Like AM that can be represented as:

$$\bigl(A_c+Km(t)\bigr)cos\bigl(2\pi f_ct\bigr)$$

Here, simply the amplitude is being varied by a sinusoid.

Therefore similarly, why can't FM be written as:


Obviously the constants are such that the frequency doesn't go negative.

Isn't the above equation intuitively correct? The frequency is being varied by a sinusoid again.

  • \$\begingroup\$ That looks like phase modulation. \$\endgroup\$ – Chu May 6 '17 at 19:55
  • \$\begingroup\$ are you kidding me? This doesn't looks like anything \$\endgroup\$ – Chirag Arora May 6 '17 at 19:57
  • \$\begingroup\$ Why do you think that this is not a correct expression for FM? \$\endgroup\$ – Dave Tweed May 6 '17 at 21:06
  • 1
    \$\begingroup\$ @Chu: Phase modulation would be \$A_c \cos(2\pi f_c t + Km(t))\$. \$\endgroup\$ – Dave Tweed May 6 '17 at 21:08
  • \$\begingroup\$ Because the derived expression for FM in every source looks like the expression of phase modulation you have mentioned. Both FM and PM have been treated equally. Also, the expression I have mentioned doesn't plot well on the graph. Therefore it's wrong but I wonder why. \$\endgroup\$ – Chirag Arora May 6 '17 at 21:19

An FM-modulated signal looks like $$A_c \cos\left(\varphi\left(t\right)\right)$$

At time \$t\$, its frequency is $${1 \over 2 \pi}{\mathrm{d}\varphi \over \mathrm{d}t}$$

And you want it to be $$f_c + K m(t)$$

So you must have $$\varphi(t) = \varphi_0 + \int_0^t f_c + K m(u) \mathrm{d}u = \varphi_0 + f_c t + K \int_0^t m(u) \mathrm{d}u$$

Hence, the expression for an FM-modulated signal is $$A_c \cos\left(\varphi_0 + f_c t + K \int_0^t m(u) \mathrm{d}u\right)$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.