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ENGINEERIN REPORT A NEW FILTERING PROCESS FOR OPTIMAL OVERSHOOT CONTROL HARRIS COMMUNICATIONS AND INFORMATION HANOUNG RadioFans.CN 收音机爱 好者资料库 HARRIS COMMUNICATIONS AND INFORMATION HANDLING RadioFans.CN 收音机爱 好者资料库 A NEW FILTERING PROCESS FOR OPTIMAL OVERSHOOT CONTROL By D A V I D L. HER S H BE R G E R Senior Engineer, FM Radio Transmitters ABSTRACT When both peak amplitude (In the time domain) and bandwidth constraints are placed upon a signal as in FM stereo broadcasting, there are conflicts among the requirements for limiting modula- tion peaks. attenuating components beyond 15 kHz. and maintaining a flat amplitude characteristic to 15 kHz. Previous attempts at overshoot control do not simultaneously satisfy all of the above re- quirements. Furthermore, some techniques currently In use can cause severe audib,e distortion under certa in progra m m ing cond I tions. Lowpass filters by deSign change the frequency distribution of a signal and by consequence change the phase relationships of the same signal Both changes are causes of overshoot. Elmlna- tion of harmonic terms deletes components that serve to reduce the peak amplitude of the signa. Phase distortion rearranges signal components as a function of ti me to form overmoci J latin9 peaks. Optimal overshoot control must perform all of the follOWing under all programming conditions. 1. Flat frequency response to 15kHz at all levels up to 100% modulation. 2. H i9 h attenu alion of freq u encies above 15k Hz. 3. Suppress overmodulation due to overshoot to an Insignificant level. 4. Insignificant T H D a nd I M distortion a t a ny level up to 100% modu la tion. 5. No degradation of audio quality. A new technique that eliminates overmodulatlon due to overshoot is presented and explained. L INTRODUCTION BAC KG R 0 UNO: FM stereo radio broadcasting is rapidly becoming a highly competitive medium. Th is cha Ilge man ifests itself in ma ny ways. includ ing the eHo rt to have a techn Ica lIy su perior sou nd. This objective usually involves a tradeoff between quality and quantity. or fidelity vs. loudness. Most audio processing innovations to dale sacrifice some amount of fidelity for some degree of loudness Increase. The Harris Dynamic TranSient Response (OTR) filter. an integral part of the Hams MS-l 5 exciter. allows a loudness increase of 2- 6 dB (dependent on limiter type) with absolutely no degrada- tion of fidelity, P R INC I P LES 0 F ST ERE 0 F M: FM stereophon I c broadcasti ng is a frequency domain m u I t I plexed (FO M) system. A left-plus-right (L + R) signal is transmitted in the band 50 Hz-15kHz. This is the monaural baseband signal. A double sideband suppressed carrier (OS B) signal modulated with left- minus-right information is transmitted at 38 kHz. To properly demodulate the DSB 38 kHz signal. a 19 kHz pilot tone is transmitted with a phase such that when it is frequency-doubled. L-R information can be synchronously detected. The composite stereo signal is shown in Fig. 1. RadioFans.CN 收音机爱 好者资料库 100 z 90 0 f- 0 45 - 0 . L. 10 L 1-R - L-R LSB FREQUENCY (kHz) FIGURE 1 FM STEREO MULTIPLEX SIGNAL SPECTRUM L-R USB 53 F WHY AUDIO LOWPASS FILTERS ARE REQUIRED: Therr: are constraints placed JPon the amplitude and bandwidth characteristics of the left-and right-channel audio signals such that the resultant L + Rand L-R signals will exceed neither their amplitude bounds nor bCindwidth allocations. Otherwise the multiplexed signals would suffer distortion and mutual interferr:nce. To control the amplitude of the Land R channel signals AGe amplifiers, peak limiters. and clipping devices arr: customarily used. Typically these processors add 0 the harmonic content of the program, producing a signal which would result in excessive bandwidth. In the better stereo generators, low- pass filters have been Included to attenuate harmonics beyond the 15kHz bandwidth of the system. Some Inexpensive sWitching type stereo generators omit the audio lowpass filters in (In attempt to eliminate overshoot. With no audio fdters, the stereo composite lowpass filter will overshoot 11SW3d This is absurd, Not only has the overshoot problem been left unsolved, but the stereo generator IS vulnerable to pilot interference and aliasing. II. CAUSES AND EFFECTS OF OVERSHOOT MECHANISMS OF OVERSHOOT IN LOWPASS FILTERS: Although te Irput to a lowpass fdter may be accurately amplitude-limited, such is not necessarily the case at the filters outr:1t Ringing and overshoot of he filter can seriously degrade the accuracy of the limiting action, Lowpass filters may overshoot 6 dB (100%) on some Signals which are not uncommon at the output of audio processing eq uipmen t. A lowpass filter changes two Independent qualities of Its Input Signal In addition to the obvious change of the amplitude vs, frequency characteristic the fdter also changes phase relationships among different frequencies In the filters passband. ThiS IS equivalent 10 Slating that different fre- quencies take different lengths of time to propagate through the filter. ASSOCiated With these two changes to the signal are two mechanisms causing overshoot 1 ATTENUATION OF HARMONICS Consider the ideal case of a lowpass filtCr with rectangular frequency response and zero time delay. ThiS filter is in fact unrealizable but nevertheless would exhibit overshoot due to elimination of harmonics, The frequency responSe: of thiS filter is shown in Fig. 2, 1 o -. FREQUENCY 15kHz FIGURE 2 IDEAL FILTER FREQUENCY RESPONSE Assume that the input signal is a 10kHz squClrewave of amplitude A. The Fourier expansion of this signal is: 00 v(t)=A ! 2: -; sin(21Tfnt) where f IS frequency. n= 1,3,5, . The squarewave Signal has components at the fundamental and odd harmonic frequencies only, Ie, 10. 30. 50. 70. etc. kHz Since the filter cuts off at 15 kHz only the fundamental (10 kHz) component of the squarewave appears at the filter output. Note that If the squarewave amplitude (A) IS one volt. then the peak value of the fundamental component (identically equal to the output signal) IS 4/pl or 1.273. This constitutes an overshoot of 27%. T e squarewave and its fundamental component are shown superposed In Fig. 3. OUTPUT OF INPUT TO FIGURE 3 SQUAREWAVE AND FUNDAMENTAL COMPONENT T IME This is only one example of many possible signals that would cause a linear phase lowpass filter to overshoot. 2. NON-UNIFORM TIME DELAY If different signals propagate through the filter with different time delays. it is possible for in- put signals separated in time to become coincident at the filters output. This could result in an overshoot. Continuing with the example of the squarewave, consider the case where only the fun- damental and third harmonic fall within the filters passband. Squarewaves in the range of 3-5 kHz satisfy this condition. The input and output of the ideal filter discussed in part 1 are shown in Fig. 4. OUTPUT OF FILTER INPUT TO FILTER + 1 -I-+-r-+-_ -+-4-TIME _ 1 -_I.-+-+_.-+-.J FIGURE 4 3-5kHz SQUAREWAVE RESPONSE: FUNDAMENTAL PLUS 3rd HARMONIC Overshoot IS 200%. Since such a filter IS Impossible to build. the response of Fig. 4 In general cannot be prodllced Rather. time delay will vary as a func ion of frequency. thereby upsetting the phase relallonsh,p between the fundamental and third harmonic. If the phase of the third harmonic IS shifted 180 de(jrees relative to the fundamental. the wavciorm of Fig. 5 results. Overshoot IS 70% or 4.6 dB. 1.70 - -OUTPUT INPUT TO FILTER +1 - -TIME - 1 - -L.-t-+-I FIGURE 5 EFFECT OF PHASE DISTORTION E XA M P l E S : A typica I fi Iter specdicatio n may P-qui re freque ncy response to be flat within 0.1 dB from 0-15 kHz and -50 dB at 19 kHz and above. By far the most practical filter meeting these specifications will be an elliptic function type filter. ThiS filter exhibits a very sharp ratr:; of cutoff and a highly nonuniform time delay characteristic. A seventh order ilter meeting these specifications has group delay (time delay) of approximately 43 microseconds wch is uniform from DC to 3.5 kHz. 45 mlcrosecords at 5 kHz. 53 microseconds at 7.5 kHz, 62 usec at 10kHz. increasing to 238 microseconds at 15 kHz which corresponds to 1.- 285 degrees of phase distortion (31.! rotations)_ Therefore the squarewave response of Fig. 5 is cer- tainly possible with this filter. INPUT Time delay generally increases with frequency within the passband of an elliptic filter. Minimum time delay IS at DC while maximum time delay within the passband occurs at the cutoff freqLlency A test signal has been devised which causes filters to overshoot pnmarlly as a function of their time delay distortion. The test signal consists of a sinewave burst immediately followed by a DC step signal. The sJnewave will accumulate maximum time delay (238 usee.) while the DC step signal will accumulate a minimal time delay (43 usee.). At the filters output the sinewave will COinCide with the beginning of the DC step signal. This phenomenon is shown In Fig. 6 Note that the overshoot IS 100% (6 dB)! FIGURE 6 SINE/STEP FILTER RESPONSE Through a combination of effects (both attenuation of harmonics and nonuniform time delay) a myriad of signal types can cause a typical elliptic lowpass filter to overshoot. A low frequency squarewave response is shown in Fig. 7. FIGURE 7 TYPICAL FILTER SQUAREWAVE RESPONSE The waveforms of Fig. 6 and Fig. 7 are common with certain types of music and/or certain types of FM limiters. To offset overshoot audio levels are simply turned down to a point where overshoots of frequent recurrence do not exceed 100% modulation. This can mean a sizeable reduction in modula- tion effectiveness, usually on theiorder of 2.5 - 6 dB! III. DEVELOPMENT OF A SOLUTION NEED FOR A NEW APPROACH: There have been several previous approaches to the problem. Although eXlstrng systems do control overshoot. they also contnbute unwanted side effects to the signal. One method for overshoot control uses a dr-lay line and an AGC stage. This system can cause gain pumping Another popular system uses alternate clipping and filtering combined with a com plementary high frequency boost and cut. This system suffers from excessive rntermodulation distor- tion and a /ugh frequency rolloff which is dependent upon signal level. CONSTRAI NTS: It IS clearly deSirable to have a filter which will eliminate harmonics above 15 kHz yet preserve the peak amplitude-limited nature of Its input signal. Note that it is not necessary to have a fdter that does not overshoot. Ringing and overshoot are completely unobjectionable prOVided that the overshoots do not exceed the 100% modulation level. From this point on, the term overshoot will denote only overshoots above 100% modulation. The filter requirements arc 1. Frequency response flat 0,5 dB 20 Hz-1S kHz at all levels up to 100% modulation. 2. Attenuation above 19kHz inclusive 50 dB minimum. 3 Overshoots not exceeding 102% modulation 4. Filter shall be transparent to steady state sinewave Signals: THO and 1M distortion 0.1% or less. 5. Any effect of eliminating overmodulating overshoots shall be inaudible. BESSEL FILTER UNSATISFACTORY: One filter that does not overshoot is the Bessel type.The Bessel filter has maximally flat time delay for a minimum phase filter However. its frequency response IS Inadequate. It has a very gradual rate of cutoff shown In Fig. 8. FIGURE 8 IDEAL BESSEL FILTER RESPONSE (GAUSSIAN FILTER) - . U A FREOUENCY (NORMALIZED) A -.,j . o - 1 - 0 e . .:III -= NON MINIMUM PHASE FILTER UNSATISFACTORY: If one were to start with a filter with suf- ficiently sharp cutoff and attempt to find a phase function resulting in minimum overshoot. the result would be a lowpass filter thaI approximates linear phase. yet stili overshoots. Even in the case of the Ideal filter discussed under Causes and Effects of Overshoot. the filter still overshoots. FILTER MUST BE NONLINEAR: It would appear that there is no filter that satisfies all the above conditions, There is no linear lime-invariant filter that satisfies all the above conditions. The state- ment that we can tolerate overshoots below a certain level implies that a nonlinear filler may work. That is. the filter may have one set of characteristics up to a certain level and other characteristics above that level. The requirements that the action be inaudible and that the fdter be transparent to sinewaves (no harmonic or intermodulatlon distortion) imply that the filter must be perfectly linear up to 100% modulation. It is feasible to have a filter which is linear up to 100% modulation and non- linear only when an overshoot above 100% is imminent. IV. SOLUTION: DYNAMIC TRANSIENT RESPONSE FILTER THEORY, IDEAL CASE: Assume that we have two Identlcallowpass filters The filters have a cutoff frequency of 15kHz with infinite attenuation above and zero attenuation below. and a uniform time delay of 100 microseconds for all frequencies. (Such a filter is of course non-causal and impossible to build.) Conslrier the situation of Fig 9 where the filters are cascaded. that IS, the output of one filter drives the second. INPUT 15 kHz IDEAL 15 kHz IDEAL FIL TER - FIL TER / T= 100 USEe. L 100 USEe. FIGURE 9 CASCADED IDEAL FILTERS . / OUTPUT After application ot a signal to the first filter. the output appears 100 usec. later with all com ponents abovr. 15 kHz removed. Phase relationships and amplitudes of cOrYponents below 15 kHz are preserved. the only change to the signal will be the elimination of components above 15kHz and 100 usec. of time delay When the first filterss output is applied to the second. the second filter will function only as a 100 usee. delay line. Since there are no components above 15 kHz at the second filters input. the second filter does not change the Signal except for the addition of time delay. Therefore. the first filter predicts the output of the second filter. ThiS prediction technique is emrloyed in the Harris DTR filter. IMPLEMENTATION: The DTR filter is a system which comprises two lowpass filters. ()rl allpass frller (phase equalizer). and nonlinear compensation circuitry. A block diagram is qiven in Fig. 10. -.- LIMITED AJOIO IN - ALL li.S INSTAN- SINGLE - IS kHl - COMPLJ - PASS I-kHl I-TANEOUS POLE M LPF SATOR / FILTER lPF LlMli EA LPF OUT FIGURE 10 DYNAMIC TRANSIENT RESPONSE LOWPASS FILTER The first filter (at extreme left) in Fig.l 0 IS a seventh order e!il)Jtic type with a cutoff frequency of 15 kHz. Th e second filler is a Iso seventh order elliptic bu I the cu toff frequency IS 1 7.5 kH z. The second lowpass filter is preceded by an allpass filler which linearIZes the lowpass filters phase from DC to the cutoff frequency of the firs