- #1
MrAlbot
- 12
- 0
Hello Physics Forums community,
I'm afraid I really need a hand in understanding Why are the Fourier Series for continuous and periodic signals using diferent notation of the Fourier Series for discrete and periodic Signals.
I have been following the book " Signals and Systems " by Alan V. Oppenheim, but I find it hard to understand when it comes to:
why in LTI systems :
in countinuous time: e^(st)----->H(s)e^(st)
and in discrete time: z^n ------> H(z)z^n
and why do we try to make it look like complex exponentials by making:
in countinuous time: s=jw
and in discrete time: z=e^(jw)
Does this has anything to do with eigenvalues or eigenfuctions?
and so far I put this in my head like:
Continuous time periodic signals ---> Fourier Series to represent it in a sum of exponentials, which can be then evaluated in frequency ending up maintaining the coeficients and substituting (Fourier transforming) the complex exponentials sum into delta functions.
Continuous time aperiodic Signals ----> the Fourier Series ends up being the Fourier transform but extending the period to infinity.
Discrete time periodic and aperiodic signals ---> trying to establish relation to countinuous signals but my brain its pointing to NULL due to the notation... :)
So this leaves me wondering... is the Fourier Series "the Fourier Transform of Periodic Signals" Or is the Fourier Series just a way to represent x(t) has a sum of exponentials so it can be easily translated into the sum of dirac delta functions in Frequency?
Because the Fourier Series is just a tool to represent a function as a sum of exponentials. And the Fourier Transform is a tool to transform the functions in time to frequency. I know its in front of my eyes... but I'm not seeing it. And I want to put it in my head the right way.
I would be really greatfull,
Thanks in advance
I'm afraid I really need a hand in understanding Why are the Fourier Series for continuous and periodic signals using diferent notation of the Fourier Series for discrete and periodic Signals.
I have been following the book " Signals and Systems " by Alan V. Oppenheim, but I find it hard to understand when it comes to:
why in LTI systems :
in countinuous time: e^(st)----->H(s)e^(st)
and in discrete time: z^n ------> H(z)z^n
and why do we try to make it look like complex exponentials by making:
in countinuous time: s=jw
and in discrete time: z=e^(jw)
Does this has anything to do with eigenvalues or eigenfuctions?
and so far I put this in my head like:
Continuous time periodic signals ---> Fourier Series to represent it in a sum of exponentials, which can be then evaluated in frequency ending up maintaining the coeficients and substituting (Fourier transforming) the complex exponentials sum into delta functions.
Continuous time aperiodic Signals ----> the Fourier Series ends up being the Fourier transform but extending the period to infinity.
Discrete time periodic and aperiodic signals ---> trying to establish relation to countinuous signals but my brain its pointing to NULL due to the notation... :)
So this leaves me wondering... is the Fourier Series "the Fourier Transform of Periodic Signals" Or is the Fourier Series just a way to represent x(t) has a sum of exponentials so it can be easily translated into the sum of dirac delta functions in Frequency?
Because the Fourier Series is just a tool to represent a function as a sum of exponentials. And the Fourier Transform is a tool to transform the functions in time to frequency. I know its in front of my eyes... but I'm not seeing it. And I want to put it in my head the right way.
I would be really greatfull,
Thanks in advance