FM Deemphasis

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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

Insert description of flowgraph here, then show a screenshot of the flowgraph and the output if there is an interesting GUI. Currently we have no standard method of uploading the actual flowgraph to the wiki or git repo, unfortunately. The plan is to have an example flowgraph showing how the block might be used, for every block, and the flowgraphs will live in the git repo.

Source Files

Python files
[1]
Block definition
[2]