Hi,

why do i get a negative frequency in fourier transform of sinusoidal

wave ? arent frequencies supposed to be +ve ? i have read a few books

and they suggest that -ve frequencies are present for complex

sinusoids. so is it possible to physically generate complex sinusoids ?

-bz

Negative frequencies are simply a mathematical slight of hand

in the same way that +6 may be represented by the sum of +11 and

-5. In the usual Fourier transform of a periodic waveform, cosine

and sine terms are generated along with their coefficients. If we

use the standard exponential identities...

Cos(x) = 1/2(exp[jwt] + exp[-jwt])

Sin(x) = -j/2(exp[jwt] - exp[-jwt])

...in place of these, a series emerges with complex

coefficients and terms including both w and -w (with the real and

imaginary components being normally drawn on separate diagrams).

The negative ones however, have the same physical presence as

minus five apples has in a school arithmetic lesson. It is just

that in combination with the other terms a tangible waveform

emerges.

Having said all of that, if you regard a phasor as a

counter-clockwise rotating line at a particular frequency then a

negative one of the same frequency would be a line revolving

clockwise at the same rate. It is easy enough to think up physical

models (e.g. motor shafts) where this could be a useful insight.

The problem is that we usually think in terms of time which, as

far as we know, goes only one way. How about then substituting

some other variable that doesn't have this limitation? The maths

would be just as valid.

I would have gone on a little longer but it is Friday and I

must make the local fish 'n chip shop before they close or I'll

starve.

Cheers - Joe