Negative frequncies are a mathematical trickery that helps us in computation of signal characterstics , just as use of imaginary numbers helps ( e.g. sq.root of negative number) in may ways
Big Aha moment on negative frequencies. I now understand clearly the connection with the Zero IF thing shifting the signal around 0 Hz before sampling by the Analog Digital Converter. The key element to understand is the parity of the cosine and sine functions : cos (x) = cos (-x), and it is therefore not possible to differentiate between a frequency above and below carrier frequency (both positives because real frequencies) in the baseband range, that will turn into a positive and negative frequency (respectively) once shifted and centered around 0 Hz. When applying the cosine function alone to these frequencies, because of the parity of the function, we lose a piece of information about the sign of the frequency, that tells whether it is a few Hertz above or below carrier frequency. The quadrature signal (sine) stores the other half of the information that enables to differentiate lower range frequencies from higher range frequencies, and therefore reconstruct the real signal frequency. Thanks a bunch !
Negative frequncies are a mathematical trickery that helps us in computation of signal characterstics , just as use of imaginary numbers helps ( e.g. sq.root of negative number) in may ways
Thanks for your great Efforts.
Big Aha moment on negative frequencies. I now understand clearly the connection with the Zero IF thing shifting the signal around 0 Hz before sampling by the Analog Digital Converter. The key element to understand is the parity of the cosine and sine functions : cos (x) = cos (-x), and it is therefore not possible to differentiate between a frequency above and below carrier frequency (both positives because real frequencies) in the baseband range, that will turn into a positive and negative frequency (respectively) once shifted and centered around 0 Hz. When applying the cosine function alone to these frequencies, because of the parity of the function, we lose a piece of information about the sign of the frequency, that tells whether it is a few Hertz above or below carrier frequency. The quadrature signal (sine) stores the other half of the information that enables to differentiate lower range frequencies from higher range frequencies, and therefore reconstruct the real signal frequency.
Thanks a bunch !
That sin formula looks wrong.
There should be a subtraction, and not an addition operation.
@@soubhikchatterjee3149 And both terms are divided by 2i.