Unitary transforms

hello forum,
a question about normalization factors in the Fourier transform pairs:

why is it that a factor 1/2*pi in only one, or 1/sqrt(2pi) in both, or no factor (in the case the complex basis functions have argument 2*pi*f) need to be in front of the Fourier transform pair?

I understand normalization and its importance in the dot product calculation of coefficients.
Sines, cosines, and complex exponentials have normalization factors equal to 1/sqrt(pi).......
in order to get modulus one....


thanks
fisico30
 

malawi_glenn

Science Advisor
Homework Helper
4,783
22
it is there for normalization as you said, and there exists several conventions which works.
 
so,

exp (i*w*t) and exp (i*2*pi*f*t) don't have the same normalization factors? Why?
 

malawi_glenn

Science Advisor
Homework Helper
4,783
22
since you have 2pi already in the exponential
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top