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1 NATURAL TEST SIGNAL © Kalervo Kuikka Theory and measurements.

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1 1 NATURAL TEST SIGNAL © Kalervo Kuikka Theory and measurements

2 NATURAL TEST SIGNAL © K.Kuikka In general Natural test signal is designed for quality measurements of audio frequency devices. It is wideband synchronous multi-tone test signal, which frequency- and power distribution equals to common music. Natural test signal is periodic test signal, in which all signal components are mathematically well-defined (frequency, phase and amplitude) and they are fixed proportional to the fundamental frequency. For these reasons it is possible to measure coarse response errors by using an oscilloscope that is trigged to the fundamental frequency. Carrying out high-performance response error measurements spectrum analyser is needed. Natural test signal is mathematically very simple => It is easy to analyse measurement results.

3 NATURAL TEST SIGNAL © K.Kuikka Generating Natural Test Signal Generating Natural Test Signal is extremely simple. Mother Signal of Natural Test Signal can be produced by summing ideal fundamental frequency square wave and inverted phase pure fundamental frequency sine wave at such a level that fundamental frequency component of summing signal will be completely disappeared. Mother Signal can also be produced by ideal band stop filter (tuned to fundamental frequency). If ideal square wave goes through band stop filter fundamental frequency component of square wave is completely disappeared.

4 NATURAL TEST SIGNAL © K.Kuikka Generating Natural Test Signal Square wave, which DC component is 0 and peak value, can be described as follows : and fundamental frequency sine wave can be described : When summing square wave and phase inverted fundamental frequency sine wave component :, we get as a result Natural Test Signal :

5 NATURAL TEST SIGNAL © K.Kuikka Generating Natural Test Signal When summing to square wave (275 Hz, uppermost picture ) in phase inverted … distortion free pure sine wave ( picture in the middle) in such a level that fundamental frequency component of square wave is fully got off then we get as a result … Natural Test Signal (undermost picture), which is very effective signal on testing all audio devices. In the picture there is Mother Signal only.

6 NATURAL TEST SIGNAL © K.Kuikka Choosing funtamental frequency Fundamental frequency of Natural Test Signal can be chosen freely. In this case fundamental frequency has been chosen such a way that spectrum of square wave equals common music signal. To avoid noise caused by power supplies of testing devices fundamental frequency is not allowed to be harmonic of mains frequency ( 50 / 60 Hz). Because of these arguments fundamental frequency is chosen 275 Hz in this application. Fundamental frequency ( 275 Hz) described in this application is suitable for testing purposes of all audio devices in middle and high frequency region. If we must carry out tests in bass region we ought to choose lower fundamental frequency ( 20 – 30 Hz).

7 NATURAL TEST SIGNAL © K.Kuikka Mother and Daughter Signals Allthough the Mother Signal itself is a very efficient test signal the character of Natural Test Singnal can still be improved by summing into it daughter signals with higher frequency than fundamental. In summing daughter signals and Mother Signal we must keep in mind that the peak value of Natural Test Signal does not become too high. The summing principle is that amplitude of daughtersignals is 0 when mother signal is at its peak value.

8 NATURAL TEST SIGNAL © K.Kuikka Mother and Daughter Signals Daughter Signals phase locked to fundamental can be generated by modulating the sine wave carrier (sin  m t, m>4, phase locked to fundamental ) with the fundamental sine wave ( sin  t ). In this case we get two Daughter Signals as follows: We can see that Daughter Signals are amount of fundamental frequency above and beneath the carrier frequency.

9 NATURAL TEST SIGNAL © K.Kuikka Mother and Daughter Signals Daughter Signals can also be generated by using a square wave as a carrier and then we get more daughter signals than two. In this case carrier is : and modulating signal: Daughter Signals are generated as follows:

10 NATURAL TEST SIGNAL © K.Kuikka Using square wave as a carrier on generating Daughter Signals is very advantageous when it makes band with on Natural Test Signal higher. Test signal is then more effective to bring forward group delay errors on higher frequencies. The sum of Daughter Signals is at any time 0 when Mother Signal is at its peak value, because (sin  t ) = 0 at this point. Summing Daughter Signals into Mother Signal does not increase the peak value of Natural Test Signal at the peaks of pure Mother Signal. On summing Daughter Signals into Mother Signal it is possible to increase signal power at desired measuring range and at the same time crest factor of Natural Test Signal becomes lower. Mother and Daughter Signals

11 NATURAL TEST SIGNAL © K.Kuikka We can generate Mother Signal (uppermost picture) of Natural Test Signal when we fully remove fundamental frequency component of ideal square wave. Pure Mother Signal has crest factor only 2.3 In picture in the middle we can see Daughter Signals made by modulating process. In this case carrier wave is square wave phase locked to fundamental frequency. When summing Daughter Signals into Mother Signal (undermost picture) we can increase signal power at “valleys” of pure Mother Signal. When we adjust the level of Daughter Signals so that summing signal reaches peak value of Mother Signal, crest factor decreases to value Mother and Daughter Signals

12 NATURAL TEST SIGNAL © K.Kuikka ”Wild” Daughter Signals If a carrier wave we use generating Daughter Signals is not phase locked to fundamental frequency, Daughter Signals obtain “wild” behaviour on scope trigged to fundamental frequency. On scope screen we can see very interesting figures, which are very strange for sine wave orientated men. On doing some measurements “wild” Daughter Signals are very effective to detect response errors.

13 NATURAL TEST SIGNAL © K.Kuikka ”Wild” Daughter Signals Fig 1 Fig 2 Fig 3 Fig 4 Fig 1 Mother Signal only Fig 2 Mother Signal an low level Daughter Signals Fig 3 The level of Daughter Dignals are adjusted to the peak level of Mother Signal Fig 4 The level of Daughter Signals are ajdusted above peak level of Mother Signal. Scope wievs at generator output. Under tests Scope was trigged to fundamental frequency.

14 NATURAL TEST SIGNAL © K.Kuikka Sweeping Daughter Signals The carrier wave we use on generating Daughter Signals is not necessary to be phase locked to fundamental frequency. That is why we can use also sweep signal as a carrier wave. In this case we get two sweeping Daughter Signals, which have frequency difference of two times fundamental frequency all the time in spite of sweeping frequency. Without risk of overdrive testing device we can drive it full dynamic range with Mother Signal and simultaneously also drive with sweeping Daughter Signals. Second order inter modulation product of Daughter Signals can be measured on frequency of two times fundamental frequency all the time during sweeping section.

15 NATURAL TEST SIGNAL © K.Kuikka Superior features Natural Test Signal has many superior features compared to other multi-tone test signals. Spectrum and power distribution of the signal equals to common music signal and signal is distinctly periodic. This feature makes very easy to see coarse wide band response errors with an oscilloscope, which is trigged to the fundamental frequency. There are free space for inter modulation products on fundamental frequency and two times fundamental. Second order inter modulation products generated to higher frequencies are directed between odd harmonics of Natural Test Signal.

16 NATURAL TEST SIGNAL © K.Kuikka Superior features Using Daughter Signals there is very easy to increase signal power at higher frequencies where power of Mother Signal is quite low. Carrier we use in generating Daughter Signals must not be phase locked to the fundamental frequency thus we can use also sweep signal as a carrier. Natural Test Signal is very sensitive signal form to detect group delay errors of a test device. Signal distorts very sensitively if group delay errors occur. Generating Natural Test Signal is very easy.

17 NATURAL TEST SIGNAL © K.Kuikka Scope wiev of sine wave Fundamental frequency = 275 Hz Spectrum of sine wave ( f = 275 Hz) Span = 6.4 KHz Y = 10 dB/div

18 NATURAL TEST SIGNAL © K.Kuikka Average spectrum of a music signal. Average result of 200 measurements. Span = 12.8 KHz Y = 10 dB/div Spectrum of Natural Test signal (fundamental frequency = 275 Hz) Fundamental frequency component has been fully removed thus lowest frequency component of Natural Test Signal is 3*275 =825 Hz Span = 12.8 KHz Y = 10 dB/div

19 NATURAL TEST SIGNAL © K.Kuikka Average spectrum of a music signal. Average result of 200 measurements. Span = 12.8 KHz Y = 10 dB/div Scope wiev of a coincidental music signal

20 NATURAL TEST SIGNAL © K.Kuikka Spectrum of Natural Test Signal ( Mother Signal only ) Span = 12.8 KHz Y = 10 dB/div Scope wiev of Natural Test Signal ( Mother Signal only ) Rise time (adjustable ) of the signal is 5.3  s in this picture.

21 NATURAL TEST SIGNAL © K.Kuikka *275Hz square wave carrier modulated by fundamental frequency sine wave generates Daughter Signals on frequencies (14*275 – 275) Hz and (14* ) Hz. In the picture we can see also Daughter Signals on frequencies (3*14*275 –275) Hz and (3*14* ) Hz. Daughter Signals are marked by blue arrows. Span = 12.8 KHz Y = 10 dB/div Scope wiev of Natural Test Signal (mother signal + daughter signals). Natural Test Signal signal seems to be quite similar character as a music signal but it is not fully coincidental. It is distincly periodic signal.

22 NATURAL TEST SIGNAL © K.Kuikka Scope wiev of a coincidental music signal Scope wiev of Natural Test Signal (Mother Signal + Daughter Signals). Natural Test Signal signal seems to be quite similar character as a music signal but it is not fully coincidental. It is distincly periodic signal.

23 NATURAL TEST SIGNAL © K.Kuikka Mearuring distortion We examined the behaviour of Natural Test signal in non linear device with a testing device specially designed on this purpose. Testing device could be adjusted to bring out different types of distortions. At first we adjusted the distortion of the testing device to 1% using pure sine wave (275 Hz). After that we changed sine wave to Natural Test Signal (Mother Signal and different kinds of Daughter Signals) having same amplitude and carried out distortion measurements. We took screenshots from scope and spectrum analyser in each measurements. In the pictures distortion products have been marked with red arrows and Daughter Signals with blue arrows.

24 NATURAL TEST SIGNAL © K.Kuikka In distortion measurement pictures testing signals have been presented as follows: sine Hz fundamental frequency sine wave natural Mother Signal of Natural Test Signal natural_13_15 Natural Test Signal including Daughter Signals at frequencies 13 and 15 times fundamental frequency natural_14_16 Natural Test Signal including Daughter Signals at frequencies 14 and 16 times fundamental frequency Measuring distortion

25 NATURAL TEST SIGNAL © K.Kuikka Quadradic distortion 1 % Signal: Sine275 At the scope screen we cannot notice any distortion We can see that second harmonic (550 Hz) is over 20 dB stronger than third harmonic (825 Hz) Span = 6.4 KHz Y = 10 dB/div Measuring distortion

26 NATURAL TEST SIGNAL © K.Kuikka Quadradic distortion 1% Signal: Natural At the scope screen we cannot notice any distortion Fundamental frequency distortion component is quite low but even harmonics components (550, 1100, 1650 Hz…) are much higher Span = 6.4 KHz Y = 10 dB/div Measuring distortion

27 NATURAL TEST SIGNAL © K.Kuikka Quadradic distortion 1% Signal: Natural_13_15 At the scope screen we cannot notice any distortion Around Daughter Signals there are generated quite high level distortion components Span = 6.4 KHz Y = 10 dB/div Measuring distortion

28 NATURAL TEST SIGNAL © K.Kuikka Quadradic distortion 1% Signal: Natural_14_16 At the scope screen we cannot notice any distortion Highest distortion component is at the frequency of 1100 Hz Span = 6.4 KHz Y = 10 dB/div Measuring distortion

29 NATURAL TEST SIGNAL © K.Kuikka Clipping distortion 1% ( positive / negative peaks ) Signal: Sine275 At the scope screen clipping both positive and negative peaks is very clearly seen. Spectrum shows that odd harmonics are stronger than even harmonics. Span = 6.4 KHz Y = 10 dB/div Measuring distortion

30 NATURAL TEST SIGNAL © K.Kuikka Clipping distortion 1% ( positive / negative peaks ) Signal: Natural At the scope screen clipping both positive and negative peaks is very clearly seen. Spectrum shows that clipping generates very many low level distortion components. Strongest distortion component is at fundamental frequency (275 Hz). Span = 6.4 KHz Y = 10 dB/div Measuring distortion

31 NATURAL TEST SIGNAL © K.Kuikka Clipping distortion 1% ( positive / negative peaks ) Signal: Natural_13_15 At the scope screen clipping both positive and negative peaks is very clearly seen. Strongest distortion component is at fundamental frequency (275 Hz). Span = 6.4 KHz Y = 10 dB/div Measuring distortion

32 NATURAL TEST SIGNAL © K.Kuikka Clipping distortion 1% ( positive / negative peaks ) Signal: Natural_14_16 At the scope screen clipping both positive and negative peaks is very clearly seen. Clipping generates many distortion components. Strongest distortion component is at the frequency of two times fundamental frequency (550 Hz). Span = 6.4 KHz Y = 10 dB/div Measuring distortion

33 NATURAL TEST SIGNAL © K.Kuikka Clipping distortion 1% ( negative peaks only ) Signal: Sine275 At the scope screen clipping negative peaks is very clearly seen. Clipping generates a great amount of even and odd distortion components. Span = 6.4 KHz Y = 10 dB/div Measuring distortion

34 NATURAL TEST SIGNAL © K.Kuikka Clipping distortion 1% ( negative peaks only ) Signal: Natural At the scope screen clipping negative peaks is very clearly seen. In spectrum view we can see distortion products to spread to wide bandwidth Span = 6.4 KHz Y = 10 dB/div Measuring distortion

35 NATURAL TEST SIGNAL © K.Kuikka Clipping distortion 1% ( negative peaks only ) Signal: Natural_13_15 At the scope screen clipping negative peaks is very clearly seen. In spectrum view we can see that summing Daughter Signals into Mother Signal increases distortion products clearly. Span = 6.4 KHz Y = 10 dB/div Measuring distortion

36 NATURAL TEST SIGNAL © K.Kuikka Clipping distortion 1% ( negative peaks only ) Signal: Natural_14_16 At the scope screen clipping negative peaks is very clearly seen. In spectrum view we can see high distortion products to spread to wide bandwidth. Span = 6.4 KHz Y = 10 dB/div Measuring distortion

37 NATURAL TEST SIGNAL © K.Kuikka Cross over distortion 1% Signal: Sine275 At the scope screen cross over distortion of sine wave is just observable. In spectrum view we can see that odd harmonics are higher than even harmonics. Span = 6.4 KHz Y = 10dB/div Measuring distortion

38 NATURAL TEST SIGNAL © K.Kuikka Cross over distortion 1% Signal: Natural At the scope screen cross over distortion is not observable. In spectrum view we can see that highest distortion component has been generated to the fundamental frequency (275 Hz). Span = 6.4 KHz Y = 10 dB/div Measuring distortion

39 NATURAL TEST SIGNAL © K.Kuikka Cross over distortion 1% Signal: Natural_13_15 At the scope screen cross over distortion is not observable. In spectrum view we can see that highest distortion component has been generated to the fundamental frequency (275 Hz). Span = 6.4 KHz Y = 10 dB/div Measuring distortion

40 NATURAL TEST SIGNAL © K.Kuikka Cross over distortion 1% Signal: Natural_14_16 At the scope screen cross over distortion is not observable. In spectrum view we can see that highest distortion component has been generated to the fundamental frequency (275 Hz). Span = 6.4 KHz Y = 10 dB/div Measuring distortion

41 NATURAL TEST SIGNAL © K.Kuikka Natural Test Signal in digital recording and MP3 compressing Tests were carried out by recording test signals sine275, natural and natural_13_15 at sampling frequency 44.1 KHz and saving recordings to the hard disk of the computer as uncompressed WAV files. WAV audio files were then compressed 192 Kbps, 128 Kbps and 96 Kbps MP3 files and they also were saved to the hard disk. When playing all recorded audio files we measured response errors of Natural Test Signal in digital recording and MP3 compressing. Testing point was output of audio card of the computer.

42 NATURAL TEST SIGNAL © K.Kuikka Uncompressed WAV file. Sampling frequency is 44.1 KHz. Signal: Sine275 Fundamental frequency sine wave is error free. Spectrum of sine wave is as clean as at the output of signal generator Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

43 NATURAL TEST SIGNAL © K.Kuikka Uncompressed WAV file. Sampling frequency is 44.1 KHz Signal: Natural Mother Signal is error free. Due to limited sampling frequency some peaks have been formed. Spectrum of Mother Signal is as clean as at the output of signal generator. Digital recording causes no dirtortion. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

44 NATURAL TEST SIGNAL © K.Kuikka Uncompressed WAV file. Sampling frequency is 44.1 KHz. Signal: Natural_13_15 Due to limited bandwidth Natural Test signal has been formed spiky but other response errors does not occur. Spectrum of Natural Test Signal is error free. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

45 NATURAL TEST SIGNAL © K.Kuikka To bit rate 192 Kbps converted MP3 file. Signal: Sine275 Compression does not cause any response errors to sine wave. Spectrum of fundamental frequency sine wave is distortion free. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

46 NATURAL TEST SIGNAL © K.Kuikka To bit rate 192 Kbps converted MP3 file Signal: Natural At the scope screen Mother Signal has become a little bit noisy. Spectrum of Mother Signal has become quite noisy. In the picture there is average test result of 30 measurements. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

47 NATURAL TEST SIGNAL © K.Kuikka To bit rate 192 Kbps converted MP3 file Signal: Natural_13_15 Natural Test Signal has become quite noisy. Spectrum of Natural Test Signal has become quite noisy. In the picture there is average test result of 30 measurements. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

48 NATURAL TEST SIGNAL © K.Kuikka To bit rate 128 Kbps converted MP3 file. Signal: Sine275 Compression has not caused any response errors to fundamental frequency sine wave. Compression has not caused any errors to the spectrum view. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

49 NATURAL TEST SIGNAL © K.Kuikka To bit rate 128 Kbps converted MP3 file Signal: Natural Mother Signal has become very noisy at the scope screen. Spectrum of Mother Signal has become very noisy. In the picture there is average test result of 30 measurements. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

50 NATURAL TEST SIGNAL © K.Kuikka To bit rate 128 Kbps converted MP3 file Signal: Natural_13_15 Natural Test Signal has become very noisy at the scope screen. Spectrum of Natural Test Signal has become very noisy. In the picture there is average test result of 30 measurements. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

51 NATURAL TEST SIGNAL © K.Kuikka To bit rate 96 Kbps converted MP3 file Signal: Sine275 At the scope screen fundamental frequency sine wave is error free. A little bit noise has been produced near the fundamental frequency. In the picture there is average test result of 30 measurements. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

52 NATURAL TEST SIGNAL © K.Kuikka To bit rate 96 Kbps converted MP3 file Signal: Natural At the scope screen Mother Signal is extremely noisy. Spectrum of Mother Signal has become extremely noisy. In the picture there is average test result of 30 measurements. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

53 NATURAL TEST SIGNAL © K.Kuikka To bit rate 96 Kbps converted MP3 file Signal: Natural_13_15 At the scope screen Natural Test Signal has became extremely noisy. Noise level is about 20 – 30 dB below the level of Daughter Signals. In the picture there is average test result of 30 measurements. Span = 6.4 KHz Y = 10 dB/div Digital recording and MP3 compressing

54 NATURAL TEST SIGNAL © K.Kuikka Conclusions During testing measurements we noticed that Natural Test Signal is very easy to use and effective test signal to carry out response error measurements. Disadvantage of Natural Test Signal is that we must use expensive spectrum analyser as an indicator. In the future we ought to examine if it is necessary to measure only distortion levels of fundamental frequency (275 Hz) and two times fundamental (550 Hz) to find out the quality of a testing device. If these two measurements are enough to find out the quality of a test device we need only normal level meter and two narrow band pass filters (275 Hz and 550 Hz) to carry out distortion test. Indicator costs will then be very low. Nowadays suitable indicator in not a problem any more. There are many analyser software on the market so we can use normal personal computer as an indicator when carrying out distortion tests with Natural Test Signal.

55 NATURAL TEST SIGNAL © K.Kuikka Testing equipments: NATURAL TEST SIGNAL GENERATOR Model: ”Kuikka 2006” TEKTRONIX TYPE 545B OSCILLOSCOPE HEWLETT PACKARD 35660A DYNAMIC SIGNAL ANALYZER FLUKE 8520A DIGITAL MULTIMETER PHILIPS FA141 integrated stereo amplifier CANON PowerShot A75 digital camera Tests and measurements have been carried out by: Kalervo Kuikka OH6AWN gsm:


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