Tech junkies gather round...

Discussion in 'Amps and Cabs [BG]' started by Joris, Nov 21, 2001.

  1. I decided to do some signal analysis on my bass guitar. I used SpectraPro by Sound Technology Inc. My conclusions are as follows:

    - The crest factor of any bass line I played was calculated at 12-15 dB. This is the difference between peak level and RMS/continuous level. No matter what I played: a cool fingerstyle groove, chords, slamming with a pick. This means an amplifier driven to the verge of clipping will be delivering 25% of its maximum continuously (at best). With heavy compression engaged the crest factor dropped to about 8 dB, at which point the amp would deliver 40% of its maximum continuously. Playing slap style or short notes (funk for example), the continuous power drops far below 1/4 of full amp power.

    - The signal is not symmetrical. The positive half of the signal reaches a peak almost twice as high as the negative half, although the average value is of course 0. This is clearly visible on the "time series" graph below. Different EQ settings, from extreme bass boost to mid boost, and different pickups (neck, bridge) were of no influence to this phenomenon. This leads me to believe that a bass amplifier always clips first at the positive half, and the negative half doesn't clip until the power increases by about a factor 2. This would validate my "waving speaker" theory: when a bass amp clips, it becomes unstable because the average value of the signal is not 0 anymore. The amp would compensate for the unbalance by shifting its center point, thereby letting the speaker cones "wave around".

    - The spectrum shows how little of the signal actually is root frequency. This measurement is made with flat EQ, pickups balanced evenly. Of course, this graph varies a lot with different EQ settings. But here, the root frequency is about 15 dB below the first harmonic peak. Some difference!

    Time series and spectrum are below.
  2. And here's the spectrum graph:
  3. BigBohn


    Sep 29, 2001
    WPB, Florida
    Eureka, Joris! If I only knew how to decipher all those purty lookn' lines.:D
  4. Very cool joris. Your calculations between style of playing and amp output / capacity makes sense. Someone had to get bored enough to do it :)

    I'll have to play with this SpectraPro software. Seems like some questions could easily be answered. Cool.
  5. MikeyD


    Sep 9, 2000
    Really cool, Joris - good work, and thanks for posting excellent plots! Is that product shareware, freeware, or - ? The graphs really do show what I've imagined the bass guitar signal would typically look like in both time and frequency domains. One can see on the time plot that the signal is periodic at about 40 Hz., yet if it were all fundamental, it would be a smooth sinusoid instead of those peaky peaks.

    This is really interesting. I should mention that -12 dB would correspond to 25% of the *voltage* and only about 6% of the power (power being proportional to the square of voltage)! This means that the peaks need about 16 (not just 4) times the power of the continuous average signal in order to reproduce without clipping! Put another way, if the peak-to-average ratio had been 10 dB (instead of 12), the amp would need a 10:1 ratio, or ten times the power overhead. You make a really important point for those who want hi-fi reproduction with no clipping.

    One could argue that short notes become "discontinuous" so the duty cycle goes down a lot. As discussed before, your measured 8 dB drop would correspond to about 16%, not 40%, of the maximum. This reinforces your point even more, I think. I also think it says a lot about the expected duty of the amp in terms of peak vs. average power draw from the outlet.

    Actually, the *average* signal level (not RMS) should be zero for the input waveform from the bass. The RMS value is "root mean squared", which would give the average value of voltage if both sides were rectified. For example, the average voltage from my AC outlet is zero, yet its RMS value is 120 volts. Anyway, while the positive peak is much higher, the average positive voltage over time is equal to the average negative voltage.

    This is really good experimenting and thinking, Joris. The average input voltage into the power amp would be zero (at least over a significant time - say several periods of the waveform), but if the amp's clipping lops off the peaks on the asymmetrical waveform, it introduces an offset. The offset would appear like a DC component artifact of the output stage's clipping. (Note that "DC" is relative - one can only define DC in terms of how long the signal exists.) Given that a typical note from a bass guitar might last several seconds (okay, let's say 10), then what we can envision is the average voltage jumping up slightly from zero to an offset value as the amp clips, then declining a bit as the note decays and the clipping reduces, then finally returning to zero abruptly as the clipping stops (peaks fall below clipping). This process would repeat for every note played at greater than clipping level. So now I can see what you're saying: this shifting offset (which itself is likely to be at a subsonic frequency) is transferred to the speakers and appears like a temporary shifting of the cone off of its neutral position. Okay - I can buy that now. I'm glad you were curious enough to back your earlier hypothesis. I really would like Bob Lee to weigh in on this as well.

    It is excellent to see the periodicity in the frequency plot at ~40 Hz. intervals - exactly what I expected. Everyone should note that the plot shows the strengths of the first 5 harmonics (~80, 120, 160, 200, and 240 Hz.) are ALL stronger than the fundamental! Still, the fundamental requires a lot of power because typical speakers have a lot of trouble reproducing it on equal footing with the harmonics.

    As one goes above about 600 Hz., one can see more non-harmonic content appearing (though at lower levels) - this stuff is probably string noise, fret noise, and the initial "clack" or whatever of the plucking. Notice also the frequency content below the fundamental: some of it is real and represents the actual signal associated with the non-continuous nature of playing a note (low frequency, non-periodic components the attack, for example). Other stuff in there probably includes artifacts of the sampling method (it gets rather imprecise because of the math and the sampling period used).

    Well, thanks for a really great and thought-provoking exhibit, Joris! Excellent work. I think we can resume discussing this "clipping" issue relative to DC now. I see the merit in your observation that DC can get generated at the output stage, but I'm still not convinced that the level of DC produced can cause damage to speakers by itself. Let's have a good discussion and pick it up where we left off a few months ago! :)

    - Mike
  6. geshel


    Oct 2, 2001
    Awesome thread (but then I'm an EE!) :D :D

    The "waving speaker" syndrome: aha! I'd noticed that with my Clarus-powered-Acme (underpowered by quite a bit, yes). I was playing a 12-string through it, up on the D and G strings, and the cone was doing a really weird arrhythmic back-and-forth shuffle - the distance moved was pretty severe too, I got scared and stopped playing.

    A friend of mine did a similar analysis, with pretty similar results (harmonics higher than the fundamental, etc), check it out here:
  7. MikeyD


    Sep 9, 2000
    Interesting article, geshel. Thanks for posting the link. I'm motivated to check out the clipping behavior of one of my amps (soon).
    - Mike
  8. Wow, I gotta get in on this! Great work Joris. It's real late right now so I'm going to bed, but I'll be taking a really close look at this tomorrow. I love this kinda stuff....:D
  9. cassanova


    Sep 4, 2000
    Hey Joris, you wanna put that in more laymans terms for those of us that have little to no clue as to what that stuff means please? :D
  10. Thanks for the replies guys, I hope this will be an interesting and lengthy topic :) and I'm looking forward to more replies :)

    Mike, about the crest factor. Although I didn't check exactly, Spectra Pro measures voltages at the sound card's input, so the dB values I gave are for signal levels, and not power levels. But I wouldn't at all be surprised if I was wrong on this. --- And of course I meant the average value to be zero and not the RMS. My bad! I'll correct it in the original post.

    You can download SpectraPro from SoundTechnology's website. You'll get a (well-protected) 1 month trial for free.

    I'm seriously thinking of buying on of their packages. I'm clueless on their prices though.

    Casanova, I'm sorry, when you dig this deep into tech terms, it gets hard to follow for non-techies. I did my best to keep it understandable, but to explain everything in laymen's terms, it would have been far over the maximum post length allowed. My FAQ doesn't cover this topic yet, but that would be the place to start reading up.
  11. Munjibunga

    Munjibunga Retired Member

    May 6, 2000
    San Diego (when not at Groom Lake)
    Independent Contractor to Bass San Diego

    Could it be that the asymmetry of the wave form between the positive and negative sides is an artifact of the particular amplifier you were using? I can't rationalize a universal condition that would lead me to expect that sort of thing with any amp. Maybe the way the tubes (or SSD's) are biased gives preference to one side of the signal. It sure seems to me that the asymmetry is something that needs to be corrected. Maybe it starts in the bass.
  12. john turner

    john turner You don't want to do that. Trust me. Staff Member

    Mar 14, 2000
    atlanta ga
    the assymetry looks like a frequency modulated frequency - meaning a higher frequency being modulated by a lower frequency. the lower frequency is affecteing the peak values of the higher one, causing the strange shape.
  13. Munjibunga

    Munjibunga Retired Member

    May 6, 2000
    San Diego (when not at Groom Lake)
    Independent Contractor to Bass San Diego
    Of course. I'dve realized that immediately if I would have just looked at the danged waveforms. JT, maybe you could run a little Fourier analysis on it and report back, eh?
  14. Munjibunga

    Munjibunga Retired Member

    May 6, 2000
    San Diego (when not at Groom Lake)
    Independent Contractor to Bass San Diego
    Nope. Never mind. Forget everything I said. Here's my theory, and I'm gonna stick with it. The positive peak occurs when the vibrating string is closest to the pickup, and the weaker negative peak is when the string is distal. There's no reason to assume that the zero reference is going to occur at the midpoint of the string's excursion through its cycle.

    OK, don't hurt me.
  15. MikeyD


    Sep 9, 2000
    Some other comments:

    (1) If Joris had shown the entire time series from the attack to the "end" of the decay, one would see that the string vibration would die out at 0 volts. This also happens to correspond to zero string velocity. Given how typical magnetic pickups work, it's the velocity of the string relative to the pickup pole that's producing the voltage. If this is true, then the string typically reaches maximum velocity at its centered position (like a pendulum).

    (2) The asymmetrical waveform he shows can be represented by a Fourier series having both odd and even harmonics. This is quite common in musical waveforms, so it doesn't represent any kind of amplifier distortion, per se. Note that [some] symmetrical waveforms contain only odd harmonics.

    (3) I'm thinking that, given how strong the 2nd-6th harmonics are relative to the fundamental, that the waveform might be more representative of plucking near the bridge. I would think that plucking bluntly near the neck (and even more so over the 12th fret) would produce more fundamental and less harmonic levels. I should resurrect and old oscilloscope I have lying around and see!

    (4) Joris, if the 12 dB was signal level, then the voltage ratio was 25%, as you observed. But the power ratio is 6.25%, which underscores the point you were making: the dynamics between the peak crest and the average power is quite pronounced. BTW - thanks for the link to the vendor.

    - Mike
  16. geshel


    Oct 2, 2001
    1) Oh yeah, I hadn't thought of that.

    2) Call me crazy, but sin(w)+sin(2*w) is a symmetrical signal. Symmetrical in that the positive and negative peaks are of the same amplitude. Also, I do not believe you can make a signal with different positive and negative amplitudes using a Fourier series? This I'm not so sure of however.

    3) Walter addressed this (in the link I posted earlier), he was suprised to find that a gentle pluck in the middle of the string still yielded high harmonic content.

    One other thing, looking at the time sequence, it looks a heck of a lot like samples of voiced speech (vowels) that I've seen! Including, especially, the asymmetry.
  17. Man! What a great thread! I'm learning so fast around you guys! It's awesome! I just got the privledge of correcting my (very expereinced) sound engineer mentor, and being right! I come!

    Thanx Guys!
  18. Blackbird

    Blackbird Supporting Member

    Mar 18, 2000
    What's wrong with me that I don't understand this?
  19. MikeyD


    Sep 9, 2000
    Symmetry requires the positive and negative amplitudes to be identical (around some center point). But there is the aspect of *shape* as well: an even function has the property that f(t) = f(-t) (e.g., a cosine); an odd function has the property that f(t) = -f(-t) (e.g., a sine). Even periodic functions can be represented by a Fourier series having only cosine terms and a constant. Odd periodic functions, alternately, can be represented by a Fourier series having only sine terms. And yes, the signal Joris showed can certainly be represented by a Fourier series - and if there were any DC offset, the constant term would take care of that.

    Yes, I was thinking that the signal would sound kind of like a growly tone (having a bite or edge to it) that one gets by plucking near the bridge. I still think that the harmonic content varies quite a bit depending on where you pluck - I know I can get very different timbres (including how strong the fundamental is) depending on where I pluck the strings.

    - Mike
  20. MikeyD


    Sep 9, 2000
    Nothing. :) This is nerd talk - there is something wrong with nerds! ;) Anyway, if you have a specific question about something, maybe it could be answered (hopefully correctly) by someone here.
    - Mike