Fourier Transform

-

Introduction:

This section will discuss the fourier transform and explains the graphical representation of the fourier transform.

The fourier transform:

Let X( t ) be a nonperiodic signal of finite duration, that is,

Such a signal is shown in Fig. (a). Let xT0(t) be a periodic signal formed by repeating x(t) with fundamental period T0 as shown fig (b ). If we let To - , we have

The complex exponential Fourier series of xT0(t)  is given by

The above equ can be written as

Let us define X(w) as

the complex Fourier coefficients ck, can be expressed as



Cosine and sine  Function


Introduction:

This section describes the cosine and sine function Pair mathematically and also explains this in detail.

 

The cosine function pair:

Proof:

 

The f(t) - F(w) correspondence is also shown in fig given below

We know that Cos w0t is real and even function of time, and we found out that its Fourier transform is a real and even function of frequency.

The Sine Function Pair:

Proof:

The f(t) - F(w) correspondence is also shown in figure given below.

 

We know that Sin w0t is real and odd function of time, and we found out that its Fourier transform is an imaginary and odd function of frequency.


Comments

Post a Comment

Popular posts from this blog

Unit Step Signal

-
Image
Introduction:          This section explains the unit step signal and also derives the unit step signal in the following way. The unit step signal: A well known discontinuous function is the unit step function u 0 * (t) which is defined as It is also represented by the waveform of Figure given below In the waveform of Figure above, the unit step function u 0 (t)  changes abruptly from 0 to 1 at t = 0. But if it changes at  t = t 0 instead, it is denoted as u 0 (t-t 0 ) . In this case, its waveform and definition are as shown in Figure given below If the unit step function u 0 (t)  changes abruptly from 0 to 1 at  t = -t 0 , it is denoted as u 0 (t  t 0 ) . In this case, its waveform and definition are as shown in Figure given below.
Read more

Road Cadastre

-
INTRODUCTION :          According to the Italian rule of the road, boards who own roads are bound to set up and to keep up to-date the cartography and the cadaster of roads and related fixtures. According to Ministerial Decree 1/6/2001, which enforces it formally, the road cadaster is a data system, representing the inventory of every road having public assignment, whose primary goal is to fix the size of the national roads network. The enforcing rule sets the survey and representation standards according to the pattern provided by the GDF (Geographic Data Files) v. 3.0 standard (CEN 1995), as emitted by Technical Committee 278 of the European Normalization Committee. MMS vehicle GIGIOne, owned by the Excellence Centre for Tele geometrics Research of Trieste University, is able to provide surveys of geometrical and descriptive characteristics in order to set up the data base of the road cadaster as requested by the Ministerial Decree. This paper describes a sample  processing and repr
Read more

Sallabus Of Geomatics Engineering

-
Image
The Ioe sallabus of Geomatics Engneering upto 4th sem is as follows. First Year First  Part Sallabus (total subject-6) ** Mathematics I [SH401] **Computer Programming [CT401] **Engineering Drawing I [ME401] **Engineering Chemistry [SH403] ** Fundamental of Thermodynamics & Heat Transfer [ME402] ** Workshop Technology [ME 403] First Year second Part  Sallabus (total subject-6) **Mathematics II [SH451] ** Engineering Drawing II [ME451] ** Basic Electronics Engineering [EX451] ** Engineering Physics [SH452] **Applied Mechanics [CE451] **Basic Electrical Engineering [EE451]   Second  Year – first Part Sallabus (total sallabus-7) **Mathematics III [SH501] **Probability and Statistics[SH 503] **Applied Physics **Applied Mechanics (Dynamics) [CE 501] ** Fundamentals of Surveying **Fundamentals of Civil Engineering ** Object Oriented Programming [CT 501] Second Year – Seco Part Sallabus (total subject-5) ** Applied Mathematics [SH 551] **Compu
Read more