Schneier on Security

Clive Robinson • September 13, 2017 11:01 AM

@ Rostislav,

To be precise, those systems are not listening for inaudible frequencies.

Actually they are at the input.

Most small surface area membrane microphones do not have a very good low frequency response. There are various ways to solve this, one is by acoustic matching the other is by a frequency response correcting circuit in the microphones detection circuit.

Because acoustic pipe engineering is not something that translates easily into the case of a phone or other hand held device the usual choice is to correct the frequency response of the membrane inside the microphone capsual by it’s detector circuit.

The frequency response of the membrane and that of the detector circuit will not be perfect inverses of each other thus you will get a flat frequency response across the entire audio band. It will be broadly flat between 300Hz and 4-5Khz which is generally more than sufficient for human speech. After 5KHz the frequency response will be not very flat and will almost certainly have peaks and roll offs. Thus the reality is that the microphone will have quite a poor high frequency roll off untill sufficiently above the Nyquist frequency of the sampling circuit.

The faithfulness the microphone will have to producing a sinewave out for a sinewave in is to do not just with the linearity of the detector amplifier but the mechanical characteristics of the membrane and it’s mountings. Whilst the human ear is relatively sensitive to differences in frequency it mainly can not pick up nonlinear behaviour in the response curve or any phase distortion either. Thus a pure sinewave can have a very high harmonic content and will tend to sound harsh or cold with odd harmonic distortion whilst warm with even harmonic distortion (which is why guitar amplifers based on Valves/Tubes sounded warmer a point not lost on drummer Jim Marshall and his guitarist customers).

There is a lot of myth about the Nyquist frequency, one of which is that it defines the maximum frequency that can be accepted by a sampling system. If people can be bothered to get a piece of graph paper out they can see that a sampling system will respond to frequences above the Nyquist frequence. It’s just that it will not respond to them in a linear way, and also it will fold the frequency of the signal around the sampling frequency in a process called “aliasing”. It’s just like an RF signal ina double balaced mixer in a Superhet radio (it’s also a similar reason you get the upper and lower sidebands on an AM signal). The simple averaged frequency response of a sampling system is quoted as “sinc(x) = sin x / x” [1] which you can draw out with the use of a calculator. From this it can be seen that a sinewave above the sampling frequency will appear at the output as being no different to a sinewave appropriatly below the sampling frequency.

Howrver there is also the “square law” to consider it is why you get harmonic distortion in systems. The most well known of which is the response of a semiconductor junction such as a diode that is used to “envelope demodulate” AM signals. What you have is the x^2 which in effect rectifies the input, and when the output is integrated by a low pass filter the modulating signal that is the envelope is recovered. As it is the envelope waveform not the carrier waveform it is “inband” to the following circuits.

[1] There are actually two sinc functions in regulat use, the unnormalised sin x / x and the normalised sin pi.x / pi.x

Clive Robinson • September 16, 2017 8:56 AM

@ Wael, Call me confused,

There’s a solution to this problem. It’s a Famous puzzle.

But how do you get two Bruces to stand on either side of a pair of doors? After all he has expressed a distinct dislike for both frontdoors and backdoors…

Clive Robinson • September 16, 2017 12:49 PM

@ Wael,

Which movie?

Do you mean,

Billy Clanton: Why, it’s the drunk piano player. You’re so drunk, you can’t hit nothin’. In fact, you’re probably seeing double.

Doc Holliday: I have two guns, one for each of ya.

If so It’ll get carved on your “………”

If not “I’ll have to redo my google fu”. I’m not keen on “Out West Westerns” there were way way to many dumb hold up the stagecoach plots. Appart from “Paint your Waggon” and “Support your local Sherif” which were both funny and “Blazing Saddles” which realy took the micky out of the Western genre I don’t watch them, to be honest they were like “Lassie films for wanabe men” and Jack London’s book “White Fang” did that wy way better.

But I do like “ScFi with a Western theme” like “FireFly” for instance, because atleast the scripts had some life in them.