Hello everyone,
I have issue understanding two conclusion made byDr. Baker in his mixed signal books as shown in page 35 and 36.
1- how can using the convulution yield from euation 2.8 to 2.9 . I applied the convultion to it and I get double summation and not as in equation 2.9!
2-the equation 2.15 is clear bu the one before it is bit strange for me, how can i derive it like him too?
mixed signal design


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This may sound like a nasty question, but really, what is your goal in doing the convolvement operation?? OUr class struggled with that back in college and while we could make it produce results, there did not seem to be much use for those results. And now, after a long electrical/electronic engineering career, as well as non-electronic engineering, I have never had any reason to even consider the convolution process or integral.
Also, "spectral response in a sample and hold data system is much simpler, because the relationship between sample rate and frequency response is so very obvious.

 

Along with what MB2 said, there are many formulas and equations used in academic teaching, which are of interest to theorists, and (perhaps) to help understand the operation of a particular electronic function or circuit, that are seldom needed or used in the actual design or application of the circuit.
This is one of those series of equations.
The theoretical study and analysis of an ideal circuit, and the engineering design(synthesis) of the real circuit are too related but separate areas of expertise.
Unfortunately the synthesis and study of the limitations of a real circuit is generally given short shrift in college, and must often be learned-while-you-earn (at least it was for me).

 

While building the foundation for understanding in engineering is important, the real world often follows those principles but the math is able to be simplified by leaving out the parts that do not apply in a particular case. Often that is the case when fighting noise in electrical circuits. Sosome parts of engineering come across as "black art"to those who lack experience.

 

This may sound like a nasty question, but really, what is your goal in doing the convolvement operation?? OUr class struggled with that back in college and while we could make it produce results, there did not seem to be much use for those results. And now, after a long electrical/electronic engineering career, as well as non-electronic engineering, I have never had any reason to even consider the convolution process or integral.
Also, "spectral response in a sample and hold data system is much simpler, because the relationship between sample rate and frequency response is so very obvious.

I am reading this chapter and I like to understand all parts of it.
I know it is just a sync function as frequency response. But I hate when I do not understand something, that is why I wanted to derive it too, but the author did not mention anything.

 

actually, I found the asnwer:
h(t)=u(t)-u(t-T)
delta(t)*h(t)=h(t)*delta(t)
we know that by calculation that :
h(t)*delta(t-nTs)=h(t-nTs)
That is it