The Pictorial Waveform Imaging Computer Science Essay

The pictural representation of the signifier or form of a moving ridge, obtained by plotting the amplitude of the moving ridge with regard to clip. There are an infinite figure of possible wave forms ( see illustration ) . One such wave form is the square moving ridge, in which a measure such as electromotive force alternately assumes two distinct values during reiterating periods of clip. Other wave forms of peculiar involvement in electronics are the sine moving ridge and rectified sine moving ridge, the proverb tooth moving ridge and triangular moving ridge, and the arbitrary wave-a recurrent wave form which takes on an arbitrary form over one complete rhythm ; this form is so repeated in consecutive rhythms

Wave form means the form and signifier of a signal such as a moving ridge traveling in a solid, liquid or gaseous medium.

In many instances the medium in which the moving ridge is being propagated does non allow a direct ocular image of the signifier. In these instances, the term ‘waveform ‘ refers to the form of a graph of the changing measure against clip or distance. An instrument called an CRO can be used to pictorially stand for the moving ridge as a repeating image on a CRT or LCD screen.

By extension of the above, the term ‘waveform ‘ is now besides sometimes used to depict the form of the graph of any changing measure against clip.

Some illustrations of moving ridge signifiers as follows

Triangular Wave forms

Square Wave forms

Sign Waves

Saw tooth Waveforms

Now we are traveling to briefly describe each of the wave forms.

Sign Waves

A moving ridge holding a signifier which, if plotted, would be the same as that of a trigonometric sine or cosine map. The sine moving ridge may be thought of as the projection on a plane of the way of a point traveling around a circle at unvarying velocity. It is characteristic of unidimensional quivers and unidimensional moving ridges holding no dissipation.

The sine moving ridge is the basic map employed in harmonic analysis. It can be shown that any complex gesture in a unidimensional system can be described as the superposition of sine moving ridges holding certain amplitude and stage relationships. The technique for finding these relationships is known as Fourier analysis

Basic Sign Wave

The footings defined below are needed to depict sine moving ridges and other wave forms exactly:

Time period ( T )

The period is the clip taken for one complete rhythm of a repeating wave form. The period is frequently thought of as the clip interval between extremums, but can be measured between any two corresponding points in consecutive rhythms.

Frequency

This is the figure of rhythms completed per second. The measurement unit for frequence is the Hz, Hz. 1A Hz = 1 rhythm per second.

Phase

A stage is one portion or part in repeating or consecutive activities or happenings logically connected within a greater procedure, frequently ensuing in an end product or a alteration. If two sine moving ridges have the same frequence and occur at the same clip, they are said to be in stage. On the other manus, if the two moving ridges occur at different times, they are said to be out of stage. When this happens, the difference in stage can be measured in grades, and is called the stage angle, .

Amplitude

The amplitude is the power of a signal. The greater the amplitude, the greater the energy carried.

HARMONICS OF SIGN WAVE

First of all we discuss that what harmonics is. A harmonic is a signal or beckon whose frequence is an built-in ( whole-number ) multiple of the frequence of some mention signal or moving ridge. The term can besides mention to the ratio of the frequence of such a signal or moving ridge to the frequence of the mention signal or moving ridge.

About all signals contain energy at harmonic frequences, in add-on to the energy at the cardinal frequence. If all the energy in a signal is contained at the cardinal frequence, so that signal is a perfect sine moving ridge. If the signal is non a perfect sine moving ridge, so some energy is contained in the harmonics.

In this first secret plan, we see the fundamental-frequency sine-wave of 50 Hz by itself. It is nil but a pure sine form, with no extra harmonic content. This is the sort of wave form produced by an ideal AC power beginning: ( Figure below )

Following, we see what happens when this clean and simple wave form is combined with the 3rd harmonic ( three times 50 Hz, or 150 Hz ) . Suddenly, it does n’t look like a clean sine wave any more: ( Figure below )

Sum of 1st ( 50 Hz ) and 3rd ( 150 Hz ) harmonics approximates a 50 Hz square moving ridge.

The rise and autumn times between positive and negative rhythms are much steeper now, and the crests of the moving ridge are closer to going level like a squarewave. Watch what happens as we add the following uneven harmonic frequence: ( Figure below )

Sum of 1st, 3rd and 5th harmonics approximates square moving ridge.

The most noticeable alteration here is how the crests of the moving ridge have flattened even more. There are more several dips and crests at each terminal of the moving ridge, but those dips and crests are smaller in amplitude than they were earlier. Watch once more as we add the following uneven harmonic wave form to the mix: ( Figure below )

Sum of 1st, 3rd, 5th, and 7th harmonics approximates square moving ridge.

Here we can see the moving ridge going flatter at each extremum. Finally, adding the 9th harmonic, the 5th sine moving ridge electromotive force beginning in our circuit, we obtain this consequence: ( Figure below )

Sum of 1st, 3rd, 5th, 7th and 9th harmonics approximates square moving ridge.

The terminal consequence of adding the first five uneven harmonic wave forms together ( all at the proper amplitudes, of class ) is a close estimate of a square moving ridge. The point in making this is to exemplify how we can construct a square wave up from multiple sine moving ridges at different frequences, to turn out that a pure square moving ridge is really tantamount to a series of sine moving ridges. When a square moving ridge AC electromotive force is applied to a circuit with reactive constituents ( capacitances and inductances ) , those constituents react as if they were being exposed to several sine moving ridge electromotive forces of different frequences, which in fact they are.

Representation of Sine Waves in Matlab

The basic MATLAB bid for bring forthing sinusoidal signal is:

A*sin ( w0*t + phi ) , Where phi is the stage displacement angle in radians.

MATLAB CODE OF SINE WAVE

End product OF SINE WAVE

A=4 ;

w0=20*pi ;

phi=pi/6 ;

t=0:0.0001: .5 ;

sine=A*sin ( w0*t + phi ) ;

secret plan ( T, sine )

Fig. Output of Sine Wave

SQUARE WAVE

The square moving ridge is a periodic wave form consisting of instantaneous passages between two degrees. The square moving ridge is sometimes besides called the Rademacher map. The square moving ridge illustrated above has period 2 and degrees and 1/2. Other common degrees for square moving ridges include and ( digital signals ) .

HARMONICS OF SQUARE WAVE

In contrast to the sawtooth moving ridge, which contains all whole number harmonics, the square moving ridge contains merely uneven whole number harmonics.

Using Fourier series we can compose an ideal square moving ridge as an infinite series of the signifier.

For a sensible estimate to the square-wave form, at least the cardinal and 3rd harmonic demands to be present, with the fifth harmonic being desirable. These bandwidth demands are of import in digital electronics, where finite-bandwidth parallel estimates to square-wave-like wave forms are used. ( The tintinnabulation transients are an of import electronic consideration here, as they may travel beyond the electrical evaluation bounds of a circuit or do a severely positioned threshold to be crossed multiple times. )

Representation OF SQUARE WAVE IN MATLAB

MATLAB CODE OF SQUARE WAVE

End product OF SQUARE WAVE

A=0.5 ;

w0=10*pi ;

rho=50 ;

t=0:0.00001:1 ;

sq=A*square ( w0*t, rho ) ;

secret plan ( T, sq )

axis ( [ 0 1 -1.1 1.1 ] )

TRIANGULAR WAVE

A trigon moving ridge is a non-sinusoidal wave form named for its triangular form.

Triangular moving ridge pictured in clip sphere.

HARMONICS OF TRIANGULAR WAVE

Like a square moving ridge, the trigon moving ridge contains merely uneven harmonics. However, the higher harmonics roll away much faster than in a square moving ridge ( relative to the reverse square of The harmonic figure as opposed to merely the opposite ) , and so its sound is smoother than a square moving ridge and is nearer to that of a sine moving ridge

It is possible to come close a trigon moving ridge with linear synthesis by adding uneven harmonics of the cardinal, multiplying every ( 4na?’1 ) Thursday harmonic by a?’1 ( or altering its stage by Iˆ ) , and turn overing off the harmonics by the reverse square of their comparative frequence to the fundamental.

This infinite Fourier series converges to the trigon moving ridge:

Representation OF TRIANGULAR WAVE IN MATLAB

MATLAB CODE OF TRIANGULAR WAVE

End product OF TRIANGULAR WAVE

degree Fahrenheit = 10000 ;

T = -1:1/fs:1 ;

x1 = tripuls ( t,20e-3 ) ;

subplot ( 211 ) , secret plan ( T, x1 ) , axis ( [ -0.1 0.1 -0.2 1.2 ] )

xlabel ( ‘Time ( sec ) ‘ ) ;

ylabel ( ‘Amplitude ‘ ) ;

rubric ( ‘Triangular Periodic Pulse ‘ )

SAWTOOTH WAVE

A wave form that increases linearly with clip for a fixed interval, returns suddenly to the original degree, and repeats the procedure sporadically, bring forthing a form resembling the dentition of a proverb.

HARMONICES OF SAWTOOTH WAVE

A sawtooth moving ridge ‘s sound is rough and clear and its spectrum contains both even and uneven harmonics of the cardinal frequence. Because it contains all the whole number harmonics, it is one of the best wave forms to utilize for synthesising musical sounds, peculiarly bowed threading instruments like fiddles and cellos, utilizing subtractive synthesis.

A sawtooth can be constructed utilizing linear synthesis. The infinite Fourier series

converges to an reverse sawtooth moving ridge. A conventional sawtooth can be constructed utilizing

In digital synthesis, these series are merely summed over Ks such that the highest harmonic, Nmax, is less than the Nyquist frequence ( half the sampling frequence ) . This summing up can by and large be more expeditiously calculated with a Fast Fourier transform. If the wave form is digitally created straight in the clip sphere utilizing a non-bandlimited signifier, such as Y = x – floor ( x ) , infinite harmonics are sampled and the ensuing tone contains aliasing distortio

Representation OF SAWTOOTH IN MATLAB

MATLAB CODE OF SAWTOOTH

End product OF SAWTOOTH WAVE

degree Fahrenheit = 10000 ;

T = 0:1/fs:1.5 ;

x1 = sawtooth ( 2*pi*50*t ) ;

subplot ( 211 ) , secret plan ( T, x1 ) , axis ( [ 0 0.2 -1.2 1.2 ] )

xlabel ( ‘Time ( sec ) ‘ ) ;

ylabel ( ‘Amplitude ‘ ) ;

rubric ( ‘Sawtooth Periodic Wave ‘ )

Equipments USED IN LABORATORY TO PERFORM CH-05

OSCILOSOPE

FUNCTION GENERATOR

SPECTRUM ANALYSER

OSCILOSCOPE

An CRO is a laboratory instrument normally used to expose and analyse the wave form of electronic signals. In consequence, the device draws a graph of the instantaneous signal electromotive force as a map of clip.

A typical CRO can expose jumping current ( AC ) or throbing direct current ( DC ) waveforms holding a frequence every bit low as about 1 Hz ( Hz ) or every bit high as several MHz ( MHz ) . High-end CROs can expose signals holding frequences up to several hundred GHzs ( GHz ) . The show is broken up into alleged horizontal divisions ( hor div ) and perpendicular divisions ( vert div ) . Time is displayed from left to compensate on the horizontal graduated table. Instantaneous electromotive force appears on the perpendicular graduated table, with positive values traveling upward and negative values traveling downward.

There are two types of CRO. Which are as follows.

Analogue Oscilloscope

Digital Oscilloscope

Analogue Oscilloscope

An parallel CRO plants by straight using a electromotive force being measured to an negatron beam traveling across the CRO screen. The electromotive force deflects the beam up and down proportionately, following the wave form on the screen. This gives an immediate image of the wave form.

Fig. 20 Analog Oscilloscope Block Diagram

Digital Oscilloscope

A digital CRO samples the wave form and uses an analogue-to-digital convertor ( or ADC ) to change over the electromotive force being measured into digital information. It so uses this digital information to retrace the wave form on the screen.

Fig. 21 Digital Oscilloscope Block Diagram

FUNCTION GENERATOR

A map generator is a piece of electronic trial equipment or package used to bring forth electrical wave forms. These wave forms can be either insistent, or single-shot in which instance some sort of triping beginning is required ( internal or external ) .

Another type of map generator is a sub-system that provides an end product proportional to some mathematical map of its input ; for illustration, the end product may be relative to the square root of the input. Such devices are used in feedback control systems and in linear computing machines.

TYPES OF FUNCTION GENERATOR

There are two types of map Generator.

Analogue

Digital

ANALOGUE FUNCTION GENERATOR

Analog map generators use a electromotive force controlled oscillator ( VCO ) to bring forth a triangular wave form of variable frequence. Sinusoidal wave forms and square moving ridges are generated from this.

DIGITAL FUNCTION GENERATOR

Digital generators use a digital to analogue convertor ( DAC ) to bring forth a moving ridge form from values stored in memory. Normally such generators merely offer sine and square waves up to the maximal generator frequence. Triangle moving ridges and other wave forms are limited to a much lower frequence.

SPECTRUM ANALYSER

A spectrum analyser or spectral analyser is a device used to analyze the spectral composing of some electrical, acoustic, or optical wave form. It may besides mensurate the power spectrum.

There are parallel and digital spectrum analysers:

An parallel spectrum analyser uses either a variable band-pass filter whose mid-frequency is automatically tuned ( shifted, swept ) through the scope of frequences of which the spectrum is to be measured or a ace heterodyne receiving system where the local oscillator is swept through a scope of frequences.

A digital spectrum analyser computes the distinct Fourier transform ( DFT ) , a mathematical procedure that transforms a wave form into the constituents of its frequence spectrum.

Some spectrum analysers ( such as Tektronix ‘s household of “ real-time spectrum analysers ” ) use a loanblend technique where the incoming signal is first down-converted to a lower frequence utilizing ace heterodyne techniques and so analyzed utilizing fast Fourier transmutation ( FFT ) techniques.

Types of Spectrum Analyzers

Analog Spectrum Analyzer

An parallel spectrum analyser uses either a variable set base on balls filter whose mid-frequency is automatically tuned ( shifted, swept ) through the scope of frequences of which the spectrum is to be measured or a ace heterodyne receiving system where the local oscillator is swept through a scope of frequences.

Digital Spectrum Analyzer

A digital spectrum analyser computes the Fast Fourier transform ( FFT ) , a mathematical procedure that transforms a wave form into the constituents of its frequence spectrum.

Some spectrum analysers use a loanblend technique where the incoming signal is first down-converted to a lower frequence utilizing ace heterodyne techniques and so analyzed utilizing FFT techniques.

9. Practical Consequence

Initial Set-up: degree Fahrenheit = 10 KHz SINE WAVE

Oscilloscope

Spectrum Analyzer

Explanation

Explanation

T = 50 Aµsec * 2 = 100 Aµsec

A = 50mV * 4 = 200 millivolt

degree Fahrenheit ( calculated ) = 1/T = 10 KHz

When frequence is ab initio set up at 10KHz, it is observed that spectrum is wider.

Change to: f = 5 KHz SINE WAVE

Oscilloscope

Spectrum Analyzer

Explanation

Explanation

T = 50 Aµsec * 4 = 200 Aµsec

A = 50mV * 4 = 200 millivolt

degree Fahrenheit ( calculated ) = 1/T = 5 KHz

If frequence is decreased to half than clip would go twice, provided amplitude remains changeless.

If frequence is decreased than bandwidth of the channel should besides be decreased. For e.g. , f = 2 KHz, T = 0.5 millisecond. When f = 4 KHz than T = 0.25 millisecond. In this manner bandwidth becomes less, because bandwidth is defined as “ differences of highest frequence and lowest frequence. ”

From the figure, it is observed that spectrum became sharper when frequence is decreased, provided amplitude is changeless.

Initial Set-up: degree Fahrenheit = 10 KHz SQUARE WAVE

Oscilloscope

Spectrum Analyzer

Explanation

Explanation

T = 50 Aµsec * 2 = 100 Aµsec

A = 50mV * 4 = 200 millivolt

degree Fahrenheit ( calculated ) = 1/T = 10 KHz

When frequence is ab initio set up at 10KHz, it is observed that spectrum is wider.

Change to: f = 5 KHz SQUARE WAVE

Oscilloscope

Spectrum Analyzer

Explanation

Explanation

T = 50 Aµsec * 4 = 200 Aµsec

A = 50mV * 4 = 200 millivolt

degree Fahrenheit ( calculated ) = 1/T = 5 KHz

If frequence is decreased to half than clip would go twice, provided amplitude remains changeless.

From the figure, it is observed that spectrum became sharper when frequence is decreased, provided amplitude is changeless.

Initial Set-up: degree Fahrenheit = 10 KHz TRIANGULAR WAVE

Oscilloscope

Spectrum Analyzer

Explanation

Explanation

T = 50 Aµsec * 2 = 100 Aµsec

A = 50mV * 5 = 250 millivolt

degree Fahrenheit ( calculated ) = 1/T = 10 KHz

When frequence is ab initio set up at 10KHz, it is observed that spectrum is wider.

Change to: f = 5 KHz TRIANGULAR WAVE

Oscilloscope

Spectrum Analyzer

Explanation

Explanation

T = 50 Aµsec * 4 = 200 Aµsec

A = 50mV * 5 = 250 millivolt

degree Fahrenheit ( calculated ) = 1/T = 5 KHz

If frequence is decreased to half than clip would go twice, provided amplitude remains changeless.

From the figure, it is observed that spectrum became sharper when frequence is decreased, provided amplitude is changeless.

Initial Set-up: degree Fahrenheit = 10 KHz SAWTOOTH WAVE

Oscilloscope

Spectrum Analyzer

Explanation

Explanation

T = 50 Aµsec * 2 = 100 Aµsec

A = 50mV * 5 = 250 millivolt

degree Fahrenheit ( calculated ) = 1/T = 10 KHz

When frequence is ab initio set up at 10KHz, it is observed that spectrum is wider.

Change to: f = 5 KHz SAWTOOTH WAVE

Oscilloscope

Spectrum Analyzer

Explanation

Explanation

T = 50 Aµsec * 4 = 200 Aµsec

A = 50mV * 5 = 250 millivolt

degree Fahrenheit ( calculated ) = 1/T = 5 KHz

If frequence is decreased to half than clip would go twice, provided amplitude remains changeless.

From the figure, it is observed that spectrum became sharper when frequence is decreased, provided amplitude is changeless.