conjugae symmetric & mirror image of the spectrum

[rramya]

I have a small doubt:

regarding the spectrum of the signal,

if the sequence is real even symmetric seq, then it is enough if we calculate spectrum for 0:N/2. since (N/2+1) to N-1 points are redundnats data points.



My doubt is

outputs 0 and N/2 will be real and unique,

and outputs 1 to N/2-1 will be conjugate symmetric with outputs N-1 to N/2+1.



whether mirror image is folded version of the original spectrum????

and whether mirror image is same as conjugate symmetric. for points(N/2+1 to N-1)

 

[Aya2002]

i need the answer for this doubt.

 

[rramya]

Hi,
If your input signal is real and even (i.e. symmetric around zero, such
that s(t) = s(-t)), then the spectrum will be real and even -- so you
don't even have to worry about those imaginary parts.


If your input signal is real and odd (i.e. anti-symmetric around zero,
such that s(t) = -s(t)), then the spectrum will be purely imaginary and
off -- so you don't have to worry about those real parts.


If your input signal is just plain real, without necessarily being odd or
even, then you can decompose it to an even part and an odd part (check
this for yourself -- it's true). Then from the above two statements, the
spectrum will be even in it's real part, and odd in it's imaginary part
-- in other words, the it'll have conjugate symmetry around zero.


hope this explanation clarifies U about conjugate symmetry.


Happy learning

Added after 59 minutes:

what is meant by "mirrored set of negative frequencies"

in the below para
real DFT “assumes” a mirrored set of negative
frequencies due to the fact that the real DFT only ever transforms
real time domain signals and never complex ones (thus producing
mirrored negative frequencies).


answer:
the real DFT is an algorithm that is only half of a
full DFT algorithm. In the time domain it doesn't have the imaginary
"half" and in the frequency domain it doesn't have the negative
frequency "half".

the word "half" is a little more specific meaning than the word
"part" because it indicates the size of "part".



Happy learning

 

[Aya2002]

thank you too much