Short note: Pre-emphasis and de-emphasis

Pre-emphasis is the boosting of the high-frequency part of the message at the FM transmitter before modulation; de-emphasis is the matching attenuation of those frequencies at the receiver after demodulation.

Why they are needed

• In FM, the output noise power spectral density rises with the square of frequency (parabolic noise spectrum): $S_N(f) \propto f^2$.
• Audio signals have most of their energy at low frequencies; the high-frequency parts are weak.
• So the high audio frequencies have the worst SNR. Pre-emphasis raises them above the noise before transmission; de-emphasis restores the original balance and, at the same time, cuts the high-frequency noise.

Circuits

 Pre-emphasis (high-pass)   De-emphasis (low-pass)
   +--[ R ]--+                o--[ R ]--+----o
 o-+         +--+--o                    |
   +--||-----+  |                      === C
       C        > r                     |
 o--------------+--o          o---------+----o

• Pre-emphasis: $H_{pe}(f) = 1 + j\dfrac{f}{f_1}$, where $f_1 = \dfrac{1}{2\pi RC}$.
• De-emphasis: $H_{de}(f) = \dfrac{1}{1 + jf/f_1}$, so $H_{pe}H_{de} = 1$ and the message is undistorted.
• Standard time constant $RC = 75\ \mu$s ($f_1 \approx 2.1$ kHz) in USA FM broadcasting; 50 µs in Europe and many other countries.

 Gain
  ^      pre-emphasis
  |          ___/
  |      ___/
  |-----/---------- 0 dB
  |      \___
  |          \___ de-emphasis
  +-----+------------> f
        f1=2.1 kHz

Benefits

• Improves output SNR of FM by about 10–13 dB for audio.
• No extra bandwidth needed (for normal audio content).
• Also used in phonograph recording, tape recording and TV sound.