Frequency Response Descriptions for LTI Systems

[@mahakhan9762]

this was really helpful for my signals midterm, thank you

[@vleeseter111]

can someone help me with this exercise?
The simplest LTI processor which approximates a digital differentiator has the difference equation:
y[n]=x[n]-x[n-1]
A less-widely used alternative is to estimate the central difference, using the equation:
y[n] : 0.5[x[n] - x[[n-2]]
Sketch the magnitude responses of the two aPProximations on the same diagram, over tñe range 0 < omgea < pi. Contrast their performance with that of an ideãl differentiator. By how many dB is each resPonse lower than that of the ideal differentiator at the frequency omega = 0.2pi?

[@faizakhazma5122]

please question :
what is it Frequency Response x(t) = e^−|t| ???

[@sepm7356]

hey sir, at around 5:30-5:50. how did you get the ω/2 on the frequency response? is it because there's only 2 terms? 3 terms would be ω/3? etc..? thanks

[@nelsonfu8390]

factor out exp(-j*omega/2) from both terms; this gives:
RHS = exp(-j*omega/2) {1/2*exp(j*omega/2) + 1/2*exp(-j*omega/2)}
we can rearrange Euler's formula to find that:
cos(theta) = 1/2 * (exp(j*theta)+exp(-j*theta))
and so the right hand side is:
RHS = exp(-j*omega/2) {cos(omega/2)}
as shown in the video :)

[@MrBezzo0]

Really useful and clearly explained, thanks!

[@wadeburns1233]

You make some great videos. Thank you.

[@nimashdilanka4906]

Thank you sir.It was really helpfull.

[@ΓάκηςΓεώργιος]

Can i use fourier series to find the H?

[@somasekharsuryadevara3484]

perfect and precise.
Thank you

[@ajlu5955]

Thanks man, it is really useful!!

[@khukhaa5711]

thank you

[@dogamertaydogan2803]

Thank you very much...

[@muniraalali2784]

Thank You !

[@bhuvi441]

Really useful thank you sir ! :)