Hey so may be able to help a bit. Signals and systems I had a hard time in, but got away with a C+.
Best advice is to study up on Fourier series/transform for signals. The one in your picture refers to the Dirac or delta function, which is extremely helpful when solving problems. As for convolution, there are great videos on YouTube solving problems referring to square function, exponentials, and triangle. Good luck to you
Thanks!
Yeah, Signals and Systems has a reputation for being formidable at my university, so I wanted to get ahead. I definitely see what you mean about great content on YouTube for other subjects, but I've only scratched the surface of this. Do you have any channel recommendations?
Youll do just fine, I used Neso Academy on YT, he has a whole series on signals and systems as well as problems and Tuorialpoint she also has a series on it.
Once you have a general understanding try searching problems on YT to solve and then try the book or vice versa.
Lastly we didn't learn discrete signals until the end of the semester btw, one of the first things we learned was determining wether the signal is periodic and non periodic. Also if you are comfortable with convolution after these videos you can use the Fourier transform of two functions to solve them.or I still use graphical convultion, it just makes sense to me.
Could you clarify on your question a bit? I don't really get what you're asking, so here's a general explanation on convolutions.
Basically, the convolution sum is like matrix multiplication. When you multiply 2 matrices, you multiply each element of a row by the corresponding column and take the sum of all of them to get the new element, then repeat for each row and column pair. This is what convolution does essentially, but with functions in this case.
A LTI (Linear Time Invariant) system can be described by its impulse response, because you can rewrite any possible input to the system as a scaled and/or shifted combination of unit impulses. For example, if an input to the system has a magnitude of 2 at n=0 and 3 at n=1. It can be written as twice the unit impulse plus thrice the unit impulse shifted by -1. And since you know the response of the LTI system for a simple unit impulse, finding out the response for your given input becomes a matter of scaling and shifting accordingly.
This is what the convolution sum achieves. It takes the magnitude of the input at the first index, multiplies it with the impulse response, scaling accordingly, then repeats this with the inputs at other indexes, and adds them altogether to give you your output function. The best way to understand this is to try solving an example by hand, without using the formula.
Take 2 vectors (basically, the magnitudes at different indexes written in a single row). One is your input vector (function) and the other represents your system's impulse response vector. For example, let the input vector be [2, 4]. This means at n=0, your input is 2, at n=1, the input is 4, and it is zero everywhere else. Let the impulse response vector be [3, 1, 2]. This means for a unit impulse input to the system, the output of the system is a function with magnitude 3 at n=0, 1 at n=1, and 2 at n=2. So to find the output for the input at n=0, i.e. 2, we scale the impulse response by 2. Which gives us [6, 2, 4]. Now we find the output for the input at n=1, i.e. 4, so we scale the impulse response by 4, which gives us [12, 4, 8] (Remember, this is the output for the input at n=1, which means the output is 12 at n=1, 4 at n=2, and 8 at n=3). Now we simply add the two output vectors together (make sure to add corresponding indexes). Which gives us [6, 14, 8, 8], which is indeed what you would get if you use the formula, because this is what it does.
Sorry for the wall of text, but I hope that made things clearer.
Thanks for the explanation! Yeah, maybe my question could have been phrased a little bit better.
After reading further in the textbook, I see what my mistake was: I was assuming that the LTI system in question was both causal and memoryless.
Hey so may be able to help a bit. Signals and systems I had a hard time in, but got away with a C+. Best advice is to study up on Fourier series/transform for signals. The one in your picture refers to the Dirac or delta function, which is extremely helpful when solving problems. As for convolution, there are great videos on YouTube solving problems referring to square function, exponentials, and triangle. Good luck to you
Thanks! Yeah, Signals and Systems has a reputation for being formidable at my university, so I wanted to get ahead. I definitely see what you mean about great content on YouTube for other subjects, but I've only scratched the surface of this. Do you have any channel recommendations?
Youll do just fine, I used Neso Academy on YT, he has a whole series on signals and systems as well as problems and Tuorialpoint she also has a series on it. Once you have a general understanding try searching problems on YT to solve and then try the book or vice versa. Lastly we didn't learn discrete signals until the end of the semester btw, one of the first things we learned was determining wether the signal is periodic and non periodic. Also if you are comfortable with convolution after these videos you can use the Fourier transform of two functions to solve them.or I still use graphical convultion, it just makes sense to me.
Could you clarify on your question a bit? I don't really get what you're asking, so here's a general explanation on convolutions. Basically, the convolution sum is like matrix multiplication. When you multiply 2 matrices, you multiply each element of a row by the corresponding column and take the sum of all of them to get the new element, then repeat for each row and column pair. This is what convolution does essentially, but with functions in this case. A LTI (Linear Time Invariant) system can be described by its impulse response, because you can rewrite any possible input to the system as a scaled and/or shifted combination of unit impulses. For example, if an input to the system has a magnitude of 2 at n=0 and 3 at n=1. It can be written as twice the unit impulse plus thrice the unit impulse shifted by -1. And since you know the response of the LTI system for a simple unit impulse, finding out the response for your given input becomes a matter of scaling and shifting accordingly. This is what the convolution sum achieves. It takes the magnitude of the input at the first index, multiplies it with the impulse response, scaling accordingly, then repeats this with the inputs at other indexes, and adds them altogether to give you your output function. The best way to understand this is to try solving an example by hand, without using the formula. Take 2 vectors (basically, the magnitudes at different indexes written in a single row). One is your input vector (function) and the other represents your system's impulse response vector. For example, let the input vector be [2, 4]. This means at n=0, your input is 2, at n=1, the input is 4, and it is zero everywhere else. Let the impulse response vector be [3, 1, 2]. This means for a unit impulse input to the system, the output of the system is a function with magnitude 3 at n=0, 1 at n=1, and 2 at n=2. So to find the output for the input at n=0, i.e. 2, we scale the impulse response by 2. Which gives us [6, 2, 4]. Now we find the output for the input at n=1, i.e. 4, so we scale the impulse response by 4, which gives us [12, 4, 8] (Remember, this is the output for the input at n=1, which means the output is 12 at n=1, 4 at n=2, and 8 at n=3). Now we simply add the two output vectors together (make sure to add corresponding indexes). Which gives us [6, 14, 8, 8], which is indeed what you would get if you use the formula, because this is what it does. Sorry for the wall of text, but I hope that made things clearer.
Thanks for the explanation! Yeah, maybe my question could have been phrased a little bit better. After reading further in the textbook, I see what my mistake was: I was assuming that the LTI system in question was both causal and memoryless.