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From Wikipedia

Square wave

A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels.

Origins and uses

Square waves are universally encountered in digital switching circuits and are naturally generated by binary (two-level) logic devices. They are used as timing references or "clock signals", because their fast transitions are suitable for triggering synchronous logic circuits at precisely determined intervals. However, as the frequency-domain graph shows, square waves contain a wide range of harmonics; these can generate electromagnetic radiation or pulses of current that interfere with other nearby circuits, causing noise or errors. To avoid this problem in very sensitive circuits such as precision analog-to-digital converters, sine waves are used instead of square waves as timing references.

In musical terms, they are often described as sounding hollow, and are therefore used as the basis for wind instrument sounds created using subtractive synthesis. Additionally, the distortion effect used on electric guitars clip the outermost regions of the waveform, causing it to increasingly resemble a square wave as more distortion is applied.

Simple two-level Rademacher functions are square waves.

Examining the square wave

In contrast to thesawtooth wave, which contains all integer harmonics, the square wave contains only odd integer harmonics.

Using Fourier series we can write an ideal square wave as an infinite series of the form

\begin{align} x_{\mathrm{square}}(t) & {} = \frac{4}{\pi} \sum_{k=1}^\infty {\sin{\left ((2k-1)2\pi ft \right )}\over(2k-1)} \\ & {} = \frac{4}{\pi}\left (\sin(2\pi ft)+{1\over3}\sin(6\pi ft)+{1\over5}\sin(10\pi ft) + \cdots\right ). \end{align}

A curiosity of the convergence of the Fourier series representation of the square wave is the Gibbs phenomenon. Ringing artifacts in non-ideal square waves can be shown to be related to this phenomenon. The Gibbs phenomenon can be prevented by the use of σ-approximation, which uses the Lanczos sigma factors to help the sequence converge more smoothly.

An ideal square wave requires that the signal changes from the high to the low state cleanly and instantaneously. This is impossible to achieve in real-world systems, as it would require infinite bandwidth.

Real-world square-waves have only finite bandwidth, and often exhibit ringing effects similar to those of the Gibbs phenomenon, or ripple effects similar to those of the σ-approximation.

For a reasonable approximation to the square-wave shape, at least the fundamental and third harmonic need to be present, with the fifth harmonic being desirable. These bandwidth requirements are important in digital electronics, where finite-bandwidth analog approximations to square-wave-like waveforms are used. (The ringing transients are an important electronic consideration here, as they may go beyond the electrical rating limits of a circuit or cause a badly positioned threshold to be crossed multiple times.)

The ratio of the high period to the total period of a square wave is called the duty cycle. A true square wave has a 50% duty cycle - equal high and low periods. The average level of a square wave is also given by the duty cycle, so by varying the on and off periods and then averaging, it is possible to represent any value between the two limiting levels. This is the basis of pulse width modulation.

Characteristics of imperfect square waves

As already mentioned, an ideal square wave has instantaneous transitions between the high and low levels. In practice, this is never achieved because of physical limitations of the system that generates the waveform. The times taken for the signal to rise from the low level to the high level and back again are called the rise timeand thefall timerespectively.

If the system is overdamped, then the waveform may never actually reach the theoretical high and low levels, and if the system is underdamped, it will oscillate about the high and low levels before settling down. In these cases, the rise and fall times are measured between specified intermediate levels, such as 5% and 95%, or 10% and 90%. Formulas exist that can determine the approximate bandwidth of a system given the rise and fall times of the waveform.

Other definitions

The square wave has many definitions, which are equivalent except at the discontinuities:

It can be defined as simply the sign function of a sinusoid:

\ x(t) = \sgn(\sin(t))

which will be 1 when the sinusoid is positive, −1 when the sinusoid is negative, and 0 at the discontinuities. It can also be defined with respect to the Heaviside step functionu(t) or the rectangular function⊓(t):

\ x(t) = \sum_{n=-\infty}^{+\infty} \sqcap(t - nT) = \sum_{n=-\infty}^{+\infty} \left ( u \left(t - nT + {1 \over 2} \right) - u \left(t - nT - {1 \over 2} \right) \right )

T is 2 for a 50% duty cycle. It can also be defined in a piecewise way:

\ x(t) = \begin{cases} 1, & |t| < T_1 \\ 0, & T_1 < |t| \leq {T \over 2} \end{cases}


\ x(t + T) = x(t)

From Yahoo Answers

Question:Which of the following is not a characteristic of a sound wave? A. It transfers energy by moving the medium perpendicular to the motion of the wave. B. It transfers energy by moving the medium parallel to the motion of the wave. C. It is a mechanical wave. D. It is longitudinal.

Answers:A Sound travels by causing molecules to vibrate back and forth in the direction of the sound wave (parallel to the direction the sound travels) It's a mechanical wave b/c it must have a medium to travel through (can't travel through a vacuum). Longitudinal b/c it doesn't have crests or troughs.

Question:I am into corporate banking, but according to an investment banker today, the financial sector is going down hill and once it has recovered, they will not be employing as many people as they used to. In order to secure a future career, I would like to know what other jobs possess the following charcterisitics: Is Challenging Problem solving (probably the second most important) Structured but has variation Nothing legal Mentally and intellectually stimulating Personal, mental and skill development Promotional prospects Progress/get promoted via how much you learn and do as opposed to the number of years of experience you have Uses computers Require maths (probably the most important of them all) Problem solving and reasoning Significant contribution to company and/or to society Allows for integrity - I want to work in a job where I can be honest Professionalism No politics (including office politics, it just renders me from contributing the best I can for the organisation I work for) Allows for communication and teamwork Prioritise on the activities that adds value- little menial tasks Assess you on skills and not on your ability to get to know the top people Isn't too competitive - some are so competitive that people will go through any means (no matter how unethical) to get to the top teaches you how businesses work and what the processes and requirement for success are I don't care how much work it takes to get promoted or how long the hours are, as long as the job is the sort that interests me. I have a degree in Accounting with Management and I am doing a PGDip in Economics with intention of doing a MSc in Economics and Finance. I am also passionate about economics and finance. If there are any jobs in the private sector with these sort of characterisitics and requires those sort of skills set, please state them It's scary to get yourself into a job that doesn't allow you to get promoted, doesn't teach you anything new, doesn't assess you on your skills related to work, have so much politics you just end up getting pushed around, drains you and bores you out of your mind. In such a job, you are nothing more than a robot droning your life away and the only thing that makes you take the job and endure it is because of money and the fear of ending up with nothing if you walk out of the door. I don't want that (and I don't think anyone else would either, but I am determined to do something about it). Don't say go to prospects.ac.uk. I have been on there and apparently corporate banking is the only thing that matches this criteria Any unhelpful comments will get thumbed down Cheers Thanks..she hulk... but I only want suggestions in the private sector - personal reasons

Answers:have you considered lecturing in economics / accounting / finance at a further education college? the money may not be as good as you are currently on (i earn about 35k per annum) but it is a challenging job, enables you to use your skills and pass these on, requires you to keep your own skills updated and think creatively and out of the box to pass on the knowledge in ways that are motivating. i moved from social work to education and it is the best move i made - good lecturers are hard to find and teh job is demanding but infinitely rewarding. also the ten weeks paid holidays every year are a very nice bonus! good luck in your career search whatever route you decide to take

Question:i'm confused.

Answers:Only the spelling. They are the same. If I saw term "acoustic wave" used, I would assume that the writer was considering the wave in a much more technical sense: much more precise in terms of the actual waveform and other characteristics of the wave at a detailed level. Like: how much energy will a certain acoustic wave, with frequency n,and amplitude y, dissipate in glass. if I saw the term "sound wave" used, I might expect a more superficial usage: like, how fast will the sound wave travel in glass? They could be used interchangeably, but usually, they are not.

Question:My science class is currently studying Earthquakes and Seismic waves etc. I have two questions left to answer and I can't find the answers. Can anyone help? 1. What types of actions are caused by the different types of (seismic) waves? 2. Where do the different seismic waves originate? Be able to describe/recognize the characteristics of each -- including the type of (seismic) wave it is (longitudinal/compression, transverse, etc)

Answers:see wiki.

From Youtube

Standing Waves :Standing WavesWe observe a very important case of interference when two counter-running plane waves of same amplitude superpose. The resulting oscillatory process is called a standing wave. In practice standing waves occur when waves are reflected from barriers. The wave which falls on the barrier and the oncoming reflected wave superpose thus forming a standing wave. Here frequency, phase, and coefficient of wave attenuation in the place of reflection are very important factors. Oscillations on each point of a standing wave have the same frequency with counter-running waves. Such points are called antinodes of a standing wave. The points where oscillation amplitude turns into zero are called standing-wave nodes. The surrounding points in the nodes do not oscillate. Every wave process with propagation of disturbance can be accompanied by the occurrence of standing waves. They may occur not only in gaseous, fluid, or solid environments but also in vacuum when electromagnetic disturbances are propagated and reflected. They may occur, for example, in long electric lines. A pure standing wave may exist only when there are no losses in the environment and the waves are fully reflected from the boundaries. Usually besides standing waves there are also progressive waves in the environment. They supply energy to the places where it is consumed and radiated. In optics it is also possible to establish a standing wave with visible maximums and minimums of an electric field. If the ...

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