Was it P.T. Barnum who said never give a sucker an even break? Or was he the one who said there's a sucker born every minute? If someone is going to make money out of it, why should you blame them for taking advantage? You will never convince the converted that they worship a false god, they won't be confused by the facts, their minds are firmly made up. My only regret is that I missed out on the televangalist scam of the 1980s. What a lost opportunity to get rich the easy way.
Sorry, thank you I don't need any FFT tutorials. I found posting that site condecendiing and insulting. There are no perversions of Fourier theory just people who don't understand it. You propose a methodology and know how to analytically pose its limits vs other techniques. I have been doing this for 40yr. as JC would say.
Mis-use of tracking spectrum analyzers is rampant these days. I fight with customers who want to do full power frequency response with them all the time. The amplifier output is looking like a tri-wave and the analyzer gives only the amplitude of the fundamental this makes for physically nonsensical graphs (some even go on the datasheets).
Also it is very easy to get an HP spectrum analyzer to give a very wrong answer (Hi-Q crystal filter for instance) without posting a sweep speed/ resolution BW warning.
And furthermore your mention of a tracking filter even though the IF in a spectrum analyzer acts just like that shows that you don't understand their exact workings. My favorite is an old HP triple conversion one with down to 3Hz crystal IF and post IF "video" filters. They provide offset of the generator and IF via an "easter egg" so you can do the equivalent of Dick Heysers' swept measurements of speakers and remove the delay.
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I can find out. It was a wonderful instrument their 20Hz to 40Mhz spectrum analyzer maybe the HP3465? All analog, virtually nobody is interested in such a low frequency range these days. The CRT has faded to illegibility and the repair bill is huge.
EDIT - HP3585A still available refurbished ($3500 from Aglient, I'm seriously tempted). 1Meg input as well as 50/75 Ohms very useful as well as 7nV/rt-Hz noise floor (incredible mixer).
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"There are no perversions of Fourier theory just people who don't understand it."
The equation for the Fourier Transform gives the increment for time as dt, the increment for frequency for the inverse transform as d(2*pi*f), in other words infinitesmally small. As an integral, delta f and delta t approach zero in the limit. What differs from that is a perversion of the theory. The theory makes no allowance for non continuous sweeps for non periodic functions.
"I fight with customers who want to do full power frequency response with them all the time. The amplifier output is looking like a tri-wave and the analyzer gives only the amplitude of the fundamental this makes for physically nonsensical graphs (some even go on the datasheets)."
There is a direct correlation between FR and square wave response. If the output at full power looks like a triangle wave and the test equipment is functioning properly, it's because the amplifier's performance stinks. In all likelihood it has an inadequate power supply whose series impedence rises sharply with decreasing frequency limiting low frequency output leading to low fall time on the lagging edge and its high end is miserable leading to poor rise time on the leading edge. Full power testing is the only way to judge what an amplifier is likely to do in real world conditions. 1 watt testing might have been fine in the 1930s when 3 watts was high power and all FR curves looked like plans for a roller coaster but it is all but worthless today. An amplifier that does not have ruler flat FR at 1 watt should be exempted from further testing unless 1 watt is all that is required of it. The entire idea of TIM came about because FR testing is performed at low output levels. The concept is similar to gain bandwidth product. As power output increases, bandwidth often decreases to an unacceptable degree. Low power testing doesn't show that. Full power testing separates the champions from the wanabees. I'm sure people who sell overpriced chintzy amplifiers with chintzy power supplies that don't perform well hate that.
If you can't hear sine waves over 20 khz, reproducing sounds above that frequency is a waste of effort. That is the inevitable conclusion of Fourier's theorem. In fact it can be worse than useless. While it offers nothing of benefit, it may create problems in the audible range that wouldn't otherwise exist. The only difference between the snake oil that says it matters and all of the other snake oil in this industry is the degree of sophistication of the victims it is targeted at.
oh nonono!
In all studies done on distortion perception the third is much more recognizable than the second. Numbers varies in the around of 1% for hd2 and 0.1% for hd3. That's ten times less.
I personally think that the claims for such high tolerance for hd2 are optimistic, but that is. The proposed wthd was weighted too lightly in my opinion. Anyway for this reason and for subjective listening tests as well, I prefer designs with a simple and monotonically decreasing harmonic spectra.
Frankly I don't get the moral indignation. I don't see weight of "inevitable conclusion of Fourier's theorem". I thought the beauty of Fourier's theorm is the duality of time and frequency domain. He could care less about what frequency response people want in their music. Frankly I've never been able to hear a 15kHz brickwall filter in the path.
I think there are a few people here that might say an amplifier that falls apart immediately after 20kHz is likley to have some "problems in the audible range that wouldn't otherwise exist". Chip amps ahoy, even they do considerably better than that.
The theoretically required limit is from zero to full output and from full output to zero in one forty-thousandth of a second. In the real world it is much less than that since there is no music that has a 20 khz full burst. Well maybe 11 khz from a crash cymbal though but usually not to full output. Someone got insulted when I pointed this out saying they didn't need to be shown the calculations . That's when I pointed out that RBCD standards exceed this for the maximum dynamic range of all live music by a very healthy margin. It also points out the absurdity of requiring phono cartridges to have a response extended beyond 20 khz unless you are going to use them to play CD-4 recordngs where the outband signals for the rear channels are above 20 khz. Any ultrasonic signal that interferes with sound in the audible ranged does it by creating intermodulation sum and difference product signals. That is reason enough to filter them out. As for RS $1 cables creating noise at -120 db on the seventh harmonic of 5 khz, I'll take my chances. If -120 db isn't good enough, chances are -135 db that the high priced cable exhibits won't be either.
If I could only get one spec for an amplifier to judge it by, it would be the weight of the power transformer. Second would be the size of the filter capacitors. IMO many used in consumer products are undersized to save money. Recently I had to repair my HK Citation 11 preamp whose 1000 mfd 100v electrolytic finally gave up the ghost. I like it because it has a built in 5 band graphic equalizer and I only paid $50 for it. I didn't have one handy so I substituted two 4800mfd 75 volt caps wired in series for 2400 mfd. I think it works better than it ever did but I have no way to be sure of that. It might be exacty the same only I don't remember and have no way to find out.
There are plenty of examples of amplifiers that can't reproduce a 20V peak to peak square wave at 10kHz but are fine at 100mV. It's a mathematical fact only for a linear system. If I collapse a cantiliver or push a driver out of its surround they are no longer linear. There are amplifiers that ring at square wave peaks under load due to some internal mis-behavior and show no small signal peaking even with the same load.
I made no mistake and nothing needs correcting. You continue to not qualify your statements with enough precision or maybe you just think we are all idiots and not worth it.
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You just described a tri-wave out, so now it's OK? 2V/usec or so for 100W amp is pretty marginal what do you save by designing with so little headroom?
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There's actually a mistake there. Assuming a 44k1 sample rate, the highest slew rate will be negative full output (not zero) to positive full output in one sample time (23uS). Any normal topology amp (blameless style with LTP input stage for example) which is at the slew rate limit with such a signal is going to have a fairly horrible figure for THD20 owing to IPS non-linearity.
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