Pre-emphasis and De-emphasis

Pre-emphasis and de-emphasis is a noise reduction technique used in FM broadcasting to improve the signal-to-noise ratio of the demodulated audio, particularly at higher audio frequencies. The technique exploits the fact that FM noise has a parabolic spectral density that increases with frequency, meaning high frequency audio components suffer more noise than low frequency components after demodulation.

Core Concept Explanation

In FM demodulation, the noise power spectral density at the output of the FM discriminator is not flat. It follows a parabolic shape, meaning noise power increases as the square of frequency. This happens because the FM discriminator is essentially a frequency-to-voltage converter, and random phase noise in the channel translates to increasing voltage noise as frequency increases. High frequency audio components like upper harmonics of musical instruments or speech consonants are therefore more vulnerable to noise than bass frequencies.

Pre-emphasis addresses this by amplifying the high frequency components of the audio signal at the transmitter before FM modulation. When the FM signal reaches the receiver and is demodulated, the audio spectrum is now non-flat, with high frequencies boosted. A de-emphasis filter at the receiver output performs the complementary attenuation, restoring the original flat audio spectrum. Since the de-emphasis filter attenuates high frequencies, it simultaneously attenuates the high frequency noise that was parabolic in shape, resulting in a significantly improved SNR across the audio band.

The net effect is that the audio signal passes through pre-emphasis followed by de-emphasis and emerges unchanged in spectral shape, while the high frequency noise that was introduced in the channel is attenuated by the de-emphasis filter. This is a reversible spectral shaping technique that trades nothing in signal quality but gains substantial noise reduction, particularly above 1 to 2 kHz where FM noise rises steeply.

Mathematical Expression

The pre-emphasis filter is a high pass network with transfer function H_pre(f) equals (1 plus j f divided by f1) divided by (1 plus j f divided by f2), where f1 and f2 are the lower and upper corner frequencies with f2 much greater than f1. For most practical implementations, this is approximated as a simple RC high pass filter with time constant tau equals 1 divided by (2 pi f1). The de-emphasis filter is a simple RC low pass filter with the same time constant tau, having transfer function H_de(f) equals 1 divided by (1 plus j 2 pi f tau).

The product of pre-emphasis and de-emphasis transfer functions H_pre(f) times H_de(f) ideally equals 1 across the audio band, ensuring the original audio signal is faithfully reproduced. The overall SNR improvement achieved by this technique is given by the de-emphasis noise reduction factor, which can be evaluated by integrating the ratio of de-emphasized noise to original FM noise. For a standard tau equal to 75 microseconds, the SNR improvement is approximately 13 dB for typical speech and music signals.

Practical Understanding

Two standard time constants are used internationally. The value of 75 microseconds is used in the United States and Japan for FM broadcasting. The value of 50 microseconds is used in Europe and most other countries. These correspond to corner frequencies of approximately 2120 Hz for 75 microseconds and 3180 Hz for 50 microseconds. Above these corner frequencies, the pre-emphasis filter boosts signal level at a rate of approximately 6 dB per octave until a second corner frequency in the pre-emphasis filter limits the boost, preventing excessive frequency deviation for high amplitude high frequency tones.

Without de-emphasis, a receiver would produce audio with unnaturally bright and harsh high frequencies because the pre-emphasis boost applied at the transmitter would not be compensated. It is therefore essential that all FM broadcast receivers include the correct de-emphasis network. The time constant of the RC circuit determines the balance between noise reduction and compatibility. Mismatched time constants between transmitter pre-emphasis and receiver de-emphasis result in non-flat frequency response in the demodulated audio.

Numerical Example

An FM receiver uses a de-emphasis network with a time constant of 75 microseconds as per the American standard. Calculate the corner frequency of this de-emphasis filter and the attenuation at 15 kHz compared to its value at 1 kHz.

Given:
tau = 75 µs (US standard de-emphasis time constant)
Frequency of interest: f1 = 1 kHz, f2 = 15 kHz

Why this formula applies:
De-emphasis is a 1st-order RC low pass filter.
Transfer function: H(f) = 1 / (1 + j2πfτ)
Magnitude: |H(f)| = 1 / sqrt(1 + (2πfτ)²)

Formula:
Corner frequency fc = 1 / (2π × tau)

Substitution:
fc = 1 / (2π × 75 × 10⁻⁶)

Calculation:
fc = 1 / (471.2 × 10⁻⁶) ≈ 2122 Hz

|H(1 kHz)| = 1 / sqrt(1 + (2π × 1000 × 75×10⁻⁶)²)
           = 1 / sqrt(1 + (0.471)²) = 1 / sqrt(1.222) ≈ 0.905

|H(15 kHz)| = 1 / sqrt(1 + (2π × 15000 × 75×10⁻⁶)²)
            = 1 / sqrt(1 + (7.069)²) = 1 / sqrt(50.97) ≈ 0.140

Attenuation ratio at 15 kHz vs 1 kHz:
= 0.140 / 0.905 ≈ 0.155 → about -16.2 dB

Final Answer:
Corner frequency = 2122 Hz
De-emphasis attenuates 15 kHz by approximately 16.2 dB relative to 1 kHz,
reducing high frequency noise significantly.

Exam Tip: Always remember the two standard time constants: 75 µs for USA/Japan and 50 µs for Europe. Corner frequency = 1/(2π × tau). GATE may give tau and ask to find fc or ask which standard has higher SNR improvement — 75 µs provides more noise reduction at high frequencies than 50 µs.

Quick Revision

• Pre-emphasis boosts high frequency audio at the transmitter before FM modulation to overcome the parabolic noise characteristic of FM demodulators.
• De-emphasis is a complementary low pass filter at the receiver that restores flat audio and simultaneously attenuates high frequency noise.
• Key formula: Corner frequency fc = 1 / (2π × tau). For tau = 75 µs, fc ≈ 2122 Hz. For tau = 50 µs, fc ≈ 3183 Hz.
• US and Japan standard: tau = 75 µs. European standard: tau = 50 µs.
• SNR improvement is approximately 13 dB for speech and music with standard time constants.
• Exam trap: Pre-emphasis and de-emphasis do not affect the demodulated audio spectrum (they cancel). Only noise is reduced by de-emphasis.
• Without pre-emphasis at transmitter, de-emphasis alone would cause audio loss at high frequencies without any noise benefit.