: ( ) be a function in the interval 2 2 and ( ) be periodic with period, . So ( ) ( ) f t T T t f t T f t T f t
Excellent does not an accident, but it comes through a hard work!! PERIODIC FUNCTIONS PERIODIC FUNCTIONS We consider the waveforms of and For these waveforms, is the angular frequency. Then, Let us introduce phase angle, , then The quantity is called the time displacement . The sine and cosine functions form a class of functions known as sinusoids or harmonics . t A y cos t A y sin 2 T The period 2 1 T f The frequency + + t A t A y cos ) cos( + + t A t A y sin ) sin( t A y sin

This preview has intentionally blurred sections. Sign up to view the full version.

Excellent does not an accident, but it comes through a hard work!!

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Fall '14

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern