FM Deemphasis

An analog deemphasis filter:

R   o--/\/\/\/---+o |                 = C                   | ---

Has this transfer function:

1            1                        ---               RC          tau H(s) = -- = -- 1            1            s +       s + --- RC          tau

And has its -3 dB response, due to the pole, at

|H(j w_c)|^2 = 1/2 =>  s = j w_c = j (1/(RC))

Historically, this corner frequency of analog audio deemphasis filters been specified by the RC time constant used, called tau. So w_c = 1/tau.

FWIW, for standard tau values, some standard analog components would be: tau = 75 us = (50K)(1.5 nF) = (50 ohms)(1.5 uF) tau = 50 us = (50K)(1.0 nF) = (50 ohms)(1.0 uF)

In specifying tau for this digital deemphasis filter, tau specifies the *digital* corner frequency, w_c, desired.

The digital deemphasis filter design below, uses the "bilinear transformation" method of designing digital filters:

1. Convert digital specifications into the analog domain, by prewarping digital frequency specifications into analog frequencies.

w_a = (2/T)tan(wT/2)

2. Use an analog filter design technique to design the filter.

3. Use the bilinear transformation to convert the analog filter design to a digital filter design.

H(z) = H(s)| s = (2/T)(1-z^-1)/(1+z^-1)

w_ca        1          1 - (-1) z^-1 H(z) = * --- * --- 2 fs       -w_ca             -w_ca 1 - -        1 + -                      2 fs              2 fs                               1 - --- z^-1 -w_ca 1 - -                                       2 fs

We use this design technique, because it is an easy way to obtain a filter design with the -6 dB/octave roll-off required of the deemphasis filter.

Jackson, Leland B., _Digital_Filters_and_Signal_Processing_Second_Edition_, Kluwer Academic Publishers, 1989, pp 201-212

Orfanidis, Sophocles J., _Introduction_to_Signal_Processing_, Prentice Hall, 1996, pp 573-583

Parameters

 * Sample Rate
 * Sampling frequency in Hz


 * Tau
 * Time constant in seconds (75us in US, 50us in EUR)

Example Flowgraph
This flowgraph implements a Broadcast FM stereo receiver using basic blocks.



Source Files

 * Python files
 * 


 * Block definition
 *