Aperture Effect In Sampling Pdf

  

Aperture is one of the three factors that create an exposure. Understanding the aperture settings makes getting to grips with taking an evenly exposed photo a lot easier.

Aperture effect The amplitude of the flat top signal must be constant, but sometimes it is not constant due to the high frequency roll off of the sampling signal. This results in the attenuation in the high frequency part of the message spectrum.

Feb 20, 2017  After watching this, your brain will not be the same Lara Boyd TEDxVancouver - Duration: 14:25. TEDx Talks 22,921,547 views. Sampling and Aliasing With this chapter we move the focus from signal modeling and analysis, to converting signals back and forth between the analog (continuous-time) and digital (discrete-time) domains. Back in Chapter 2 the systems blocks C-to-D and D-to-C were intro. Application Note AD-03 Effects of Aperture Time and Jitter in a Sampled Data System Mark Sauerwald. To get an idea of what effect this has on the sampling. Sampling is an important technique for waveform. Acquisition, but high-frequency sampling is adversely affected by sampling circuit non-idealities such as finite aperture time [1-6]. This paper discusses the effect of finite aperture time, the lowpass action of an RC sampling circuit modeled by a switch with. AD-03 Effects of Aperture Time and Jitter in a Sampled Data. Aperture effects may be the dominant source of noise in. In the sampling instant or aperture jitter. In flat top sampling,due to the lengthening of the sample, amplitude distortion as well as adelay of T/2 was introduced.This distortion is referred to as Aperture effect. Post navigation 700+ REAL TIME.NET Interview Questions and Answers Pdf →.

Aperture Effect In Sampling Pdf File

Using different aperture also opens up more creative avenues through unique effects. This post will teach you what they are and how to use them to your advantage.

Step 5 – What Is Aperture?

The best way to understand the aperture definition is to think of it as the pupil of an eye. The wider it gets, the more light it lets in.

Together, the aperture settings, shutter speed, and ISO produce an exposure. The diameter of the aperture size changes, allowing more or less light onto the sensor. This depends on the situation and the scene being photographed.

Creative uses of different aperture sizes and their consequences are tackled in Step 4. Put simply, when talking about light and exposure, wider aperture settings allow more light and narrower ones allow less.

Aperture can be confusing. Some people will say a wide or narrow aperture, but others might say a large aperture. What is the difference? A wide aperture refers to the wide opening in the lens, where f/1.2-f/2.4 is being discussed.

A large aperture refers to the number of f/stop, where f/32 or f/22 is being discussed. A low aperture and wide aperture are the same things – one talks about the size of the number and the other relates to the size of the opening.

Step 4 – How Is Aperture Measured and Changed?

Aperture size is measured using something called the f-stop scale. On your digital camera, you’ll see ‘f/’ followed by a number. This f-number denotes how wide the aperture is. The size affects the exposure and depth of field (also tackled below) of the final image.

What may seem confusing is that the lower the number, the wider the aperture. This means that your camera aperture settings will be wide open at a smaller f-stop number, like f/1.4 (maximum aperture).
At higher numbers, like f/16 or f/22, you’ll get a narrow aperture.

Why a low number for a high aperture? The answer is simple and mathematical, but first, you need to know the f-stop scale.

The scale is as follows: f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22.

The most important thing to know about these numbers is this; as the numbers rise, the aperture settings decrease to half its size. Half meaning that it allows 50% less light through the lens.

This is because the numbers come from an equation used to work out the size of the aperture setting from the focal length. You’ll notice, on modern day cameras, that there are aperture settings in-between those listed above.

These are 1/3 stops, so between f/2.8 and f/4 for example, you’ll also get f/3.2 and f/3.5. These are just here to increase the control that you have over your settings.

Now things begin to get a little harder. If you get confused, skip to Step 3 as the most important part has been covered.

For example, say you have a 50mm lens with an aperture setting of f/2. To find the width of the aperture, you divide the 50 by the 2, giving you a diameter of 25mm.

Then take the radius, multiply it by itself (radius squared) and multiply that by pi. The whole equation looks something like this: Area = r²*pi.

Here Are a Few Examples:

A 50mm lens at f/2: 50mm/2 = a lens opening 25mm wide. Half of this is 12.5mm and using the equation above (pi * 12.5mm²) we get an area of 490mm².

A 50mm lens at f/2.8: 50mm/2.8 = a lens opening 17.9mm wide. Half of this is 8.95mm and using the equation above (pi * 8.95mm²)we get an area of 251.6mm².

Now, it doesn’t take a genius to work out that half of 490 is less than 251 – this is because the numbers used are rounded to the nearest decimal point. The area of f/2.8 will still be exactly half of f/2

Step 3 – How Does Aperture Affect Exposure?

Before we talk about anything else, let’s look at the exposure triangle.

The change in aperture size correlates with exposure. The larger the aperture size, the more exposed the photo will be. The best way to demonstrate this is by taking a series of photos and keeping everything constant with the exception of the aperture.

All the images in the slideshow below were taken at ISO 200, 1/400 of a second and without a flash. Only the aperture size changes throughout.

This set of photos was taken before the recent purchase of my f/1.4 so the photos are in the following order: f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22.


A good way to see the changing size of the aperture is to look at the size of the out of focus white circle at the bottom left of the image. The main creative effect of aperture, however, isn’t exposure, but depth of field.

Step 2 – How Does Aperture Affect Depth of Field?

Now, the depth of field is a big topic. For now, I shall summarize it by saying that it is all about the distance at which the subject will stay in focus in front of and behind the main point of focus.

Aperture Effect In Sampling Pdf

In terms of how the depth of field is affected by aperture settings, the wider the aperture setting (f/1.4), the shallower the depth of field. The narrower the aperture size (f/22), the deeper the depth of field.

Before I show you a selection of photos taken at different apertures, take a look at the diagram below. If you don’t understand exactly how this works, it doesn’t matter too much.

For now, it’s important for you to know the effects.

Here is an example of a photo taken at f/1.4. With the subject moving away from the lens, it’s easy to see the effect that the shallow DoF has on the photo.


As mentioned, here’s a selection of photos all taken on aperture priority mode. The exposure remains constant and the only changing variable is the aperture.

The photos below are in this order: f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22. Notice how the depth of field increases every time the aperture size is decreased.


Step 1 – What Are the Uses of Different Apertures?

The first thing to note is that there are no rules when it comes to choosing an aperture. It depends greatly on whether you are going for artistic effect or to accurately balance the light in a scene.

To best make these decisions, it helps to have a good knowledge of traditional uses for the different aperture listed below.

  • f/1.4 – This is great for low light situations. It also gives a shallow DoF. Best used on shallow subjects or for a bokeh effect.
  • f/2 – This range has much the same uses, but an f/2 lens can be picked up for a third of the price of an f/1.4 lens.
  • f/2.8 – Still good for low light situations, but allows for more definition in facial features due to a deeper DoF. Good zoom lenses usually have this as their widest aperture.
  • f/4 – Autofocus can be temperamental. This is the minimum aperture setting you’d want to use for portraits in decent lighting. You risk the face going out of focus with wider apertures.
  • f/5.6 – Good for photos of two people but not very good in low light conditions though. Here, use a bounce flash.
  • f/8 – This is good for large groups as it will ensure that everyone in the frame remains in focus.
  • f/11 – More often than not, here is where your lens will be at its sharpest. Perfect aperture for portraits.
  • f/16 – Shooting in the sun requires a small aperture, making this a good ‘go-to’ point for these conditions.
  • f/22 – Best for landscapes where noticeable detail in the foreground is required.

As I said before, these are only guidelines. Now that you know exactly how the aperture setting will change a photo, you can experiment yourself and have fun with it!

You think you know everything about photography? Check out our new post to see if you’re a photography nerd next!

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There are three types of sampling techniques:

  • Impulse sampling.

  • Natural sampling.

  • Flat Top sampling.

Impulse Sampling

Impulse sampling can be performed by multiplying input signal x(t) with impulse train $Sigma_{n=-infty}^{infty}delta(t-nT)$ of period 'T'. Here, the amplitude of impulse changes with respect to amplitude of input signal x(t). The output of sampler is given by

$y(t) = x(t) ×$ impulse train

$= x(t) × Sigma_{n=-infty}^{infty} delta(t-nT)$

$ y(t) = y_{delta} (t) = Sigma_{n=-infty}^{infty}x(nt) delta(t-nT),..,.. 1 $

To get the spectrum of sampled signal, consider Fourier transform of equation 1 on both sides

$Y(omega) = {1 over T} Sigma_{n=-infty}^{infty} X(omega - n omega_s ) $

This is called ideal sampling or impulse sampling. You cannot use this practically because pulse width cannot be zero and the generation of impulse train is not possible practically.

Natural Sampling

Natural sampling is similar to impulse sampling, except the impulse train is replaced by pulse train of period T. i.e. you multiply input signal x(t) to pulse train $Sigma_{n=-infty}^{infty} P(t-nT)$ as shown below

The output of sampler is

$y(t) = x(t) times text{pulse train}$

$= x(t) times p(t) $

$= x(t) times Sigma_{n=-infty}^{infty} P(t-nT),..,..(1) $

The exponential Fourier series representation of p(t) can be given as

$p(t) = Sigma_{n=-infty}^{infty} F_n e^{j nomega_s t},..,..(2) $

$= Sigma_{n=-infty}^{infty} F_n e^{j 2 pi nf_s t} $

Where $F_n= {1 over T} int_{-T over 2}^{T over 2} p(t) e^{-j n omega_s t} dt$

$= {1 over TP}(n omega_s)$

Substitute Fn value in equation 2

Aperture Effect In Sampling Pdf

$ therefore p(t) = Sigma_{n=-infty}^{infty} {1 over T} P(n omega_s)e^{j n omega_s t}$

$ = {1 over T} Sigma_{n=-infty}^{infty} P(n omega_s)e^{j n omega_s t}$

Substitute p(t) in equation 1

$y(t) = x(t) times p(t)$

$= x(t) times {1 over T} Sigma_{n=-infty}^{infty} P(n omega_s),e^{j n omega_s t} $

$y(t) = {1 over T} Sigma_{n=-infty}^{infty} P( n omega_s), x(t), e^{j n omega_s t} $

To get the spectrum of sampled signal, consider the Fourier transform on both sides.

$F.T, [ y(t)] = F.T [{1 over T} Sigma_{n=-infty}^{infty} P( n omega_s), x(t), e^{j n omega_s t}]$

$ = {1 over T} Sigma_{n=-infty}^{infty} P( n omega_s),F.T,[ x(t), e^{j n omega_s t} ] $

According to frequency shifting property

$F.T,[ x(t), e^{j n omega_s t} ] = X[omega-nomega_s] $

$ therefore, Y[omega] = {1 over T} Sigma_{n=-infty}^{infty} P( n omega_s),X[omega-nomega_s] $

Flat Top Sampling

Aperture Effects On Images

During transmission, noise is introduced at top of the transmission pulse which can be easily removed if the pulse is in the form of flat top. Here, the top of the samples are flat i.e. they have constant amplitude. Hence, it is called as flat top sampling or practical sampling. Flat top sampling makes use of sample and hold circuit.

Theoretically, the sampled signal can be obtained by convolution of rectangular pulse p(t) with ideally sampled signal say yδ(t) as shown in the diagram:

i.e. $ y(t) = p(t) times y_delta (t), .. , ..(1) $

Special

To get the sampled spectrum, consider Fourier transform on both sides for equation 1

$Y[omega] = F.T,[P(t) times y_delta (t)] $

By the knowledge of convolution property,

$Y[omega] = P(omega), Y_delta (omega)$

Here $P(omega) = T Sa({omega T over 2}) = 2 sin omega T/ omega$

Nyquist Rate

It is the minimum sampling rate at which signal can be converted into samples and can be recovered back without distortion.

Nyquist rate fN = 2fm hz

Nyquist interval = ${1 over fN}$ = $ {1 over 2fm}$ seconds.

What Is Aperture Effect In Sampling

Samplings of Band Pass Signals

In case of band pass signals, the spectrum of band pass signal X[ω] = 0 for the frequencies outside the range f1 ≤ f ≤ f2. The frequency f1 is always greater than zero. Plus, there is no aliasing effect when fs > 2f2. But it has two disadvantages:

  • The sampling rate is large in proportion with f2. This has practical limitations.

  • The sampled signal spectrum has spectral gaps.

To overcome this, the band pass theorem states that the input signal x(t) can be converted into its samples and can be recovered back without distortion when sampling frequency fs < 2f2.

Aperture Effect In Sampling Pdf Download

Also,

$$ f_s = {1 over T} = {2f_2 over m} $$

Where m is the largest integer < ${f_2 over B}$

and B is the bandwidth of the signal. If f2=KB, then

$$ f_s = {1 over T} = {2KB over m} $$

For band pass signals of bandwidth 2fm and the minimum sampling rate fs= 2 B = 4fm,

the spectrum of sampled signal is given by $Y[omega] = {1 over T} Sigma_{n=-infty}^{infty},X[ omega - 2nB]$