Stereo Multiplex Encoder (MPX) for FM Transmission

The invention relates to the implementation of a stereo multiplex encoder (MPX) for FM transmission with a digital signal processor.

Such methods are known, for example, from US 4,835,791 A, US 5,115,468 A and DE 42 10 069 A. In all these documents is to avoid the aliasing either a Hilbert transformer or a PSN (Phase Shift Network), thus also a computationally intensive Method used.

The goal of the invention is to provide a much less computationally intensive process without degrading quality.

According to the invention, the following innovations are used:<ul id="ul0001" list-style="none" compact="compact"><li>1. Using vestigial sideband modulation instead of the usual double sideband modulation in stereo transmission.</li><li>Second Matching the sampling frequency to the modulation frequency (fmod = fs / 2). The data is processed at the sampling frequency of 76 kHz. This allows the antialiasing filter of the DAC to be used which generates the vestigial modulated signal.</li><li>Third The resulting aliasing products automatically select the modulation and sampling frequency in this application to provide the necessary level boost for the lower sideband.</li><li>4th Improvement of the frequency-dependent channel separation between left and right by adjusting the phase of the pilot tone and level adjustment of the center signal. This compensates for the ripple and phase nonlinearities in the antialiasing filter of the DAC.</li></ul>

The invention will be explained in more detail below with reference to the drawing. It shows the<dl id="dl0001" compact="compact"><dt>Fig. 1</dt><dd>the function of the output frequency as a function of the input frequency in the amplitude modulation, the</dd><dt>Fig. 2</dt><dd>the amplification of the amplitude of the lower sideband when sampling an amplitude-modulated signal with the sampling frequency fmod = fs / 2, the</dd><dt>Fig. 3</dt><dd>the resulting spectrum in the sampling of an amplitude modulated signal, the</dd><dt>Fig. 4</dt><dd>generating the modulator at a sampling rate fs = 2 * fmod, the</dd><dt>Fig. 5</dt><dd>generating the pilot tone with the frequency 19 kHz at a modulation frequency fmod = 38 kHz and a sampling rate fs = 76 kHz, the</dd><dt>Fig. 6</dt><dd>generating the multiplex signal from the left and right stereo signal and the</dd><dt>Fig. 7</dt><dd>a real anti-aliasing filter, you can see ripple in the passband of the anti-aliasing filter.</dd></dl>

Theoretical basics:

By selecting the sampling rate and modulation frequency (amplitude modulation), deliberate aliasing effects are generated, which ultimately yield the desired modulation signal.

Amplitude Modulation:

In the amplitude modulation of an analog signal with the frequency fe and the modulation frequency fmod (Figure 1) creates a spectrum with the frequencies<maths id="math0001" num=""><math display="block"><mrow><mtext>f1 = fmod-fe</mtext></mrow></math><img file="EP1292015A2_D0001.tif" /></maths><maths id="math0002" num=""><math display="block"><mrow><mtext>f2 = fmod + fe</mtext></mrow></math><img file="EP1292015A2_D0002.tif" /></maths>

scanning:

When sampling an analog signal with an Analog Digital Converter (ADC) without anti-aliasing filter, the following relationship between input and output signal frequency results:

Up to half the sampling frequency (input signal), the sequence at the output of the ADC accurately represents the sequence of the input signal. If the input frequency is further increased, the frequency of the output sequence decreases again. Aliasing occurs.

Linking modulation and sampling:

The amplitude modulated signal is sampled. If the sampling frequency is twice the modulation frequency, aliasing occurs for the upper sideband of the amplitude modulated signal, with the upper sideband reflected into the lower sideband. The phase difference is zero, so the resulting lower sideband will double the amplitude (Figure 2).

It saves the SSB (single sideband) modulation with the filter method necessary increase of the sideband.

Digital / analog conversion:

The spectrum of the number sequence that arises in the above-described method is periodic. The spectrum of the baseband (0 to 38kHz) is periodically convolved with the multiples of the sampling frequency (76 KHz).

Each Digital Analog Converter (DAC) has a low-pass filter on the output, which hides the unwanted frequencies and leaves only the baseband. The anti-aliasing filter of a DAC is designed to have exactly 6 dB of attenuation at half the sampling frequency. Interesting is the range around 38 kHz. Due to the periodicity of the spectrum, the single-sideband modulation has again become a double-sideband modulation. Therefore, at the analogue output one can measure residual sideband modulation. (Picture 3). The filter passes half of the original fraction with respect to the carrier frequency and has a filter characteristic which gives an odd symmetry in the amplitudes of the upper and lower sidebands. In the case of this odd filtering, the amounts of the two sidebands in the demodulation add up to the correct baseband signal for all modulation frequencies.

Modulator:

The modulator is a sine signal at 38kHz for standard MPX. Using the method described above, the sampling rate must be 76kHz. A 38 kHz sine, sampled at a frequency of 76 kHz, is a sequence of '+ 1' and '-1'. (Fig. 4).

Pilot tone:

The pilot tone has exactly half the frequency of the modulator, and is phase locked at 0 °. The phasing of the pilot tone is adjustable. From this context, the four samples of the pilot tone result (Figure 5). The pilot tone level is 10% of the max. Modulation level.<maths id="math0003" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">s</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext></mtext><mtext mathvariant="italic">= A</mtext><mtext>sin (45 ° + φ)</mtext></mrow></math><img file="EP1292015A2_D0003.tif" /></maths><maths id="math0004" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">s</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext> = </mtext><mtext mathvariant="italic">A</mtext><mtext>* Sin (135 ° + φ)</mtext></mrow></math><img file="EP1292015A2_D0004.tif" /></maths><maths id="math0005" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">s</mtext></mrow><mrow><mtext>3</mtext></mrow></msub><mtext> = A · sin (225 ° + φ)</mtext></mrow></math><img file="EP1292015A2_D0005.tif" /></maths><maths id="math0006" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">s</mtext></mrow><mrow><mtext>4</mtext></mrow></msub><mtext> =</mtext><mtext mathvariant="italic">A</mtext><mtext>· Sin (φ + 315 °)</mtext></mrow></math><img file="EP1292015A2_D0006.tif" /></maths><dl id="dl0002" compact="compact"><dt>S1..S4</dt><dd>the four different pilot sound samples</dd><dt>A</dt><dd>amplitude</dd><dt>φ</dt><dd>Phase offset</dd></dl>

Multiplex signal:

The input has two digital sequences of numbers (left, right) with a sample rate of 76 kHz. A matrix generates therefrom the middle and side signal (FIG. 6):<maths id="math0007" num=""><math display="block"><mrow><mtext>M = L + R</mtext></mrow></math><img file="EP1292015A2_D0007.tif" /></maths><maths id="math0008" num=""><math display="block"><mrow><mtext>S = LR</mtext></mrow></math><img file="EP1292015A2_D0008.tif" /></maths>

The modulator is, as described above 'a number sequence + 1, -1, + 1 .... For the side signal is obtained after the modulation therefore the sequence<maths id="math0009" num=""><math display="block"><mrow><mtext>+ S = LR</mtext></mrow></math><img file="EP1292015A2_D0009.tif" /></maths><maths id="math0010" num=""><math display="block"><mrow><mtext>-S = -L + R</mtext></mrow></math><img file="EP1292015A2_D0010.tif" /></maths><maths id="math0011" num=""><math display="block"><mrow><mtext>+ S = LR</mtext></mrow></math><img file="EP1292015A2_D0011.tif" /></maths>       Etc...

The sideband is located after the modulation in the frequency range of 22 to 38 kHz. The sequence of the modulated sideband signal is added to the center signal.<maths id="math0012" num=""><math display="block"><mrow><mtext mathvariant="italic">M + S = M +</mtext><mtext>(LR) = (L + R)</mtext><mtext mathvariant="italic">+</mtext><mtext>(</mtext><mtext mathvariant="italic">LR</mtext><mtext>)</mtext><mtext mathvariant="italic">=</mtext><mtext>2</mtext><mtext mathvariant="italic">L</mtext></mrow></math><img file="EP1292015A2_D0012.tif" /></maths><maths id="math0013" num=""><math display="block"><mrow><mtext mathvariant="italic">MS = M</mtext><mtext>(</mtext><mtext mathvariant="italic">LR</mtext><mtext>)</mtext><mtext mathvariant="italic">=</mtext><mtext>(</mtext><mtext mathvariant="italic">L + R</mtext><mtext>)</mtext><mtext mathvariant="italic">-</mtext><mtext>(</mtext><mtext mathvariant="italic">LR</mtext><mtext>)</mtext><mtext mathvariant="italic">= 2R</mtext></mrow></math><img file="EP1292015A2_D0013.tif" /></maths><maths id="math0014" num=""><math display="block"><mrow><mtext mathvariant="italic">M + S = M +</mtext><mtext>(</mtext><mtext mathvariant="italic">LR</mtext><mtext>)</mtext><mtext mathvariant="italic">= (L + R</mtext><mtext>) + (</mtext><mtext mathvariant="italic">LR</mtext><mtext>)</mtext><mtext mathvariant="italic">= 2L</mtext></mrow></math><img file="EP1292015A2_D0014.tif" /></maths>       <i>Etc...</i>

It can be seen from this that, instead of the matrix followed by a modulator, it is also possible to use a switch which is switched back and forth between 2L and 2R. To equalize the filter ripple (Figure 7) of the DAC, the mid-level signal must be slightly lowered in level. If one waives this comparison (switch method), a simpler algorithm is obtained at the expense of a poorer channel separation.

The modulation in the DSP is calculated by alternately adding and subtracting the side signal from the center signal. In order to obtain the complete multiplex signal, the pilot tone must be added. For this there are four periodically repeating coefficients stored in a table.

The sequence of numbers of the multiplex signal results in summary to<maths id="math0015" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">MPX</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">= M</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">+ S</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">+ Pilot</mtext></mrow><mrow><mtext>1</mtext></mrow></msub></mrow></math><img file="EP1292015A2_D0015.tif" /></maths><maths id="math0016" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">MPX</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">= M</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">- p</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">+ Pilot</mtext></mrow><mrow><mtext>2</mtext></mrow></msub></mrow></math><img file="EP1292015A2_D0016.tif" /></maths><maths id="math0017" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">MPX</mtext></mrow><mrow><mtext>3</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">= M</mtext></mrow><mrow><mtext>3</mtext></mrow></msub><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">S</mtext></mrow><mrow><mtext>3</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">+ Pilot</mtext></mrow><mrow><mtext>3</mtext></mrow></msub></mrow></math><img file="EP1292015A2_D0017.tif" /></maths><maths id="math0018" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">MPX</mtext></mrow><mrow><mtext>4</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">= M</mtext></mrow><mrow><mtext>4</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">- p</mtext></mrow><mrow><mtext>4</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">+ Pilot</mtext></mrow><mrow><mtext>4</mtext></mrow></msub></mrow></math><img file="EP1292015A2_D0018.tif" /></maths><maths id="math0019" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">MPX</mtext></mrow><mrow><mtext>5</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">= M</mtext></mrow><mrow><mtext>5</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">+ S</mtext></mrow><mrow><mtext>5</mtext></mrow></msub><mtext></mtext><msub><mrow><mtext mathvariant="italic">+ Pilot</mtext></mrow><mrow><mtext>1</mtext></mrow></msub></mrow></math><img file="EP1292015A2_D0019.tif" /></maths><dl id="dl0003" compact="compact"><dt>MPX₁...</dt><dd>Number sequence of the multiplex signal</dd><dt>M₁...</dt><dd>Number sequence of the center signal</dd><dt>S₁...</dt><dd>Number sequence of the side signal</dd><dt>pilot₁...Pilot₄</dt><dd>Number sequence of the four pilot tone coefficients (periodic)</dd></dl>

Modulator matching to a DAC:

All previous considerations are based on an ideal antialiasing low-pass filter in the DAC. However, real low passes have a ripple in the passband and a non-constant group delay.

The ripple effect is as follows: To recover the L, R signal from the M, S signal, the inverse matrix must be formed.<maths id="math0020" num=""><math display="block"><mrow><mtext>2</mtext><mtext mathvariant="italic">L</mtext><mtext>=</mtext><mtext mathvariant="italic">M</mtext><mtext>+</mtext><mtext mathvariant="italic">S</mtext><mtext>= (</mtext><mtext mathvariant="italic">L + R</mtext><mtext>) + (</mtext><mtext mathvariant="italic">LR</mtext><mtext>)</mtext></mrow></math><img file="EP1292015A2_D0020.tif" /></maths><maths id="math0021" num=""><math display="block"><mrow><mtext>2</mtext><mtext mathvariant="italic">R</mtext><mtext>=</mtext><mtext mathvariant="italic">M</mtext><mtext>-</mtext><mtext mathvariant="italic">S</mtext><mtext>= (</mtext><mtext mathvariant="italic">L + R</mtext><mtext>) - (</mtext><mtext mathvariant="italic">LR</mtext><mtext>)</mtext></mrow></math><img file="EP1292015A2_D0021.tif" /></maths>

The side signal is in a different frequency range than the center signal. Due to deviations of the side signal level of 0 dB due to ripples of the anti-aliasing filter, the inverse matrix no longer works exactly and one obtains a channel crosstalk. Similar conditions apply to the constancy of the group delay (linearity of the phase). The effects of the anti-aliasing low-pass filter of the DAC are thus expressed in a frequency-dependent channel separation. To compensate for these effects, the phase of the pilot tone and the level of the center signal can be adjusted.