Spectral Components for Angle Modulation | Frequency Modulation | Phase Modulation

[@EngineeringFunda]

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[@shaileshgupta6432]

sir can you make a video on Hilbert's Transforms..........as it is an important topic in Analog Communication Techniques.

[@alloc7260]

Sir you written title of phase modulation but derived for Freq. Modulation

[@yurigansmith]

Gee, this man can write extremely fast! I would like to know whether he has a special technique...

[@EngineeringFunda]

I dont know

[@Music-tp8gg]

Fast forwarding editing brother.

[@CC.cinematics]

Can you please tell what is bessels function and if you have discussed it in any other video

[@EngineeringFunda]

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[@sahithkumarchekuri9092]

Sir here we are not doing integration for the message signal for phase modulation. So we will get only kp*amplitude of message signal only.
I.e delta f=kp* amplitude of message signal.
How did you got fm downwards.
If it is in frequency modulation we will do integration for message signal so we get fm downwards.
PLEASE EXPLAIN SIR

[@bijivemulasairakeshreddy4739]

yes sir same doubt ,how are u getting fm in denominator

[@hmvarshney5222]

chutiya teacher hai! Sine vaali equation kahin use nahi ki, ab achanak se le aaya. Khud nahi pata ise pehle kya padhaya tha.

[@nehaagarwal925]

In the previous lecture no 51 he has derived the used equation
The formulae is for singletone modulating signal Ecos(wmt). So after integration we get sine term.

[@nehaagarwal925]

@@hmvarshney5222 rather being disrespectful to someone's hardwork listen carefully 🙄

[@yurigansmith]

This was well explained. Nevertheless, a sine/cosine as modulating signal is a standard textbook example. But what about arbitrary signals? It would be interesting to see how the resulting spectrum can be derived, when the original spectrum (of the modulating signal) is known.

[@EngineeringFunda]

Spectral shape will remain same, it is depending on carrier signal frequency.

[@yurigansmith]

@@EngineeringFunda I'm not sure what you mean by "spectral shape will remain same". If the original modulating signal m(t) has the spectrum M(jw), and we have the modulated signal u(t)=cos(w_c*t + m(t)), with m(t) arbitrary maybe even non-periodic signal, then the resulting spectrum U(jw) is still located around w_c, but does not have the same shape like the original spectrum M(jw), which is only the case for AM. In my opinion in the general case of FM the resulting spectrum U(jw) is a (infinite) convolution power series of M(jw), hence even if M(jw) is band-limited, U(jw) is not. Neverthess, it still has the component M(jw) as part of the series (summation over k) for k=1. The components for larger k on the other hand contribute to the "smearing out" of U(jw).
(k-th convolution power of M(jw) = k-times convolution of M(jw) with itself)

[@robomachant6271]

can some one say in 2:40 equation where he write cos( wm t) but in previous video he write it as sin (wmt) if he write it in cos form then intigration of sin is - cos x so it must be - m cos (wmt)

[@AnuragSingh-no9gn]

Sir what is besel functions

[@ydeepika18]

Sir in exams we can write the same answer for the Fm

[@EngineeringFunda]

Yeah