negative frequencies in spectrum?

significance of negative frequency

can anyone please tell me the significance of negative frequencies in the spectrum?
how do we physically explain the introduction of negative frequencies when we do fourier analysis for modulation techniques?

why negative frequencies are needed in spectrum

frequency basically is no of rotations (or cycles) per second

and there are two possible directions of rotations ..one clockwise and one anticlockwise

so we can associate one direction to +ve frequencies and the other direction to -ve..
for differentiation

negative frequencies are needed in the spectrum

ysenthilece said:

frequency basically is no of rotations (or cycles) per second

and there are two possible directions of rotations ..one clockwise and one anticlockwise

so we can associate one direction to +ve frequencies and the other direction to -ve..
for differentiation

Click to expand...

but is not this the phase concept ?

I know if fc is the carrier frequency and fm is modulant and if in AM I have fc, fm and fc+fm and fc-fm then if fm>fc I have a negative frequency. But this is a math speculation. I am wrong ?

//Felipe

single sided spectrum frequency

All real signals will have negative frequencies mirroring those of the positive frequencies, ie a 1kHz sinusodal will have frequency components of 1kHz and -1kHz. Any signal that does not satisfy this is not real, ie fictitious. This is a consequence of the fourier transform, and is more of a mathematical phenomenon.

There are times when these concepts actually come into play.

1. When people talk about bandwidth, it refers by default to single-sided bandwidth, which covers only the positive side of the spectrum. Sometimes, they talk about double-sided bandwidth, which would cover both sides of the spectrum. Since real signals have symmetric spectrums, the double-sided bandwidth is always double of single-sided ones.

2. During sampling, the spectrum of the signal is made periodic. You must remember that the negative spectrum is also made periodic as well. Eg. for a sinusoid of frequency 1kHz sampled at 5kHz, sampled spectrum has frequency components of 1+5, -1+5, 1+10, -1+10 .....

why are negative frequencies needed in a spectrum

The Fourier representations include negative values of n wich reflects in negative values of frequency, these lack physical significance since there are not negative frequencies. Whereas, mathematicaly, it is a powerfull tool for analysing signals and systems.

Negative frequencies are just a mathematical resource to analysis and synthesis.

why negative frequency need in the spectrum

Listo said:

ysenthilece said:

frequency basically is no of rotations (or cycles) per second

and there are two possible directions of rotations ..one clockwise and one anticlockwise

so we can associate one direction to +ve frequencies and the other direction to -ve..
for differentiation

Click to expand...

but is not this the phase concept ?

I know if fc is the carrier frequency and fm is modulant and if in AM I have fc, fm and fc+fm and fc-fm then if fm>fc I have a negative frequency. But this is a math speculation. I am wrong ?

//Felipe

Click to expand...

it is not phase concept ..like phase concept is ..having a reference and the relative shift with respect to that is phase....

but moving in anticlockwise and clockwise direction corresponds to positive frequencies...u can understand better physically considering rotation ..the simple harmonic theory concept...

u cannot visualise this much in real time signal's case..as they possibly move along the positive time axis..in this case negative frequencies can be considered only for
mathematical convenience...


like we will involve with sinusoids like cos(wt) ..this correspons to superposition of
exp(jwt) and exp(-jwt) superposition of postive and negative frequencies...


""""""""""""I know if fc is the carrier frequency and fm is modulant and if in AM I have fc, fm and fc+fm and fc-fm then if fm>fc I have a negative frequency. But this is a math speculation. I am wrong ?"""""""""""""


ya if fm>fc one frequency will go to the negative side...correspondingly one from the negative side will come from the negative side to positive side..to maintain the
conjugate pairs......and it is just that as fc is usually higher it is taken as reference and there are 2 additional frequencies fc+fm and fc-fm appear...if fm is greater
we will get fm+fc and fm-fc ..

but this won't happen in practical cases...as the spectrum overlaps and results in distortion..it won't be an AM wave...