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ESP 411 | Special Assignment Report | | Mark awarded | |

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Contents Table of Figures 3 Acronyms Used 3 PART 1 Filtering in the Frequency Domain 3 Introduction 3 Review of Prior Knowledge 4 Complex Numbers 4 Fourier series 4 Fourier Transform 4 Convolution Theorem 5 Overview 5 2-D FFT 6 DFT 6 IDFT 7 2-D FFT 7 Comparison with 1-D FFT 8 2-D FFT and Image Processing 8 Image Smoothing and Sharpening 9 Smoothing 9 Sharpening 11 Conclusion 13 PART 2 Application of Filtering in the Frequency Domain 13 Introduction 13 Gaussian Filter Theoretical Analysis 13 Gaussian Low Pass Filter 14 Gaussian High Pass Filter 14 Gaussian Filter Design 15 Practical Results 16 Conclusion 17 References 18

Table of Figures Figure 1: Input Signal Transformed to Frequency Domain 5 Figure 2: Flow Diagram of Filtering in the Frequency Domain 5 Figure 3: Spatial VS Frequency Domain 5 Figure 4: 2-D Sinusoidal Wave 7 Figure 5: Flow Diagram of Filtering in the Frequency Domain 9 Figure 6: Graphical Representation of an Ideal Low Pass Filter 10 Figure 7: Image that was smoothed 11 Figure 8: Graphical Representation of an Ideal High Pass Filter 11 Figure 9: Edges Clearly Shown before Pass Band Attenuation Edited 12 Figure 10: Final Result of an Image sharpened 12 Figure 11: Graphical Representation of a Gaussian Filter 13 Figure 12: Graphical Representation of a Gaussian Low Pass Filter 14 Figure 13: Graphical Representation of a Gaussian High Pass Filter 15 Figure 14: Original Image and its FFT 16 Figure 15: Smoothed Image and FFT 16 Figure 16: Edged Image and its FFT 17 Figure 17: Sharpened Image and its FFT 17

Acronyms Used 1-D | One dimensional | 2-D | Two dimensional | FT | Fourier transform | FFT | Fast Fourier transform | DFT | Discrete Fourier transform | IDFT | Inverse Discrete Fourier transform | HP | High Pass | LP | Low Pass | P | Power | GSM | Global systems for mobile communication |

PART 1 Filtering in the Frequency Domain

Introduction

This report will cover the topic of filtering in the frequency domain which is a very common image and signal processing technique. There will be an in depth study on filtering in the frequency domain, covering topics like 1-d FFT’s; 2-d FFT’s, image smoothing and image sharpening. In Part 2 a practical application is given on a Gaussian filtering technique that is designed to either smoothen or sharpen the image.

Review of Prior Knowledge

This section is purely to review basic knowledge of the Fourier series. The Fourier series can be used to illustrate any periodic function as the sum of sine and cosine values. Any non-Periodic function can be transformed into the Fourier series with the use of Fourier transforms (FT). There are continuous FT; Discrete FT and Single/multivariate FT.

Complex Numbers

From [5]

C=R+jI

C=Ccosθ+jsinθ

C= R2+ I2

Euler’s representation is:

C=Cejθ, ejθ=cosθ+jsinθ

Fourier series

From [5] ft= n=-∞∞cnej(2πnT)t cn= 1TT/2T/2f(t)×ej(2πnT)tdt

Fourier Transform

This is used to transform a continuous time/spatial domain signal into a frequency domain signal. Equation to convert to frequency domain is [5]:

Ift= Fμ= -∞∞f(t)×e-j2πμtdt

And transforming it back (the inverse Fourier transform)[5]: ft= I-1Fu= -∞∞F(μ)×ej2πμtdt

Figure [ 1 ]: Input Signal Transformed to Frequency Domain

The following image shows an input signal transformed to the frequency domain signal [8]:

Convolution Theorem

This theorem is very important as it will be used throughout the discussing and computing of filtering in the frequency domain. It states that multiplication in one domain is convolution in the other. The following is the equations used [5]. ft*ht= -∞∞f(τ)×ht- τdτ

Thus the Fourier transform is

Ift*ht=-∞∞f(τ)[-∞∞ht- τdt]dτ

And through reversing the order of integration you get

Ift*ht=F(μ)×H(μ)

This covers about most of the basic knowledge and theorems needed for filtering in the frequency domain. DFT, IDFT and 2-d Fourier transforms will be discussed further on.

Overview

One of the common signal (even image) processing techniques is filtering in the frequency domain. This will result in the signal being smoother or sharper; the signal can be de-blurred and even restored to previous state. Note that for images the FFT ‘scans’ over the image while splitting each part up into ‘frequencies’.

Figure [ 3 ]: Spatial VS Frequency Domain

Figure [ 2 ]: Flow Diagram of Filtering in the Frequency Domain

To be able to filter in the frequency domain the image must be transformed from the spatial domain into the frequency domain (via FFT). Then the resulting complex image must be must be multiplied with a chosen filter and the converted back into the spatial domain. The following figure and flow diagram will help clarify things [7].

Thus the image and filter is designed and their frequency domain is calculated through the use of:

Ift= Fμ= -∞∞f(t)×e-j2πμtdt

Keep in mind that the FFT used for image processing is going to be the 2-d FFT. This is because the image is 2 dimensional thus its FFT values will be stored in a 2-d array of values. The 2-d explanation will follow in the next section.

Then the two spatial domains must be convoluted together. But since it is easier to multiply two data sets than to convolute them, we decide to multiply them in frequency domain. This is the reason for the FFT in the previous step.

One can now view the processed image but take note it is still in frequency domain thus the FFT is transformed inversely to obtain final value ft= I-1Fu= -∞∞F(μ)×ej2πμtdt

The final steps to filter in the frequency domain are [6]: 1. Multiply the image/photo inputted by (-1)x+y ,this will help center the transform 2. Compute the 2-d DFT (F(u,v)) of the resulting image obtained prior. 3. Multiply the DFT with the filter, Hu,v=Fu,v×G(u,v) . 4. Calculate the 2-d IDFT transform, and obtain the real part, named Hx,y. 5. Finally multiply the result by (-1)x+y to obtain final image

2-D FFT

In frequency application on does not always get is I dimensional and periodic signals. You can get anything from continuous signals to 2/3 dimensional signals. This section will discuss 2-d FFT but also cover the other principles like DFT and IDFT that helps show how 2-d FFTs work.

DFT

Discrete Fourier transforms are used calculate a signals’ frequency spectrum and with that information you can examine frequency, amplitude and phase. Secondly the DFT can find a systems frequency response from the impulse response. It is helpful especially since it calculates multiple samples, over an interval. The samples don’t even have to be periodic. Note that when talking about FFTs in this report it means fast Fourier transform which means basically that it’s a DFT calculated efficiently.

The following is the equation for DFT [5]:

Fm= n=0M-1fn×e-j2πmnM ,m=0,1,2,3,…,M-1

M is the number of samples taken.

IDFT

Inverse Discrete Fourier transforms are used to reverse the DFT applied to the signal. It basically uses F(u) discrete data points to get f(n). The following is the equation for IDFT [5]: fn= m=0M-1Fm×ej2πmnM ,n=0,1,2,3,…,M-1

For image processing the DFT and IDFT takes on a bit of a different form [5]:

DFT: Fu= x=0M-1fx×e-j2πuxM , IDFT: f(x)=1M u=0M-1F(u)×ej2πuxM ,u,x=0,1,2,3,…,M-1

There are also some DFT properties to take note of [5]:

Periodicity

Fu= Fu+kM ,fx= f(x+kM)

Convolution

fx*hx= m=0M-1fm×hx-m ,m=0,1,2,3,….,M-1

2-D FFT

2-d FFTs are used when there are horizontal and vertical spatial points that need to be transformed into the frequency domain. Thus when the image function, f(x,y), is separated into a combination of harmonic functions. The standard equation for the 2-d Fourier transform and the 2-d inverse is [10]:

Fu,v= -∞∞fx,y×e-j2πxu+yvdxdy fx,y= -∞∞F(u,v)×ej2πxu+yvdudv

Figure [ 4 ]: 2-D Sinusoidal Wave

Below is an image of a 2-d sinusoid that will usually use the above equation if there is a need to examine it [10].

But for a more effective method the 2-d D/FFT is better for image processing. As it allows for you to insert the image size to determine how many samples needs to be taken, because f(x,y) is a digital image with the size M X N. The direct transform is [5]:

Fu,v= x=0M-1y=0N-1fx,y×e-j2π(uxM+vyn) ,x=0,1,2,3,…,M-1 ,y=0,1,2,3,…,N-1

And the inverse transform is [5]: fx,y= 1MN u=0M-1v=0N-1Fu,v×ej2π(uxM+vyn) ,u=0,1,2,3,…,M-1 ,v=0,1,2,3,…,N-1

These equations can be simplified as shown in the Comparison section below, so that the2-d operation consists out of two 1-d operations.

Comparison with 1-D FFT

Remember that:

Fμ= -∞∞f(t)×e-j2πμtdt ft= -∞∞F(μ)×ej2πμtdt

Fu,v= -∞∞fx,y×e-j2πxu+yvdxdy fx,y= -∞∞F(u,v)×ej2πxu+yvdudv

Where 1-d FFTs have only 1 frequency axis for horizontal frequencies, the 2-d FFTs have 2 frequency axes for horizontal and vertical frequency, which makes it perfect for image processing [9]. There is an easy way to use 2-d FFTs with 1-d FFTs as you are able to split 2-d function, equation given below.

Fu,v= y= -∞∞[x= -∞∞f(x,y)×e-j2πuxdx]×e-j2πvydy

Thus where the 1-d usually transforms the rows first, for 2-d application it will transform the rows first then the columns. Thus 1-d FFTs are used for data that is one dimensional like audio or energy signals and 2-d FFTs are used for data that is two dimensional like images

2-D FFT and Image Processing

As we now know the Fourier transform splits the image into ‘frequencies’ and measures the amplitude at each point. To elaborate the Fourier transform measures the spatial ‘frequency’ in the image. Thus an image with lots of jagged at abrupt color transitions contains many high frequencies. The same is true for low frequencies but for long, smooth color transitions.

In image processing 2-d FFT will almost always be used. It will be used in the filtering applications as this is the mathematical concept that allows images to be represented in the frequency domain (remember images are 2 dimensional). Thus before convolution (or multiplication) takes place the 2-d FFT will be calculated of the image and filter. This will allow multiplication to takes place.

Practical uses for 2-d FFT are in image processing. Firstly you can un-blur or un-sharp an image by simply reversing the filtering process (as discussed in the section about smoothing and sharpening). This can be used if an important picture, like a criminal stealing, is blurred and unable to identify. Secondly it can be used in image compression which is helpful in order to view photos on smaller devices or to safe space on the storage device. Next a few practical uses for image smoothing and sharpening is given. This is given because a 2-d Gaussian FFT is used in part 2.

Applications for a image smoothing [5] can be: * Satellite and aero imagery to remove any unwanted scan lines in the obtained image. * In OCR systems to bridge small gaps in texts and paragraphs. * Can be used in the publishing (advertising, magazines etc.) world to remove faults and lines to give a smoother and subtle result.

Applications for a image sharpening [5] can be:

Image Smoothing and Sharpening

Image smoothing and sharpening is used in many aspects in the real world like image processing and statistics. In this report we will look more in depth into image processing. To be more specific we will look at blurring, highlighting details and noise reduction.

The flow diagram is given again below as these are the steps in which the smoothing and shaping will be achieved in. The smoothing and sharpening section will cover more of the different theorems and concepts that will be used if you want the exact steps check the overview section.

Figure [ 5 ]: Flow Diagram of Filtering in the Frequency Domain

Smoothing

The goal of smoothing is to capture important patterns in the data while leaving out unwanted factors like noise. Edges and noise contribute to the high frequency components of an image’s Fourier transform [5]. Thus the individual points (like noise) are reduced while points lower than the neighboring points are increased leading to a smoother image. The smoothed values can be convoluted with the original image in order to obtain the final image [1].

For image smoothing (also known as blurring) an ideal low pass filter is used as it attenuates high frequency values. A graphical representation is given below [3]:

Figure [ 6 ]: Graphical Representation of an Ideal Low Pass Filter

An ideal low pass filter is specified as [3]:

Hu,v= 1 Du,v≤ D00 Du,v> D0

Du,v= (u- P2)2+(v- Q2)2

Now note: * D(u,v) is the distance between the origin and the point (u,v) * D0 is a positive constant, also known as the cut-off frequency * P and Q are the sizes of the zero padded image

One way to indicate cut-off frequency is through circles enclosing a specific amount of power in the image given [3].

PT=u=0P-1v=0Q-1Pu.v=u=0P-1v=0Q-1|Fu,v|2

α=100 × u=0P-1v=0Q-1P(u,v)PT

Thus looking at the above equation, with a radius of D0 , the DFT will enclose as certain percent of power known as α. Thus using the above equations one can filter the image given, in order to smoothen out the ‘high frequency’ values of the image. Also through increasing/decreasing the radius D0 the blurriness can be more/less. Below is given an example of image smoothing [2].

Figure [ 7 ]: Image that was smoothed

There are other algorithms that can be used in place of just the ideal high pass filter namely: * Butterworth low pass filter * Gaussian low pass filter * Laplacian smoothing * Additive smoothing * Kernel smoother

Further discussion on the Gaussian low pass filter algorithm will be discussed in Part 2.

Sharpening

The goal of sharpening is to enhance high frequency aspects while eliminating low frequency components. Edges and noise contribute to the high frequency components of an image’s Fourier transform [5]. Thus the individual points (like noise) are increased while points lower than the neighboring points are decreased leading to a sharper image. The smoothed values can be convoluted with the original image in order to obtain the final image [1].

Figure [ 8 ]: Graphical Representation of an Ideal High Pass Filter

For image sharpening an ideal high pass filter is used as it attenuates low frequency values. A graphical representation is given below [3]:

An ideal high pass filter is specified as [3]:

Hu,v= 0 Du,v≤ D01 Du,v> D0

Du,v= (u- P2)2+(v- Q2)2

Now note: * D(u,v) is the distance between the origin and the point (u,v) * D0 is a positive constant, also known as the cut-off frequency * P and Q are the sizes of the zero padded image

Keep in mind that the ideal high pass filter can be designed through the use of the low pass filter with the identity:

HHPu,v= 1- HLP(u,v)

One way to indicate cut-off frequency is through circles enclosing a specific amount of power in the image given [3].

PT=u=0P-1v=0Q-1Pu.v=u=0P-1v=0Q-1|Fu,v|2

α=100 × u=0P-1v=0Q-1P(u,v)PT

Thus looking at the above equation, with a radius of D0 , the DFT will enclose as certain percent of power known as α. Thus using the above equations one can filter the image given, in order to attenuate out the ‘low frequency’ values of the image, this will cause the higher frequency lines to be more visible and clearer while the smaller frequency values fade away. Also through increasing/decreasing the radius D0 the sharpness can be more/less.

Figure [ 9 ]: Edges Clearly Shown before Pass Band Attenuation Edited

Figure [ 10 ]: Final Result of an Image sharpened

Note that when applying the above algorithm that the lower frequencies will basically become zero. A way to get a final image result you can apply some attenuation to increase the filters pass band a bit. This basically allows that smaller frequencies are still passed through a bit but not enhanced as the higher frequencies are. Below is given an example the image edge detection and the final sharper result after attenuation has been brought into consideration [4].

There are other algorithms that can be used in place of just the ideal high pass filter namely: * Butterworth high pass filter * Gaussian high pass filter * Laplacian sharpening

Further discussion on the Gaussian high pass filter algorithm will be discussed in Part 2.

Conclusion

One can see now that there is no limit in analyzing signals in the frequency domain. Filtering in the frequency domain is a sub part to that, and this allows one endless control over signal, images and even motion pictures. With knowledge about 2-d FFTs one gains a lot of control over any form of signals (1 – 3 dimensional).

PART 2 Application of Filtering in the Frequency Domain

Introduction

The purpose of this part was to apply filtering in the frequency domain onto an image. A Gaussian low- and high pass filter will be used, in order to smoothen and sharpen the image given as input. The filter is designed out of first principles using Matlab to help simulate the results.

Gaussian Filter Theoretical Analysis

Figure [ 11 ]: Graphical Representation of a Gaussian Filter

In previous sections the ideal low- and high pass filters were discussed, and their uses in image processing. Gaussian filters are filters whose impulse response is a Gaussian function. They are more advantages than the ideal filters because of almost no overshoot and minimal rise and fall time. They are applied. They also have a minimal group delay. Below is an illustration of a Gaussian filter [11]:

Gaussian Low Pass Filter

The Low pass filters will attenuate any high frequencies, like noise, and smoothen out the image. The equations are [3]:

Hu,v= e-D2(u,v)2×D02

Du,v= (u- P2)2+(v- Q2)2

Now note: * D(u,v) is the distance between the origin and the point (u,v) * D0 is a positive constant, also known as the cut-off frequency * P and Q are the sizes of the zero padded image

The filter that is designed as a result of these equations is [3]:

Figure [ 12 ]: Graphical Representation of a Gaussian Low Pass Filter

Thus with a lower cutoff frequency the image will be smoother (more blurry).

Gaussian High Pass Filter

High pass filters will attenuate any low frequencies and sharpen the image. The equations are [3]:

Hu,v=1- e-D2(u,v)2×D02

Du,v= (u- P2)2+(v- Q2)2

Now note: * D(u,v) is the distance between the origin and the point (u,v) * D0 is a positive constant, also known as the cut-off frequency * P and Q are the sizes of the zero padded image

The filter that is designed as a result of these equations is [3]:

Figure [ 13 ]: Graphical Representation of a Gaussian High Pass Filter

Thus with a lower cutoff frequency the image will be sharper.

Gaussian Filter Design

For designing these filters the following steps were taken in order to achieve the desired results. Firstly the image was grayed then the 2-d FFT was calculated of the grayed original image. The FFT is taken because it is easier to analyze the picture in that domain and it eliminates convolution in the spatial domain so that there can now be multiplied in the frequency domain (later on).

Next the Low pass filter is designed. This step is done for both the smoothing and shaping part of the program. It will use the size of the MxN image to determine the new radius size (or D(u,v) in the equations. It also needs a cutoff frequency for the filter which will impact the blurriness or sharpness of the image.

Now for the LP filter the following is done. The LP filter transfer function H(u,v) is now multiplied with the images’ FFT imageFFT(u,v). This is done over the entire range of image size (thus for loops). This new LP FFT will now be reconverted with a 2-d IFFT, to obtain the newly sharpened image in spatial domain. The original and smoothed image is outputted along with the original and filtered images’ FFT.

For the HP filter the following is done. The Low pass filter transfer function H(u,v) is changed with the filter identity to get the HP filters transfer function:

HHPu,v= 1- HLP(u,v)

Note that the HP filter transfer function Hu,v is correct but if you multiply it with the images’ FFT imageFFT(u,v) you will get a result where the edges are clearly visible but the lower frequency values are almost completely attenuated. Thus the resulting image isn’t a clear sharpen image of the original. To account for this the pass band attenuation is increased to allow some lower frequencies to pass. The equation for this is:

Hnewu,v= a+b×Hold(u,v)

After this the old HP function and the new HP function is multiplied with the images’ FFT imageFFT(u,v). This is done over the entire range of image size (thus for loops). This new/old HP FFT will now be reconverted with a 2-d IFFT, to obtain the newly sharpened image in spatial domain. The original, edged and sharpened image is outputted along with the original and edged images’ FFT.

Practical Results

The following results were obtained from the practical simulation, in the LP result the cutoff frequency was 0.1 and in the HP result the cutoff frequency was 0.025.

Firstly the original image that was used and its frequency response:

Figure [ 14 ]: Original Image and its FFT

Figure [ 15 ]: Smoothed Image and FFT

Secondly the smoothed image and its frequency response:

Figure [ 16 ]: Edged Image and its FFT

Lastly the edged and sharpened image and their frequency responses:

Figure [ 17 ]: Sharpened Image and its FFT

Conclusion

As one can clearly see there was definite smoothing and sharpening that took place. The original image was sent through the filter correctly and it gave the desired results. There are a lot of real world applications for the Gaussian filters [11]. In GSM devices for wireless communication. In Gaussian frequency-shift keying. And of course in image processing, more accurately the Canny Edge Detector.

References

[1]http://en.wikipedia.org/wiki/Smoothing

[2]http://commons.wikimedia.org/wiki/File:Wiener_filter_-_my_dog.JPG

[3]http://ee.lamar.edu/gleb/dip/04-2%20-%20Using%20frequency%20filters.pdf

[4] http://stackoverflow.com/questions/6094957/high-pass-filter-for-image-processing-in-python-by-using-scipy-numpy

[5] http://www-old.me.gatech.edu/me6406/Frequency%20domain%20filtering%20%28SH%20Foong%29.pdf

[6] http://www.learningace.com/doc/347059/6d3ac23cdaf98dd756762d6e0bf99373/lec012_frequency

[7] http://www.scratchapixel.com/lessons/mathematics-physics/discrete-cosine-transform-dct/one-dimensional-dct/

[8] http://www.twi-global.com/technical-knowledge/published-papers/analysis-of-cross-correlation-and-wavelet-de-noising-for-the-reduction-of-the-effects-of-dispersion-in-long-range-ultrasonic-tes/

[9]http://www.mee.tcd.ie/~sigmedia/pmwiki/uploads/Teaching.4S1b/handout4_4s1.pdf

[10] http://cmp.felk.cvut.cz/~hlavac/TeachPresEn/11ImageProc/12FourierTxEn.pdf

[11] http://en.wikipedia.org/wiki/Gaussian_filter…...

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...signal Speech Signal Processing Speech Production Speech Waveform Characteristics ● ● ● Loudness Voiced/Unvoiced. Pitch. – Fundamental frequency. Formants. ● Spectral envelope. – Speech Waveform Characteristics Voiced Unvoiced s s Short-Time Speech Analysis ● Segments (or frames, or vectors) are typically of length 20 ms. – – Speech characteristics are constant. Allows for relatively simple modeling. ● Often overlapping segments are extracted. The Spectrogram ● A classic analysis tool. – Consists of DFTs of overlapping, and windowed frames. ● Displays the distribution of energy in time and frequency. A spectrogram Short time ACF /m/ /ow/ /s/ ACF |DFT| Sound Propagation Sound propagates from the source to the receiver through a combination of four main propagation modes: ● ● ● ● direct propagation path reflection from walls diffraction around objects refraction due to temperature differences in the layers of air. For that reason sound is delayed and attenuated by different amounts. Reflection One happens when a sound wave encounters a medium with different impedance from which it is travelling in, for example when the sound propagating in the air hits the walls of a room (fig. 1). Sound reflects from walls, objects, etc. Acoustically, reflection results in: Sound reverberation - for small round-trip delays (less than 100 ms), Echo - for longer round-trip delays. fig.......

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...Signal and system are the two major components in Signal Processing. The term signal refers to a physical quantity having the characteristic of varying with respect to time and space. Signal may be either continuous-time or discrete-time, with either analog or digital values [1]. The signals which are represented by a continuous function are called continuous signals and those which are described by number sequences are called discrete signals [2]. We have seen about a signal in brief. The second component in signal processing is a system which is a process whose input and output are signals. Signal processing is a vast area comprising the concepts of electrical engineering, systems engineering and applied mathematics that deals with both the analog and discrete time signals, represented by variation in time or spatial physical quantities. Precise statistical depiction is required for the development of improved signal processing algorithms of natural signals [3]. The major operations of Signal processing includes 1) signal acquisition and reconstruction, 2) Quality improvement including filtering, smoothing and digitization, 3) feature extraction 4) signal compression and 5) prediction [4] [5]. Analog signal processing, Discrete-time signal processing, Non-linear signal processing and Digital signal processing are the four major categories of signal processing. The signal processing performed over analog signals for the purpose of any of the major operations of signal......

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...Ali Rizwan - Calvez Fabien 4.1 - Localization of the source during the time 4.2 - Estimation of the instantaneous speeds 5- Signal Processing Project Signal Processing Project 2D location tracking radar by using sound waves Fourth step: Real-time monitoring of a sound wave 5.1 - Acquisition of a real sound signal 5.2 - Merging of information with another group 6 - Conclusion Ali Rizwan and Calvez Fabien Table of contents: 12Introduction First step: Estimation of arrival direction of sound waves 2.1 - Limits of the detection 2.2 - First method Annex: 7 - Figures 2.3 - Second method 82.4 - Conclusion about the two methods 3Second step: Localization of wave sources in a plane Matlab programming 3.1 - Localization of a sound wave 3.2 - Estimation of the performances 4Third step: Tracking of a sound wave ENSEIRB-MATMECA 1/16 2009-2010 Ali Rizwan - Calvez Fabien 1Introduction Signal Processing Project 2 - First step: Estimation of arrival direction of sound waves The most widespread localization system used by common people is the Global Positioning System (GPS). Yet we cannot use it inside buildings, because of the low reception level of the signals. Instead Wi-Fi waves can be used or even sound waves. This is the second method that is introduced in this project. The goal of this project is to localize a sound source in a simple but realist example the implied issues linked to the design of this system. In this project an......

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...Samer Abboud Signal Processing Final Report 29/5/2014 There are there objectives to this report, as we will see in the three following problems. The first objective is to build a VI to find the magnitude response of each filter while changing the 5 designs of filters(Elliptical, Chebychev, Inverse Chebychev, Butterworth and Bessel) and changing the filter types (Lowpass, Highpass, Bandpass, Bandstop). The second objective which is seen in problem 2 is to generate a pulse with uniform white noise, passing it through a median type filter. Theoretical Part 1: In problem 1 we have a case structure for the 4 different types of filters. Those four types ( Lowpass, Highpass, Bandpass, Bandstop) require nearly the same input, changing slightly. the inputs are filter design, filter type, impulse response, high and low frequencies, the order of the filter, sampling rate and the attenuation and ripples in those filters that need those inputs. At the output of the case structure, we are transforming the signal into a Fourier transform and passing it through an array subset, multiplying with a logarithm of base 10, passing it through a bundle to finally be displayed on the waveform graph. All this is put inside a while loop with a 50 ms wait. Theoretical Part 2: In problem 2 we are inserting a certain number of samples into a pulse VI as well as a uniform white noise VI, while specifying some characteristics like width and delay and noise level. After we add the pulse to......

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...Signals IT/242 May 29, 2014 Sokly Vann Signals Today’s technology will use the old, the new and a combination of the two to achieve the desired results. Society has become dependent on this technology and the many types of signals that support it. Data, Voice and Video Signals all play a major role in the daily lives of millions of people around the world. They all seem to be alike but different. The Difference Data is a binary type signal that is be used in many different ways. Data is used in pictures, web sites, emails, programs and many other applications and software. Voice can be in the form of analog or digital signals. Depending on the application or use the frequency and bandwidth required may change to acquire the desired performance. Video signals also can be in the form of analog and digital (William Stallings/Pearson Education, Inc., 2009). VIOP and PBX Voice over Internet Protocol (VIOP) is the new technology in telephone systems. VIOP uses a packet switched network similar to the internet. VIOP passes digitized voice data. The advantage is more communication through the same amount of bandwidth. Public Branch Exchange (PBX) is a small telephone network within a company. This network has several lines to a local phone service to allow calls to go in and out of the company. The PBX internal calls are routed internally, and any calls to the outside take one of the available outside lines. VOIP can be used in a PBX system. This could be an......

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...weaknesses 13. Explain - to give facts that elucidate 14. Fact – something that can be proven to be true 15. Illustrate – to give examples 16. Infer – to make a conclusion based on fact 17. Interpret – to offer an explanation 18. Justify – to give good reasons 19. Opinion – belief based on what a person thinks or feels 20. Predict – to make a guess about the future 21. Prove – to show something is true by giving facts 22. Question – to ask 23. Reflect – to think about 24. Relate – to show how things are alike or connected 25. Sequence – to put in the correct order 26. State – to give the main points or reasons\ 27. Summarize – to briefly cover the main points 28. Trace – to tell about the progress or growth Transition and Signal Words for Essays Sequence and Chronological Order Stems After Afterwards Ago Already At last At the same time As Before During Eventually Even now Finally (the) final First, first of all Following For a time Further, furthermore Immediately Initially In the first place In the meantime Last, lastly Later Long after Meanwhile Next Now Not long after Once On (date) Preceding Presently Second, secondly Several Sometimes Soon, soon after Some Subsequently Suddenly Then Thereafter Third To begin with Today Until While Compare and Contrast Stems Although Also As opposed to As well as But By comparison Compared with Conversely Despite Different from Either…or Even......

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...Usage of language in the sentence structure of FIR Submitted by: rana irfan Submitted to: Dr Athar Khurshid University of Management and Technology Usage of language in the sentence structure of FIR Introduction Filing an FIR may have become easier over the years, but what you write in it can leave both you and the policemen in a bit of a linguistic tizzy. The main reason is the customary use of Urdu/Persian words while registering an FIR. It begins at the outset with the bayan azaane (a compound Urdu-Persian word for statement description or expression) of the tehreer (complainant) being taken down. The contents usually follow with an average of six more similarly confusing words. If a complainant is mystified, so are the policemen, both officers and the lower ranks. It is natural that trainee cops would not have used such alien terms earlier but The officers get first-hand experience of how an FIR is registered as well as how a police station works in this part of their training. It's also during this time that they learn about such words. Initially we tell them the meaning of the words but gradually they get equipped to use such words said the SHO. Words like Daryaft (revelation) mushtaba (suspect) waqua (place of occurrence) nakal (copy) insdaad jarayam ( prevention of crime) could be easily found in the FIR copy though for the meaning you either Google it or ask......

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...------------------------------------------------- % Sample signal at 50 Hz ------------------------------------------------- ------------------------------------------------- Fs = 50; %50 hertz ------------------------------------------------- dt = 1/Fs; ------------------------------------------------- StopTime = 1; ------------------------------------------------- t2 = (0:dt:StopTime-dt)'; ------------------------------------------------- ------------------------------------------------- Fc = 15; ------------------------------------------------- x2 = sin(2*pi*Fc*t2); ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- figure(3); ------------------------------------------------- hold on; ------------------------------------------------- plot(t1,x1,'b'); ------------------------------------------------- plot(t2,x2,'ro',t2,x2,'r'); ------------------------------------------------- xlabel('time (in......

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...Explain the differences between data, voice, and video signals in 200 to 300 words. Include a description comparing the differences between a private branch exchange (PBX) and Voice over Internet protocol (VoIP). Solution: Data signal is a mode of physical data transmission usually in binary code in signals or pulses from one source point to one or more destination point. Data is transformed into electromagnetic signals prior to transmission across a network. Data and video signal are typically encoded utilizing a digital methodology where voice is typically encoded utilizing an analog format. In analog technology, sound is recorded in its original form. Therefore, for instance, if making a recording of the sound, the audio is taken straight from the microphone and stored onto the storage media. The wave from the microphone is an analog wave, and therefore the wave on the tape is analog as well. That wave on the tape can be read, amplified and put through a sound system to produce the original sound. In digital technology, the video or data is turned into numbers that are stored on a digital device such as a computer. The more samples that are taken the more closely the digital data reflect the original data or video signal. Another option is that the data and video are directly encoded into digital format to start with and does not require sampling. In addition to this, Voice signals are generally less data intensive as only the audio part is captured and is......

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...Digital Signal Processing The acronym DSP can stand for one of two things: digital signal processing which refers to the technique used to process signals digitally or digital signal processor which would refer to a specialized kind of microprocessor. Since the introduction of general-purpose microprocessors in the 1980’s, a wider range of modern technology now includes digital signal processing technology. This includes cellular phones, CD players, computers, DVD players, video recorders, computer monitors, and many other similar devices. DSP is also taking over analog circuitry in TV sets and telephones. One of DSP’s major applications is signal compression and decompression. Signal compression enables things such as call waiting and image projection on computer screens. DSP involves a great deal of math, both complex and simple. The design of a DSP chip enables it to perform these functions very rapidly which produces hundreds of millions of samples very quickly. This provides “real time” performance meaning the signal is live. This can be seen in loud speakers and cell phones. Most major electronics companies utilize DSP in their technology including Texas Instruments, Intel, and Motorola. An example of “real time” performance could be viewed in a lab that we did. We had two separate groups: one group made a “receiver” and the other group made a “transmitter.” Across the room, one group had their receiver and set up the microphone on a stand a certain amount of......

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