I've watched many of your videos. I'm confused about the "time constants" of systems. My book has a problem that asks to find time constants, but the phrase is never mentioned in the chapter.
@fingerboy18 The time constant is the amount of time it takes for an exponentially decaying signal to become smaller by a factor of e (to reach 0.3679 times its original value). In the signal x(t) = exp(-t/C), C is the time constant. The response of an LTI system is characterized by the poles of its transfer function; the time constant of a pole is the inverse of the real part of the pole. So the time constant of a system is the largest time constant of all of its poles.
@DarrylMorrell Thank you Darryl. I've noticed that my textbook isn't very good at explaining the real world properties of systems, which is necessary for me to understand the topic. I appreciate the time and effort you've put in to help us.
I still donot understand how the output was written in 6:21. How did the x[tau] remain as a constant infront of the impulse function?Shouldn't the system somehow change x[tau] too? Some help please?
@apparentlife22 The Fundamental idea is that x(t) is expressed as an integral (which is a limit of sums); Each term in the sum is a value x(tau) times a delta function which is shifted by tau. Because the system is linear, it operates on each delta function to produce the corresponding impulse response; the x(tau), since it is not a function of t, is a constant as it passes through the system.
@DarrylMorrell well i think i understand it now. This system is Linear. and we know for a linear system, constant *input ===[Linear system]==> constant *output. The 'constant' itself doesn't change due to the linearity property of the system, so , the x(tau) doesn't change.
Wow as an EE I am impressed... it's not easy to teach this stuff! My Fourier Analysis professor was joke compared to you... kudos!
supaamazinazn 4 weeks ago
I've watched many of your videos. I'm confused about the "time constants" of systems. My book has a problem that asks to find time constants, but the phrase is never mentioned in the chapter.
fingerboy18 1 month ago
@fingerboy18 The time constant is the amount of time it takes for an exponentially decaying signal to become smaller by a factor of e (to reach 0.3679 times its original value). In the signal x(t) = exp(-t/C), C is the time constant. The response of an LTI system is characterized by the poles of its transfer function; the time constant of a pole is the inverse of the real part of the pole. So the time constant of a system is the largest time constant of all of its poles.
DarrylMorrell 1 month ago
@DarrylMorrell Thank you Darryl. I've noticed that my textbook isn't very good at explaining the real world properties of systems, which is necessary for me to understand the topic. I appreciate the time and effort you've put in to help us.
fingerboy18 1 month ago
Thank you from Perth. Cheerz
DionysusAlmighty 2 months ago in playlist Signals and Systems
Thank you from Sweden, Stockholm
vahidshirvani 3 months ago
Thanks Mr.DarrylMorrell for your nice videos about signals and systems.
ENGINEERED2012 1 year ago
'whoops, and i did this wrong'
.
.
'argh'
mauroprovatos 1 year ago
I still donot understand how the output was written in 6:21. How did the x[tau] remain as a constant infront of the impulse function?Shouldn't the system somehow change x[tau] too? Some help please?
apparentlife22 1 year ago
@apparentlife22 The Fundamental idea is that x(t) is expressed as an integral (which is a limit of sums); Each term in the sum is a value x(tau) times a delta function which is shifted by tau. Because the system is linear, it operates on each delta function to produce the corresponding impulse response; the x(tau), since it is not a function of t, is a constant as it passes through the system.
DarrylMorrell 1 year ago
@DarrylMorrell well i think i understand it now. This system is Linear. and we know for a linear system, constant *input ===[Linear system]==> constant *output. The 'constant' itself doesn't change due to the linearity property of the system, so , the x(tau) doesn't change.
apparentlife22 1 year ago
@apparentlife22 it can become easier to understand if you look into convolution of a discrete time signal.
mauroprovatos 1 year ago
Comment removed
apparentlife22 1 year ago
Comment removed
apparentlife22 1 year ago
Black magic, got it.
Link1088 1 year ago