DC component etc.
Hi
Yes, you are right that the answer is correct. I believe what led me to think that there is an issue with the answer is my not-very-good understanding of the DC component. So, I think I should work on it.
Please note that Q2 and Q3 are very much related to each other. I have separated them so that you can refer to the referenced examples easily. The question Q5 is a totally different one and an important one and I really need your help with it. Thank you.
I understand that I'm asking too many questions in this post. But I believe asking all these questions together might help you to better understand where I'm going wrong. You can take your time and address the queries when you have time.
Q1:
The concept of DC component is inherent to Fourier series and not to Fourier transform. Am I correct? Kindly let me know.
Q2:
When finding FS of a function, the FS looks at the function in symmetric terms along the x-axis. In other words, the FS tries to symmetrize the function along the x-axis. Then, the DC component tells us that what constant value should be added to symmetrized FS version so that the function gets raised to its actual position.
Let me elaborate on what I said above. I could have told you the value of DC components for these two
examples, Example 3.4 and Example 3.5, by just looking at the given figures. For instance, in Example 3.4, you can easily notice that a square wave has been lifted by a constant value of "1/2". In other words, you need to subtract "1/2" from the given version of the function to get symmetric version. Likewise, we can easily notice that the triangular wave for Example 3.5 is already symmetrical along x-axis therefore DC value is zero.
Do I have the concept right?
Q3:
Now I myself going to point out some loopholes in my own understanding of the DC component. Please look at this
example about raised cosine function which, according to the answer given, has DC component of "1/2". According to what I said above the DC component should have been "1" because "1" should be subtracted from the given function to get a symmetric version. Simply stated, the given function is a raised cosine function using a constant value of "1". Where am I going wrong with this example?
Likewise, in this
example about exponential function, the given DC component is "0.504". I don't see how we can find a "symmetrized version" in this case because I don't see any symmetry along x-axis in this case. This means that the DC component is not all about symmetry along x-axis.
Now it is clear that my understanding of DC component is flawed. Please guide me.
Q4:
Please have a look
here.
Q5:
Many a time, there are differences between a mathematical model of something and the real thing which that model represents. The mathematical model is only there to help us do the calculations easily. My question to you: 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 know your answer to the above question. But I suspect that you don't think that the current exists in form of odd harmonics and you are of the the opinion that Fourier representation is just a mathematical tool in this regard. But still in many topics, such as filters, we talk and practically it looks like as if Fourier representation is as much real as it could be. For instance, it is often said that this filter can reject low frequencies etc. I can give you more examples here to state my confusion but I'm sure you already understand where I'm having difficulty. Please help me. Thank you.
Regards
PG