PG1995
Active Member
Hi
I have re-read my queries, Q2, and Q3, and think that I stated my confusion as clearly as possible. So, I would request you that you have another look on what I said there, if possible, so that you can know what goes inside my mind and how to guide me in right direction. Actually in Q2 I was telling you how I view the DC component, and in Q3 I was trying to show you that why my so-called understanding of the DC component is flawed. Okay, let me state it otherwise. What is the DC component in FS and what does it tell us? When is the DC component zero, and when it's zero, what does it tell us? Thank you.
If you don't mind, I would say that I'm not satisfied with this reply, or you can say I'm missing your point. For the sake of continuity, the following was my question.
Is mathematical FS or FT representation of some function an exact replicate of that function? For example, if you have connected a wire to a source supplying an electric current in form of a square wave, then do you think that electric current is flowing in form of pulses (i.e. square wave) or in form of odd harmonics of sine wave? Putting it differently, do you think electrons are moving form of pulses (i.e. square wave) or odd harmonics of a sine wave?
I don't think it's matter of viewpoint we hold on to because FS or FT is mathematics and not metaphysics. Let me elaborate on this. Light having wavelength range of roughly 630-760 nm produces sensation of red color in a human brain. But how can I know that the sensation that I see as red doesn't produce in you the sensation that I see as green? We both might agree that the color is red, but how can I know that you see the color red in the same way as I see it? It's a metaphysical situation. But wavelength range of 630-760 nm is an exact mathematical formulation and it can be confirmed scientifically. So, if you say that it's just a matter of viewpoint that whether 'square wave electric current' exists as pulses or as odd harmonics of a sine function then I don't get it because physically either current can exist as pulses or odd harmonics and not both. I hope you can see where I'm having trouble. Thank you.
Regards
PG
I'll start with questions Q2 and Q3.
Where did you get the idea about needing a symmetric function when the DC component is subtracted? It's not even clear what your definitions of symmetric and symmetrize are.
I have re-read my queries, Q2, and Q3, and think that I stated my confusion as clearly as possible. So, I would request you that you have another look on what I said there, if possible, so that you can know what goes inside my mind and how to guide me in right direction. Actually in Q2 I was telling you how I view the DC component, and in Q3 I was trying to show you that why my so-called understanding of the DC component is flawed. Okay, let me state it otherwise. What is the DC component in FS and what does it tell us? When is the DC component zero, and when it's zero, what does it tell us? Thank you.
Q5: Tricky question!. I view the mathematics as correct and exact. But I view all physics theories we know as an approximation. Even quantum mechanics is well known to be only approximately correct. The interesting thing is that non-relativistic quantum mechanics and electromagnetic field theory in vacuum are truly linear theories. That is, they are exactly linear in the mathematical sense, and hence the Fourier theory is an exactly correct and equivalent viewpoint within the theory. However, we know those theories are only approximate representations or models of reality. So, you have to make your own interpretation here. I think the question is not provable one way of the other, and it is a viewpoint we might hold on to. I don't have a strong opinion one way or the other.
If you don't mind, I would say that I'm not satisfied with this reply, or you can say I'm missing your point. For the sake of continuity, the following was my question.
Is mathematical FS or FT representation of some function an exact replicate of that function? For example, if you have connected a wire to a source supplying an electric current in form of a square wave, then do you think that electric current is flowing in form of pulses (i.e. square wave) or in form of odd harmonics of sine wave? Putting it differently, do you think electrons are moving form of pulses (i.e. square wave) or odd harmonics of a sine wave?
I don't think it's matter of viewpoint we hold on to because FS or FT is mathematics and not metaphysics. Let me elaborate on this. Light having wavelength range of roughly 630-760 nm produces sensation of red color in a human brain. But how can I know that the sensation that I see as red doesn't produce in you the sensation that I see as green? We both might agree that the color is red, but how can I know that you see the color red in the same way as I see it? It's a metaphysical situation. But wavelength range of 630-760 nm is an exact mathematical formulation and it can be confirmed scientifically. So, if you say that it's just a matter of viewpoint that whether 'square wave electric current' exists as pulses or as odd harmonics of a sine function then I don't get it because physically either current can exist as pulses or odd harmonics and not both. I hope you can see where I'm having trouble. Thank you.
Regards
PG