Thank you for this episode. May I point out to other viewers that the multiplication shown in this episode is the real reason why electrical engineers use the imaginary number as the Y-axis to represent a wave of signal in the polar representation of signal. If you don't ever want to multiple 2 waves, ever, then the Y-axis can be just an ordinary y, and you still manipulate the wave in the polar representation perfectly fine. The sad thing is, no professor will tell this trade secret to outsiders. And, to become an insider, all institutions in the word make you study calculus and laplace transformation and maxwell equation and artificial intelligence taking away 20 years of your time as an initiation even though calculus is not needed in the multiplication in the first place, let alone the other subjects. Once you put 20 years into it, other departments will not accept you as a freshman because you are too broke to pay for another study's tuition/fees.
Hi sir, regarding the addition of the exponents. can you please explain to me in detailed how to multiply one exponent to the other? You said "product of exponent end up summing the powers of those exponents" so (e^2*pi *t) * (e^j*2 *pi*100*t) adds what? how does it happen? Thank you a lot!
e^j*2pi*t * e^j*2pi*100*t gives you e^j*2pi*101*t because you add those two together (for example, b^n * b^m = b^(n+m) e^-j*2pi*t * e^j*2pi*100*t, however, gives you e^j*2pi*99t, because you add 100 to -1, resulting in 99
I always get confused when it comes to phasors and complete waves and complex numbers.The following circumstance I cant quite get intuition about: power and euler. If I take V(t)=Vcos(iwt) and cos(iwt)=RE(e^iwt) and a resistive load. Then I(t)=V/Rcos(iwt). It is stated that P which is only real in this case is equal to V(t)•I(t)*, where I(t)* is complex conjugate of I(t). Now if I do that math I only get the amplitude of the power but lose the time dependence. If I use your approach and express sinusoids directly in euler form not featuring RE( ) I get the full picture with time dependence. I guess my question is: It is clear that RE(a)•RE(b) =/= RE(a•b) but what is generally true about RE(a•b*) if a and b are sinusoids? It puzzles me that this magically yields the real power if a and b correspond to voltage and current. I fail to see the underlying symmetries. Some answer or literature would be appreciated.
how to multiply two square waves of different frequencies? say one square wave is of 50Hz and another of 10 kHz and both are having same magnitude, then?
Thank you for this episode. May I point out to other viewers that the multiplication shown in this episode is the real reason why electrical engineers use the imaginary number as the Y-axis to represent a wave of signal in the polar representation of signal. If you don't ever want to multiple 2 waves, ever, then the Y-axis can be just an ordinary y, and you still manipulate the wave in the polar representation perfectly fine. The sad thing is, no professor will tell this trade secret to outsiders. And, to become an insider, all institutions in the word make you study calculus and laplace transformation and maxwell equation and artificial intelligence taking away 20 years of your time as an initiation even though calculus is not needed in the multiplication in the first place, let alone the other subjects. Once you put 20 years into it, other departments will not accept you as a freshman because you are too broke to pay for another study's tuition/fees.
Thanks for this episode Barry. I think this is the information I need to prove the Collatz Conjecture. Cheers!
thank you so muchhhh, hopefully your videos will be enough to cover my DSP and Communication class this semester :)
How many no of spectrum, if two sine fn are multiplied .?
Hi sir, regarding the addition of the exponents. can you please explain to me in detailed how to multiply one exponent to the other? You said "product of exponent end up summing the powers of those exponents" so (e^2*pi *t) * (e^j*2 *pi*100*t) adds what? how does it happen? Thank you a lot!
e^j*2pi*t * e^j*2pi*100*t gives you e^j*2pi*101*t because you add those two together (for example, b^n * b^m = b^(n+m)
e^-j*2pi*t * e^j*2pi*100*t, however, gives you e^j*2pi*99t, because you add 100 to -1, resulting in 99
You are awesome!
Thank you for your help you did it all right ✅ 🙏
For the multiplication of sinusoids, would this apply to sin(2pi 100 t) and sin(2pit) as well?
Thanks a lot Barry!
I always get confused when it comes to phasors and complete waves and complex numbers.The following circumstance I cant quite get intuition about: power and euler. If I take V(t)=Vcos(iwt) and cos(iwt)=RE(e^iwt) and a resistive load. Then I(t)=V/Rcos(iwt). It is stated that P which is only real in this case is equal to V(t)•I(t)*, where I(t)* is complex conjugate of I(t). Now if I do that math I only get the amplitude of the power but lose the time dependence. If I use your approach and express sinusoids directly in euler form not featuring RE( ) I get the full picture with time dependence. I guess my question is: It is clear that RE(a)•RE(b) =/= RE(a•b) but what is generally true about RE(a•b*) if a and b are sinusoids? It puzzles me that this magically yields the real power if a and b correspond to voltage and current. I fail to see the underlying symmetries. Some answer or literature would be appreciated.
how to multiply two square waves of different frequencies? say one square wave is of 50Hz and another of 10 kHz and both are having same magnitude, then?
Best