Need for pre-emphasis and de-emphasis in FM

Pre-emphasis and de-emphasis are needed in FM to improve the signal-to-noise ratio at high audio frequencies.

1. Noise in FM rises with frequency. The FM discriminator output noise PSD is $S_{N}(f) \propto f^2$ (triangular noise voltage, parabolic noise power). So high-frequency audio components get much more noise.
2. Audio signals are weak at high frequencies. Most speech and music energy is below 1–2 kHz.
3. Together, these make the SNR of the high audio frequencies very poor.

Solution

• Pre-emphasis at the transmitter: a high-pass RC network boosts high audio frequencies before modulation, $H_{pe}(f) = 1 + jf/f_1$.
• De-emphasis at the receiver: a low-pass RC network after demodulation, $H_{de}(f) = 1/(1 + jf/f_1)$, restores the original response and attenuates the high-frequency noise at the same time.
• Since $H_{pe}H_{de} = 1$, the signal is unchanged but the output noise falls, giving about 10–13 dB SNR improvement. Standard time constant: 75 µs (USA) or 50 µs (Europe), $f_1 = 1/(2\pi RC) \approx 2.1$ kHz for 75 µs.

 Gain   pre-emph  _/
  |           __/
  |----------/--------- 0 dB
  |          \__
  |             \_ de-emph
  +---------+---------> f
           f1