Interpretation of Square wave response

[murphyslabrat]

So at Headphone.com, they have a feature where you can compare detailed data on most of the headphones on a graph, including frequency response arcs, distortion products, impedance vs. frequency, and square wave response. Most of these are self explanatory, but I don't get the last one.

First, what is a square wave? I am assuming that it's a waveform with a steady amplitude across the duration of the tone, but I don't know for sure.

Then, the data is all over the place, so what am I watching for? Is it a measurement of delay in the response? Is it a measurement of the ability of the elements to maintain a certain amplitude? Is it the ease with which it conducts alien's mind-reading rays? How do I use it?

 

[Born2bwire]

http://en.wikipedia.org/wiki/Square_wave

A square wave has infinite bandwidth and can be used to give an idea of the frequency response and the damping of the system.

 

[CycloWizard]

A square wave is a step up followed by a step down. It is a good way to look at the inductance and time constants of a system.

 

[Paperdoc]

Normal sound is composed of sine waves. In an electrical circuit the voltage (or current, depends what you examine) varies smoothly up and down - you've probably seen these graphs - and the resulting sound put out by a speaker ideally will reproduce this variation in terms of pressure waves in the air that your ear can hear. A square wave, on the other hand, jumps instantly from the maximum (+) voltage to the minimum (-) voltage and then back again instantly. The simplest of these, the ones used for the test you are looking at, are "50% square waves" - that is, they spend exactly half the time in the + voltage region, and half the time in the - region, with instantaneous changes between. The "baseline" is exactly half way between the top and bottom voltages. The frequency of a square wave can be anything you like, just like a sine wave, so you can make a square wave with the same fundamental frequency as a sine wave.

What is special about square waves is that, from the perspective of a mathematical model, it is actually composed of a summation of an infinite series of pure sine waves, each of which is an odd-numbered multiple of the fundamental frequency. So passing a true square wave through a circuit or an earphone is equivalent to passing through it simultaneously a large range of frequencies. How the square wave gets distorted from its original shape tells us something about how the circuit or earphone reproduces all those frequencies.
1. If the square corners of the wave are simply rounded off, that indicates the device has low high-frequency performance.
2. If the square corners actually show overshoot and undershoot, or "ringing", the device is over-emphasizing the high frequencies.
3. If the flat top and bottom portions of the square wave are sloped back towards the baseline (the middle of the voltage range) , the device is not putting out enough bass frequency power.
4. If the flat portions are sloped farther away from the baseline, the bass frequencies are being overemphasized.
5. If the flat portion is not merely sloped, but actually curved down towards the baseline, then there is quite poor reproduction of the lowest bass frequencies. In the website you mentioned this is seen in the special curves for a 50 Hz square wave. That's a very low frequency, and no real speaker of earphone will do a really good job here. The curves they show typically have some of this curved sag in the 50 Hz square wave test. The point is to compare different earphones and see which is more severe in its low-frequency fall-off.

 

[murphyslabrat]

So, basically it is measuring the attack and fade of a 50hz and 500hz tone?

 

[bobsmith1492]

No, it's looking at the frequency response.

For a 50Hz square wave, you can check the response at all the odd multiples of the basic frequency (50Hz):

- 50
- 150
- 250
- 350

... and so on up.

Using a square wave is like applying a series of impulse responses: http://en.wikipedia.org/wiki/Impulse_response

Impulse responses are commonly used to check the frequency response of a system and square waves do the same thing, more or less (they don't have the entire range of frequency content like an impulse does).

 

[Paperdoc]

As bobsmith1492 says, the way the square wave is NOT square tells you about the frequency response of the system. In this case, the significant limiter in the "system" is the earphones under test, and the rest of the system is assumed to be "perfect".

Realize that a 500 Hz square wave will allow you to assess the frequency response at 500, 1500, 2500, 3500, 4500, 5500, ... etc frequencies. So that covers a lot of the main area for hearing, although it does not get you a good picture of the stuff over 10 KHz. On the other hand, it cannot tell you anything about frequencies under 500 Hz. So the second test does that for you. Not surprisingly, they show that a tiny device like an earphone trying to push large volumes of air is less successful that at higher frequencies.

An impulse test is another way to do this - it is like doing the first half of a square wave, but no more. That is, the signal instantaneously rises from zero to max in the + or Up or Out direction (speaker cone movement), and then stays there. The sensor measures the response over a VERY long time. Using Fourier Transform methods one can convert that data into a frequency response curve. A square wave is really a repeating sequence of impulse tests, but with two significant limits. One is that is does NOT wait for a VERY long time for data acquisition, and that limits the lowest frequency data that can be analyzed. The other is that it does repetitive tests, but in opposite directions. Although one often assumes the response will be the same no matter which way the signal changes, a square wave allows you to verify whether or not that is true. But the real advantage of a square wave is that it presents a repeating pattern, and we humans are almost pre-programmed to recognize repeat patterns and understand at least a part of what they tell us. So once we see and understand the details of the pattern, it is easier for us to compare those patterns to interpretation guidelines to get to the real information we want. In this case, it's frequency response.

 

[TecHNooB]

Thank you square wave for being such an easy signal to transform

 

[murphyslabrat]

So, I'm resuscitating an older thread, but I came up with another question: while most headphones appear to have a linear curve on the 50hz and 500hz square waves, some have non-linear responses. I am assuming this has no significance, am I correct?

 

[TuxDave]

So, I'm resuscitating an older thread, but I came up with another question: while most headphones appear to have a linear curve on the 50hz and 500hz square waves, some have non-linear responses. I am assuming this has no significance, am I correct?

It's strange how having a degree in engineering changes the way you read things. A linear response to me implies (one of many) that:

If
Input Wave1 ---> Output Wave1
and
Input Wave2 --> Output Wave2

Then applying both inputs at the same time will result in the sum of the two output waves. A basic linear system with a linear response.

However I doubt you're talking about that and you're basically saying that if you connect the dots between the the response at the two frequencies, it's a straight line vs a curved line? Can you provide a picture?

 

[Paperdoc]

In OP's Nov 12 post, he's talking about how to interpret Frequency Response curves. These actually are derived by running 50 Hz and 500 Hz square waves through the headphones and using Fourier Transforms on the results. This Frequency Response Curve really means: if you supply to the device (headphone in this case) a pure sine wave at a specified frequency, and with a signal peak-to-peak (or RMS) voltage at a fixed value for all test frequencies, what is the strength of the resulting output of the device (in this case, loudness of the sound)? The graph is just sound intensity output versus frequency of the input signal (at constant amplitude of the input signal). The ideal response curve is flat, which results in no emphasis or de-emphasis (weakness) of sound at any particular frequency compared to others. No device is ideal, and all devices fall off near each end of the frequency range.

An earphone that has significant boosts or low spots in the Frequency Response curve will alter the sound, compared to what it should be. Weak response below 100 Hz will reduce all the bass notes, and most small speakers and earphones have this problem - that is why in multi-speaker systems there is a dedicated subwoofer unit that has great low-frequency response and poorer elsewhere, combined with a crossover network in the speaker / amplifier circuits that directs only low frequencies to the subwoofer, middle frequencies to the midrange speakers, and very high frequencies to "tweeters". Headphones don't usually have multi-speaker units and can't do this. One thing they can do, though, to compensate, is sealing to the head. If the small air space between earphone and ear can be "sealed", most of the air pressure pulses created by the earphone will actually reach the eardrum, and this is especially important for low frequencies.

Reduced output in the frequencies above 5 KHz make the fine details of the music less clear and reduces the "crispness" of the sound. For those who can remember enough, compare AM radio quality to FM radio. By design, AM radio transmitters always cut off ALL frequencies above 5 KHz (for bandwidth reasons), which is why people think FM sounds so much better.

 

[William Gaatjes]

So, basically it is measuring the attack and fade of a 50hz and 500hz tone?

As Paperdoc and Bobsmith have explained it is about harmonics.

You have the fundamental frequency f which can be 50 Hz.
Then you have the harmonics which are the multiple frequencies of the fundamental frequency f.

50 Hz ,100Hz, 150Hz, 200Hz , etc.

50 Hz is the first harmonic or base frequency or fundamental frequency.
100 Hz is the second harmonic.
150 Hz is the third harmonic.


As explained, A squarewave is build up of odd harmonics.

f + 3f +5f, etcetera.

A triangle is also build up of odd harmonics. EDIT : corrected this.

f + 3f + 5f, etcetera. But the harmonics drop of faster.

A sawtooth for example is build up of even and odd harmonics.

f + 2f + 3f, etcetera.

Now there is one thing i did not see mentioned.
The amplitude of each harmonic decreases as well with the increasing number of n*f. It does not do this in a linear fashion And Joseph Fourier has dedicated part of his life in solving the math.

It is a bit of math, but it is repetitive. Once you see it in your mind, it gets easy.

http://en.wikipedia.org/wiki/File:Fourier_Series.svg


This applets gives some idea .
http://www.eecircle.com/applets/001/001.html
EDIT : Not the best applet i have discovered.

 

[toslat]

The Fourier series of a triangular waveform is also made up of odd harmonics. http://mathworld.wolfram.com/FourierSeriesTriangleWave.html

The Fourier coefficients for a square wave are proportional to 1/n,where n is the order of the harmonic.

 

[William Gaatjes]

The Fourier series of a triangular waveform is also made up of odd harmonics. http://mathworld.wolfram.com/FourierSeriesTriangleWave.html

Indeed. I guess i am confused with another signal.

The Fourier coefficients for a square wave are proportional to 1/n,where n is the order of the harmonic.

True.
For everybody who want to play around, i found a fun applet.

An java applet that allows full manipulation with sound.

http://www.falstad.com/fourier/

 

[uclabachelor]

Feeding a square wave into an audio amplifier (or any linear system for that matter) tests a whole slew of characteristics such as stability under various impedances (capacitive, inductive, resistive, or combination of the three), frequency response, and slew rate.

Frequency response can be estimated from the rise time of resulting output wave.

Stability can be estimated from the amount of "ringing", undershoot, and overshoot.

Slew rate can be measured by taking delta V / delta t over a linear portion of the rise/fall edge of the output wave.

You can also get steady state errors from a step input, but for audio applications, it's assumed to be 0 because if it isn't zero, you'd be blowing speakers.