salil87 said:
Just wanted to know if negative frequency has any significance?
no more significance than negative numbers do.
for
real sinusoidal signals, where we define the origin of time (t=0) so that the sinusoid has even symmetry, then you cannot tell the difference between a frequency f and it's negative, -f.
x(t) = A \cos( 2 \pi f t ) = A \cos( 2 \pi (-f) t )
if t=0 were defined so that the sinusoid had odd symmetry, of course negating the frequency would negate the signal:
y(t) = A \sin( 2 \pi f t ) = -A \sin( 2 \pi (-f) t ).but the "real" reason that negative frequencies exist for electrical engineers is that sometimes we represent signals as
complex quantities
x(t) = A e^{ j 2 \pi f t } = A \cos( 2 \pi f t ) + j A \sin( 2 \pi f t )
as you can see, negating f will negate the second term (the imaginary part), but not the first term (the real part). so there is a significant difference between the positive and negative frequency.
even though signals we really see and really measure are
real, often inside of a device, the mathematical operations we do on a signal (this is what "DSP" is about) are done to a complex representation of it (which might be called a
"phasor", not to be confused with Star Trek) where the sign on f will be significant. we have formalized some of these operations with concepts and techniques called the
"analytical signal" which uses another concept called the
"Hilbert transform".
so, do negative numbers really exist and have significance?
