Pre-emphasis in FM broadcasting; stereo encoder

Why pre-emphasis and de-emphasis are used

In FM, noise at the discriminator output is not flat: its power spectral density rises as $f^2$ (parabolic noise). Audio signals, on the other hand, have most energy at low frequencies and little at high frequencies. So the high audio frequencies have a very poor SNR.

• Pre-emphasis (at the transmitter, before the modulator): a high-pass RC network, $H_{pe}(f) = 1 + jf/f_1$, boosts high audio frequencies so that they stand well above the noise.
• De-emphasis (at the receiver, after the discriminator): a low-pass RC network, $H_{de}(f) = 1/(1 + jf/f_1)$, brings the boosted frequencies back to their original level. It attenuates the high-frequency noise by the same amount.
• Since $H_{pe}H_{de} = 1$, the message is undistorted, but the noise is reduced. The improvement is about 10–13 dB.
• Standard time constant: 75 µs ($f_1 = 2.12$ kHz) in the USA and 50 µs in Europe and most other countries.

 Pre-emph          De-emph
 o-+-[R]-+-o       o-[R]-+-o
   +-||--+ |             |
     C     > r          === C
 o---------+-o     o-----+-o

Stereo encoder

A stereo encoder forms one composite baseband signal from the left and right audio channels for FM stereo broadcasting.

 L --+-->(+)--L+R-->[LPF]----------->( Σ )-->
     |    ^                            ^ ^  to FM
 R --|----+                            | |  mod.
     +-->(-)--L-R-->[LPF]-->[Bal.mod]--+ |
          ^ (R)                 ^ 38k    |
                  [19k osc]->[x2]        |
                      |                  |
                      +--19 kHz pilot----+

1. Matrix network: adder and subtractor make $L+R$ (for mono compatibility) and $L-R$.
2. LPF (15 kHz) and pre-emphasis on both.
3. Balanced modulator: $L-R$ DSB-SC modulates a 38 kHz sub-carrier (sidebands 23–53 kHz).
4. 19 kHz pilot oscillator and doubler: gives the 38 kHz sub-carrier; the 19 kHz pilot is also added at low level so receivers can regenerate the 38 kHz carrier.
5. Adder: composite signal

$$m(t) = (L+R) + (L-R)\cos(2\pi\,38\text{k}\,t) + A_p\cos(2\pi\,19\text{k}\,t)$$

 |  L+R      pilot    L-R DSB-SC
 |______       |    ____    ____
 |      |      |   |    |  |    |
 +------+------+---+----+--+----+---> f (kHz)
 0     15     19  23   38      53

This 53 kHz composite signal frequency-modulates the main carrier.