# what is the maning of e^jw in fourier transform?

1. ## Re: what is the maning of e^jw in fourier transform?

Hi,

You can also read the book

signal processing and linear systems by BP lathi.

Cheers. •

2. ## what is the maning of e^jw in fourier transform?

Friend, back to basic, I suggest this book, it begin from very simple DSP concept and math until intermediate level,

Signal Processing First
McClellan, Schafer, Yoder

Pratical MATLAB examples also included in the book. •

3. ## what is the maning of e^jw in fourier transform?

using e^iw is just a notation.Suppose you have a signal
x(t)=Acos(fct).In frequency domain you represent it with a delta function at f=fc(X-axis) and height A.
Instead if x(t) is written as Real part of(e^iw),then in frequency domain you have two delta functions one representing a positive frequency and another a negative frequency both with amplitudes A/2.
The use of e^jw is just to simplify the integrations encountered and to get a reasonable mathematical frequency domain description. •

4. ## what is the maning of e^jw in fourier transform?

How much is 10^iQ?? 5. ## Re: what is the maning of e^jw in fourier transform?

Hi, all
Key to thisproblem taylor series .

exp(x) =1+ x/1! + (x²/2! )+.....x^n /n!+....
exp(jΘ)= 1 + j Θ/1! +(jΘ)²/2!+((jΘ)^3)/3!....
= 1+ jΘ-Θ²/2!-jΘ^3/3!
because J*J=-1

suppose Θ is x then
separate real and imajinary part

(1-x^2+x^4/4!-x^6/6!+......)+j(x-x^3/3!+x^5/5!-)
=cos(x)+jsin(x)

cos(x)=1-x^2+x^4/4!-x^6/6!+......
sin(x)=x-x^3/3!+x^5/5!-

exp(jx) is a point on unit circle. It is two dimentional vector having magnitude 1
When this vector is multiplied with any other it changes other vectors direction
(we call it phase shift) magnitude remain same. It is 1 at angle Θ.

Verify Cos(x)+jSin(x) magnitude =Cos²Θ+Sin²Θ =1
phase =arctan(sin(x)/tan(x))=x

In fourier transform we apply phase shift to each vector and then sum it up to have domain transform

Complex numbers are just vectors (not scalers) dont treat them as real number.
better understood as magnitude and phase ir r(exp(jΘ))
r = magnitude Θ = direction

Properties of calculus applies to natural no e and not 10, Evident from first equation

Read good books on applied mathematics

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