NOISE MINIMIZATION IN IMAGES AND COMMUNICATION

MAJOR PROJECT REPORT

MAJOR PROJECT REPORT- NOISE MINIMIZATION TECHNIQUES

MAJOR PROJECT REPORTODD SEM (2012-2013) 2012ALOK SHIVAM (9909102226) and G.KRISHNA CHAITANYA(9909102223)B.TECH(ECE), JAYPEE INSTITUTE OF INFORMATION TECHNOLOGY12/12/2012

CERTIFICATE

This is to certify that the work titled NOISE MINIMIZATION TECHNIQUES submitted by ALOK SHIVAM and G. KRISHNA CHAITANYA in partial fulfillment for the award of degree of bachelors of technology (`ECE) of Jaypee Institute of Information Technology University, Noida has been carried out under my supervision. This work has not been submitted partially or wholly to any other University or Institute for the award of this or any other degree or diploma.

Signature of Supervisor ..Name of SupervisorMr. KAPIL DEV TYAGIDesignationSr. LECTURERDate12TH DECEMBER, 2012

ACKNOWLEDGEMENT

We would like to take this opportunity to express our gratitude towards our teacher, project co-coordinator and mentor KAPIL DEV TYAGI SIR for his undying support and fruitful directives to help us in making this project, and boosting our confidence. We salute his able guidance and suggestions without which the project would have been almost impossible to meet its goal. We take immense pleasure in thanking JIIT, NOIDA for providing us with an opportunity to work at the temple of technology and providing us an opportunity to work in their PROJECT LAB. We would like to give special thanks to Mr. B. Suresh sir for being a constant source of guidance throughout the project.We would also like to thank our parents who boosted us morally and were a constant support to us and acted like a backbone for the project. We would like to thank god for all the blessings he bestowed upon us and for giving us the strength to do this project.

ALOK SHIVAM

G.KRISHNA CHAITANYA

OBJECTIVES OF THE PROJECT

1. TO STUDY AND IMPLEMENTAION OF NOISE MINIMIZATION TECHNIQUESa. In imagesb. In communication systemc. In wireless communication

2. To study algorithms that could reduce noise during signal transmission.

3. To study research works and research papers to develop an algorithm on own

4. To analyze the effect of noise from different transmission angles.

5. To carry out real time noise minimization

6. To work for noise minimization in video signals.

CHAPTER 1:- INTRODUCTION

With communication advancing day by day, noise reduction is one area which has been a concern for communication during all times. Todays advancements have come up with highly efficient tools and techniques for noise minimization.Noise is one such signal which is not in the control of the provider or the user, it can be in any form and providing a noise free communication to the user is a big challenge for modern day industries.In common use, the word noise means any unwanted sound. In physics and analogue electronics, noise is a mostly unwanted random addition to a signal; it is called noise as a generalisation of the acoustic noise, heard when listening to a weak radio transmission with significant electrical noise. Signal noise is heard as acoustic noise if the signal is converted into sound (e.g., played through a loudspeaker). High noise levels can block, distort, change or interfere with the meaning of a message in human, animal and electronic communication. In signal processing or computing it can be considered random unwanted data without meaning; that is, data that is not being used to transmit a signal, but is simply produced as an unwanted by-product of other activities. "Signal-to-noise ratio is sometimes used to refer to the ratio of useful to irrelevant information in an exchange.Noise reduction is the process of removing noise from a signal. All recording devices, both analogue and digital, have traits which make them susceptible to noise. Noise can be random or white noise with no coherence, or coherent noise introduced by the device's mechanism or processing algorithms.In electronic recording devices, a major form of noise is hiss caused by random electrons that, heavily influenced by heat, stray from their designated path. These stray electrons influence the voltage of the output signal and thus create detectable noise.This report presents various aspects of noise in images, wired and wireless communication, study and implementation of minimization algorithms on matlab, comparisons between the techniques and providing results and analysis of the research work done. Finally the most effective and simple technique is recommended for implementation for each type of communication.

CHAPTER 2:- NOISE MINIMIZATION IN IMAGES

2.1 INTRODUCTIONImages taken with both digital cameras and conventional film cameras will pick up noise from a variety of sources. Further uses of these images require that the noise will be (partially) removed for artistic work or marketing, or for practical purposes such as computer vision..2.1.1 Types of noise in imagesIn salt and pepper noise (sparse light and dark disturbances), pixels in the image are very different in color or intensity from their surrounding pixels; the defining characteristic is that the value of a noisy pixel bears no relation to the color of surrounding pixels. Generally this type of noise will only affect a small number of image pixels. When viewed, the image contains dark and white dots, hence the term salt and pepper noise. Typical sources include flecks of dust inside the camera and overheated.In Gaussian noise, each pixel in the image will be changed from its original value by a (usually) small amount. A histogram, a plot of the amount of distortion of a pixel value against the frequency with which it occurs, shows a normal distribution of noise. While other distributions are possible, the Gaussian (normal) distribution is usually a good model, due to the central limit theorem that says that the sum of different noises tends to approach a Gaussian distribution.In either case, the noise at different pixels can be either correlated or uncorrelated; in many cases, noise values at different pixels are modeled as being independent and identically distributed, and hence uncorrelated.In selecting a noise reduction algorithm, one must weigh several factors:

whether sacrificing some real detail is acceptable if it allows more noise to be removed (how aggressively to decide whether variations in the image are noise or not) the characteristics of the noise and the detail in the image, to better make those decisionsDigital cameras have become very popular over the last several years for both professional and personal use. Under most conditions, digital cameras are an efficient, convenient way to take pictures.The development of a noise reduction technique which can be used to decrease the visible noise in images taken using exposure times greater than 1/4 second.Using this noise reduction technique, people who have taken images in low-light situations are able to take advantage of the many benefits of digital photography.Images taken with both digital cameras and conventional film cameras will pick up noise from a variety of sources. further uses of these images require that the noise will be (partially) removed - for aesthetic purposes as in artistic work or marketing, or for practical purposes such as computer vision.

2.2 NOISE REDUCTION METHODS :

2.2.1.Pixel Substitution :The first method utilized to reduce the noise consisted of substituting one pixel value for another. A program was written to scan through a dark image looking for pixels with values above the threshold input to the program. These pixels will be referred to as 'hot' pixels. When a hot pixel was found, the program located the lowest pixel value within two pixels from the hot pixel. The locations of each of the hot and cold pixels were recorded in a data file used when processing images. For each of the hot pixel locations, the digital count in that location was replaced by the value in the corresponding cold pixel. Figures 5 and 6 show the results of the substitution method. A reduction in the amount of noise is evident in the processed image.

Figure 1: Original 30 Second Image Figure 2: Pixel Substitution

Additionally, an artifact was discovered at many of the edges in the image. The artifat was caused by having a hot pixel in the dark part of the image and the corresponding cold pixel in the lighter area. While some reduction in the noise has been achieved, the presence of this edge artifact was unacceptable, so another approach had to found.

2.2.2 SALT AND PEPPER :In salt and pepper noise (sparse light and dark disturbances), pixels in the image are very different in color or intensity from their surrounding pixels; The defining characteristic is that the value of a noisy pixel bears no relation to the color of surrounding pixels. Generally this type of noise will only affect a small number of image pixels. When viewed, the image contains dark and white dots, hence the term salt and pepper noise. Typical sources include flecks of dust inside the camera and overheated.This type of noise can be caused by dead pixels, analog-to-digital converter errors, bit errors in transmission, etc.This can be eliminated in large part by using dark frame subtraction and by interpolating around dark/bright pixels.

CODE:WITH USING FUNCTIONS:I = imread('C:\Users\9909102213\Desktop\nayanatara.gif'); imshow(I) J = imnoise(I,'salt & pepper',0.02); figure, imshow(J) K = filter2(fspecial('average',3),J)/255; figure, imshow(K) L = medfilt2(J,[3 3]); figure, imshow(L)

WITH OUT USING MATLAB FUNCTIONS:A = imread('C:\Users\9909102213\Desktop\nayanatara.gif');imshow(A)J = imnoise(A,'salt & pepper',0.02);figure, imshow(J)%PAD THE MATRIX WITH ZEROS ON ALL SIDESmodifyA=zeros(size(J)+2);B=zeros(size(J));for x=1:size(J,1)for y=1:size(J,2)modifyJ(x+1,y+1)=J(x,y); end endfor i= 1:size(modifyJ,1)-2for j=1:size(modifyJ,2)-2window=zeros(9);inc=1;for x=1:3for y=1:3window(inc)=modifyJ(i+x-1,j+y-1);inc=inc+1;endendmed=sort(window);B(i,j)=med(5);endendB=uint8(B);figure,imshow(B);

Fig 3 fig 4

2.2.3 GUASSIAN NOISEIn Gaussian noise, each pixel in the image will be changed from its original value by a (usually) small amount. A histogram, a plot of the amount of distortion of a pixel value against the frequency with which it occurs, shows a normal distribution of noise. While other distributions are possible, the Gaussian (normal) distribution is usually a good model, due to the central limit theorem that says that the sum of different noises tends to approach a Gaussian distribution.In either case, the noise at different pixels can be either correlated or uncorrelated; in many cases, noise values at different pixels are modeled as being independent and identically distributed, and hence uncorrelated.

CODE:RGB = imread('C:\Users\9909102213\Desktop\nayanatara.gif'); I = rgb2gray(RGB); J = imnoise(I,'gaussian',0,0.025); imshow(J) L = filter2(fspecial('average',3),J)/255; figure, imshow(L) K = wiener2(J,[5 5]); figure, imshow(K);

2.2.4 POISSION NOISE :Poisson noise or shot noise is a type of electronic noise that occurs when the finite number of particles that carry energy, such as electrons in an electronic circuit or photons in an optical device, is small enough to give rise to detectable statistical fluctuations in a measurement. 2.2.4.1 CODE:

RGB = imread('C:\Users\9909102213\Desktop\nayanatara.gif'); I = rgb2gray(RGB); J = imnoise(I,'poisson');imshow(J) ;L = filter2(fspecial('average',3),J)/255; figure, imshow(L); K = wiener2(J,[5 5]); figure, imshow(K) ;

2.2.5 SPECKLE NOISE:Speckle noise is a granular noise that inherently exists in and degrades the quality of the active radar and synthetic aperture radar (SAR) images. Speckle noise in conventional radar results from random fluctuations in the return signal from an object that is no bigger than a single image-processing element. It increases the mean grey level of a local area. Speckle noise in SAR is generally more serious, causing difficulties for image interpretation. It is caused by coherent processing of backscattered signals from multiple distributed targets. In SAR oceanography, for example, speckle noise is caused by signals from elementary scatters, the gravity-capillary ripples, and manifests as a pedestal image, beneath the image of the sea waves.

2.2.5.1 CODE:RGB = imread('C:\Users\9909102213\Desktop\nayanatara.gif'); I = rgb2gray(RGB); J = imnoise(I,'speckle',v)imshow(J) L = filter2(fspecial('average',3),J)/255; figure, imshow(L) K = wiener2(J,[5 5]); figure, imshow(K)

2.2.5.2 CODE:- COINSA=imread('C:\Users\9909102213\Desktop\coins.gif');

B=bitget(A,1);figure,subplot(2,2,1);imshow(logical(B));title('Bit plane 1');

B=bitget(A,2);subplot(2,2,2);imshow(logical(B));title('Bit plane 2');



B=bitget(A,5);figure,subplot(2,2,1);imshow(logical(B));title('Bit plane 5');




RECONSTRUCTION:- A=imread('C:\Users\9909102213\Desktop\coins.gif');B=zeros(size(A));B=bitset(B,8,bitget(A,8));B=bitset(B,7,bitget(A,7));B=bitset(B,6,bitget(A,6));B=bitset(B,5,bitget(A,5));B=bitset(B,4,bitget(A,4));B=bitset(B,3,bitget(A,3));B=bitset(B,2,bitget(A,2));B=bitset(B,1,bitget(A,1));

B=uint8(B);figure,imshow(B);

2.2.6 CONCLUSION:We used the Nayantara Image(figure 1) in png format ,adding four noise (Speckle, Gaussian ,Poisson and Salt & Pepper) in original image with standard deviation(0.025) De-noised all noisy images by all filters and conclude from the results that: (a)The performance of the Wiener Filter after de-noising for all Speckle, Poisson and Gaussian noise is better than Mean filter and Median filter. (b)The performance of the Median filter after de-noising for all Salt & Pepper noise is better than Mean filter and Wiener filter.

CHAPTER 3:- NOISE MINIMIZATION IN COMMUNICATION

3.1 BASICS OF COMMUNICATIONA COMMUNICATION SYSTEM:-A communication system is set of individual communication networks, transmission systems, relaystations, tributary stations, and data terminal equipments (DTE) usually capable of interconnection and interoperationto form an integrated whole. The components of a communications systemserve a common purpose, are technically compatible, use common procedures, respond to controls, and operate in unison. A modern day telephony system is an example of communication system.

3.1.1 Sampling Sampling is a process where you convert continuous time signals(analog signals) into discrete time signals(digital system). On paper CT signals are represented by "full lines" where as DT signals are only "points" chosen from the original CT signals. Now it is clear that DT signals are a rough representation of their respective CT signals. Now the question arises, why do we need sampling? We need it because it is very efficient to use "rough" DT signals in telecommunication instead of "precision" CT signals. Now you may ask, if we're use "rough" DT signals doesn't the information that is to be transmitted and henceforth received is also "rough" or inaccurate? That's where the sampling theorem comes in.The sampling theorem gives you a rule using which you can use DT signals to transmit/receive the information accurately. ST simply states that the 'sampling frequency' should be greater than or equal to twice the frequency of the CT signal, where sampling frequency is frequency of sampled signals(DT signals) to be obtained by Sampling.It simply means that when you're taking samples(choosing those "points" from "full line") from the CT signal, do it in such a manner that the samples("chosen points") are more closely spaced. And also take higher number of samples(that is choose higher number of points from the CT signal).

3.1.2 QuantizationQuantization is the process of mapping a large set of input values to a smaller set such as rounding values to some unit of precision. A device or algorithmic functionsthat perform quantization is called aquantizer. The error introduced by quantization is referred to as quantization erroror round off error. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compensationalgorithms.Because quantization is a many-to-few mapping, it is an inherently non-linear and irreversible process (i.e., because the same output value is shared by multiple input values, it is impossible in general to recover the exact input value when given only the output value).

3.1.3 Encoding Encodingis the process by which information from a source is converted into symbols to be communicated.Decodingis the reverse process, converting these code symbols back into information understandable by a receiver.One reason for coding is to enable communication in places where ordinary spoken or written language is difficult or impossible. For example, semaphore, where the configuration of flagsheld by a signaller or the arms of a semaphore towerencodes parts of the message, typically individual letters and numbers. Another person standing a great distance away can interpret the flags and reproduce the words sent.

3.2 NOISE IN COMMUNICATIONNoise affects communication by somehow altering the message. In a very basic model of communication, a message has to pass from the receiver to the recipient through a channel.Noise is something that interferes with the transmission of the message through the channel. An easy way to think of this is to picture static on a TV. The static is the noise that interferes with the transmission of the TV program through the channel of your cable box or satellite dish. This makes it difficult to understand the message sent by the TV program; you may not hear what someone on TV says correctly, and so misinterpret what they say, for example.Noise doesn't necessarily have to be something external that affects the channel. It can also be something internal to the recipient that affects how they receive the message. An example of this is if someone is in a bad mood. Being in a bad mood makes you more likely to interpret other people's messages as negative or hostile; the noise of your emotion affects how you see what they're trying to communicate.3.2.1 Types of noise in communication are classified as:-

EXTERNAL NOISE: - noise external to the system is external noiseATMOSPHERIC NOISE: - noise due to natural electric disturbances such as lightning.SOLAR NOISE: - noise due to solar radiationsIndustrial noise: - electric motor, generator, aircraft produce EM sig. In the range 1 Hz-600 Hz.INTERNAL NOISE: - noise internal to a system is internal noiseSHORT NOISE: - it arises in electric devices because of discrete nature of current flow, it is Gaussian in nature.FLICKER NOISE: - it is due to imperfect surface behaviour of semi-conductor devicesTHERMAL NOISE: - NOISE generated due to random motion of free charged particles.3.3 FILTERINGAfilteris a device or process that removes from a signalsome unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequenciesand not others in order to suppress interfering signals and reduce background noise.Alow-pass filteris anelectronic filter that passes low-frequency signalsandattenuates(reduces theamplitudeof) signals with frequencies higher than thecutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called ahigh-cut filter, ortreble cut filterwhen used in audio applications. A low-pass filter is the opposite of ahigh-pass filter. Aband-pass filteris a combination of a low-pass and a high-pass.3.3.1 Butterworth filterTheButterworth filteris a type ofsignal processing filterdesigned to have as flat afrequency responseas possible in thepassband. It is also referred to as amaximally flat magnitude filter.3.3.2 Chebychev filterChebyshev filtersareanalogordigitalfilters having a steeperroll-offand morepass bandripple(type I) orstop bandripple (type II) thanButterworth filters. Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the range of the filter, but with ripples in the pass band.Response of a 1st Oder chebychev filter.3.3.3 Comparison of the response of each filters3.3.4.2 Matlab code for designing a filter(5th Oder Butterworth filter)fs = 1e4;t = 0:1/fs:5;n = sin(2*pi*1000000*t); sw = 0.1*cos(2*pi*5*t);swn = sw + n;figure(1)plot(sw);figure(2)plot(n);figure(3)plot(swn);

Fc = 500 ; %cut off frequency

w = Fc/(2*fs); [b,a]=butter(5,w,'low'); %5th order butterworth LPF[h,w]=freqz(b,a,1024);

y=filter(b,a,swn);figure(4)plot(y);

figure(5)plotHandle=plot(w/pi*2*fs,abs(h));set(plotHandle,'LineWidth',2.5);title('Frequency Response of a 5th Order Butterworth LPF');xlabel('Frequency (Hz)')ylabel('Magnitude');grid;

OUTPUT:-

a b c dInput signal, noise signal , received signal and the response of the filter respectively.3.3.4.2 Matlab code for noise reduction using low pass filtering for recorded sound[y,fs]=wavread('11863__medialint__nord-analog-howling-wind-storm (1).wav'); ch1=y(:,1); time=(1/44100)*length(ch1);t=linspace(0,time,length(ch1));figure(1)plot(y); L=length(ch1); NFFT = 2^nextpow2(L); % Next power of 2 from length of yY = fft(y,NFFT)/L;Y1=log10(Y);figure(2) f = fs/2*linspace(0,1,NFFT/2+1);plot(f,2*abs(Y1(1:NFFT/2+1))) ; [b,a]=butter(10,3000/(44100/2),'high');Y1=filtfilt(b,a,Y1); % freqz(b,a)figure(3) plot(f,2*abs(Y1(1:NFFT/2+1))) ; title('Single-Sided Amplitude Spectrum of y(t)');xlabel('Frequency (Hz)');ylabel('|Y(f)|')xlim([0 50000])OUTPUT:-

3.4 EMPHERICAL MODE DECOMPOSITION ALGORITHM

4.1 INTRODUCTION:-

EMD is a method of breaking down a signal without leaving the time domain. It can be compared to other analysis methods like Fourier Transforms and wavelet decomposition. The process is useful for analyzing natural signals, which are most often non-linear and non-stationary. This parts from the assumptions of the methods we have thus far learned (namely that the systems in question be LTI, at least in approximation).

EMD is a method of breaking down a signal without leaving the time domain. It can be compared to other analysis methods like Fourier Transforms and wavelet decomposition. The process is useful for analyzing natural signals, which are most often non-linear and non-stationary. This parts from the assumptions of the methods we have thus far learned (namely that the systems in question be LTI, at least in approximation). EMD filters out functions which form a complete and nearly orthogonal basis for the original signal. Completeness is based on the method of the EMD; the way it is decomposed implies completeness. The functions, known as Intrinsic Mode Functions (IMFs), are therefore sufficient to describe the signal, even though they are not necessarily orthogonal. The reasons are described in Huang et al., published in the Royal Society Proceedings on Math, Physical, and Engineering Sciences: "...the real meaning here applies only locally. For some special data, the neighbouring components could certainly have sections of data carrying the same frequency at different time durations. But locally, any two components should be orthogonal for all practical purposes" . The fact that the functions into which a signal is decomposed are all in the time-domain and of the same length as the original signal allows for varying frequency in time to be preserved. Obtaining IMFs from real world signals is important because natural processes often have multiple causes, and each of these causes may happen at specific time intervals. This type of data is evident in an EMD analysis, but quite hidden in the Fourier domain or in wavelet coefficients. Some examples of data to which the EMD method may be applied quite effectively are seismic readings, results of neuroscience experiments, electrocardiograms (which we will examine later), gastroelectrograms, and sea-surface height (SSH) readings. IMF:1.The EMD will break down a signal into its component IMFs. 2.An IMF is a function that: has only one extreme between zero crossings, and has a mean value of zero.

4.2 APPLICATION:EMD is most useful (and as we will see later, perhaps only useful) for non-linear, non-stationary signals, and natural signals. As an example of this, we have applied the EMD to several signals, two of which are the raw data from electrocardiograms that we found on the web. The horizontal axis represents sample number, as sampling rate was not available for both.

Fig4.2.1 ECG signal

Fig4.4.2 Plots run from c14 on the upper left to c1 on the lower right.

Each IMF represents a different part of the signal, giving a fairly good breakdown of different causation parts of the total composite heartbeat. While the wave in ecg.mat (of which we still cannot determine a cause) causes the EMD some problems, the signal ekg.mat was broken down fairly efficiently, especially in IMF c3, where each heartbeat has been identified as a single entity amidst the other lesser parts that together compose a single beat.

Part of the importance of the EMD is the way it decomposes signals over which Fourier Transforms stumble. Because of the way the EMD keeps signals in their own domain, it can deal with signals which would otherwise be considered "poorly-behaved." When a signal enters a new domain, the way certain select characteristics change with the original variable are totally lost. While the signal may be accurately retrieved, the signal cannot be effectively analyzed in the new domain without this information. The EMD does not have this problem. When it decomposes a time-domain signal into IMFs, for instance, each mode function contains information about how the frequency of the original signal changes in time. Because of this, the EMD needs not assume the slightest pretention towards linearity or time-invariance.

(a) the blue curve is the input signal x(t), red circles represent the local maxima, and the green squares are local minima. (b) Black line is upper and lower envelopes represented by cubic spline interpolation, and the red line is the mean envelope m11(t). (c) the blue curve represents the input signal minus the mean envelop (h11 (t) = x(t) m11 (t)), and the black line is the envelopes. (d) The blue signal is the first IMF (c1 (t)) since it meets the IMF requirements. (e) Blue curve is the input signal minus the first IMF (residual r1(t) = x(t) c1 (t)), to be considered as new input signal. (f) Blue curve is the second IMF (c2 (t)) together with its upper, lower and mean envelopes

4.3 CODE:

CODE 1 :% EMD: Emprical mode decomposition x = ecg(500)';%x1 = 3.5*ecg(2700).';%y1 = sgolayfilt(kron(ones(1,13),x1),0,21);%n = 1:30000;%del = round(2700*rand(1));%mhb = y1(n + del);%t = 0.00025:0.00025:7.5;%plot(t,mhb);%axis([0 2.5 -4 4]);%grid;%xlabel('Time [sec]');%ylabel('Voltage [mV]');%title('Maternal Heartbeat Signal');%t=-10:0.1:10; %x=2*sin(2*pi*t); %n=10; imf = emd(x,n) % % x - input signal (must be a column vector) % n - number of intrinsic mode functions % imf - Matrix of intrinsic mode functions (each as a row) subplot(4,1,1);plot(t,x) subplot(4,1,2); plot(t,x1) subplot(4,1,3); plot(t,x2) subplot(4,1,4); plot(t,x3)

CODE 2:

function imf = emd(x,n); c = x(:)'; % copy of the input signal (as a row vector) N = length(x); %------------------------------------------------------------------------- % loop to decompose the input signal into n successive IMFs imf = []; % Matrix which will contain the successive IMF, and the residue for t=1:n % loop on successive IMFs %------------------------------------------------------------------------- % inner loop to find each imf h = c; % at the beginning of the sifting process, h is the signal SD = 1; % Standard deviation which will be used to stop the sifting process while SD > 0.3 % while the standard deviation is higher than 0.3 (typical value) % find local max/min points d = diff(h); % approximate derivative maxmin = []; % to store the optima (min and max without distinction so far) for i=1:N-2 if d(i)==0 % we are on a zero if sign(d(i-1))~=sign(d(i+1)) % it is a maximum maxmin = [maxmin, i]; end elseif sign(d(i))~=sign(d(i+1)) % we are straddling a zero so maxmin = [maxmin, i+1]; % define zero as at i+1 (not i) end end if size(maxmin,2) < 2 % then it is the residue break end % divide maxmin into maxes and mins if maxmin(1)>maxmin(2) % first one is a max not a min maxes = maxmin(1:2:length(maxmin)); mins = maxmin(2:2:length(maxmin)); else % is the other way around maxes = maxmin(2:2:length(maxmin)); mins = maxmin(1:2:length(maxmin)); end % make endpoints both maxes and mins maxes = [1 maxes N]; mins = [1 mins N]; %------------------------------------------------------------------------- % spline interpolate to get max and min envelopes; form imf maxenv = spline(maxes,h(maxes),1:N); minenv = spline(mins, h(mins),1:N); m = (maxenv + minenv)/2; % mean of max and min enveloppes prevh = h; % copy of the previous value of h before modifying it h = h - m; % substract mean to h % calculate standard deviation eps = 0.0000001; % to avoid zero values SD = sum ( ((prevh - h).^2) ./ (prevh.^2 + eps) ); end imf = [imf; h]; % store the extracted IMF in the matrix imf % if size(maxmin,2)> channel impulse response Guard interval Resistance to frequency selective fading Each subchannel is almost flat fading Simple equalization Each subchannel is almost flat fading, so it only needs a one-tap equalizer to overcome channel effect. Efficient bandwidth usageThe subchannel is kept orthogonality with overlap

Disadvantages The problem of synchronization Symbol synchronization Timing errors Carrier phase noise Frequency synchronization Sampling frequency synchronization Carrier frequency synchronization Need FFT units at transmitter, receiver The complexity of computations

4.3 Matlab code for noise minimization in an OFDM signalclear allclcclose M = 4; no_of_data_points = 64; block_size = 8; cp_len = ceil(0.1*block_size); no_of_ifft_points = block_size; no_of_fft_points = block_size; data_source = randsrc(1, no_of_data_points, 0:M-1);figure(1)stem(data_source); grid on; xlabel('Data Points'); ylabel('Amplitude')title('Transmitted Data "O"') % Perform QPSK modulationqpsk_modulated_data = pskmod(data_source, M);scatterplot(qpsk_modulated_data);title('MODULATED TRANSMITTED DATA'); num_cols=length(qpsk_modulated_data)/block_size;data_matrix = reshape(qpsk_modulated_data, block_size, num_cols); cp_start = block_size-cp_len;cp_end = block_size; % cyclic prefixingfor i=1:num_cols, ifft_data_matrix(:,i) = ifft((data_matrix(:,i)),no_of_ifft_points); for j=1:cp_len, actual_cp(j,i) = ifft_data_matrix(j+cp_start,i); end ifft_data(:,i) = vertcat(actual_cp(:,i),ifft_data_matrix(:,i));end % 4. Convert to serial stream for transmission[rows_ifft_data cols_ifft_data]=size(ifft_data);len_ofdm_data = rows_ifft_data*cols_ifft_data; % Actual OFDM signal to be transmittedofdm_signal = reshape(ifft_data, 1, len_ofdm_data);figure(3)plot(real(ofdm_signal)); xlabel('Time'); ylabel('Amplitude');title('OFDM Signal');grid on; noise = randn(1,len_ofdm_data) + sqrt(-1)*randn(1,len_ofdm_data); avg=0.4;for i=1:length(ofdm_signal) if ofdm_signal(i) > avg ofdm_signal(i) = ofdm_signal(i)+noise(i); end if ofdm_signal(i) < -avg ofdm_signal(i) = ofdm_signal(i)+noise(i); endendfigure(4)plot(real(ofdm_signal)); xlabel('Time'); ylabel('Amplitude');title('OFDM Signal with noise');grid on; channel = randn(1,block_size) + sqrt(-1)*randn(1,block_size); after_channel = filter(channel, 1, ofdm_signal); % 2. Add Noiseawgn_noise = awgn(zeros(1,length(after_channel)),0); % 3. Add noise to signal... recvd_signal = awgn_noise+after_channel; % 4. Convert Data back to "parallel" form to perform FFTrecvd_signal_matrix = reshape(recvd_signal,rows_ifft_data, cols_ifft_data); % 5. Remove CPrecvd_signal_matrix(1:cp_len,:)=[]; % 6. Perform FFTfor i=1:cols_ifft_data, % FFT fft_data_matrix(:,i) = fft(recvd_signal_matrix(:,i),no_of_fft_points);end % 7. Convert to serial streamrecvd_serial_data = reshape(fft_data_matrix, 1,(block_size*num_cols));scatterplot(recvd_serial_data);title('MODULATED RECEIVED DATA'); % 8. Demodulate the dataqpsk_demodulated_data = pskdemod(recvd_serial_data,M);scatterplot(recvd_serial_data);title('MODULATED RECEIVED DATA');figure(5)stem(qpsk_demodulated_data,'rx');grid on;xlabel('Data Points');ylabel('Amplitude');title('Received Data "X"')

4.4 Output and results

CONCLUSIONS FROM THE PROJECT We used the Nayantara Image(figure 1) in png format ,adding four noise (Speckle, Gaussian ,Poisson and Salt & Pepper) in original image with standard deviation(0.025) De-noised all noisy images by all filters and conclude from the results that: (a)The performance of the Wiener Filter after de-noising for all Speckle, Poisson and Gaussian noise is better than Mean filter and Median filter. (b)The performance of the Median filter after de-noising for all Salt & Pepper noise is better than Mean filter and Wiener filter. Part of the importance of the EMD is the way it decomposes signals over which Fourier Transforms stumble. Because of the way the EMD keeps signals in their own domain, it can deal with signals which would otherwise be considered "poorly-behaved." When a signal enters a new domain, the way certain select characteristics change with the original variable are totally lost. While the signal may be accurately retrieved, the signal cannot be effectively analyzed in the new domain without this information. The EMD does not have this problem. When it decomposes a time-domain signal into IMFs, for instance, each mode function contains information about how the frequency of the original signal changes in time. Because of this, the EMD needs not assume the slightest pretention towards linearity or time-invariance. The EMD is obviously far superior when used for the right purposes. For outputs of linear, time-invariant systems the EMD is all but worthless, and time-consuming to calculate besides. For non-linear, non-stationary signals like so many signals are in the real world, however, the EMD is not only a useful method but possibly the only computational method of analysis. Taking our example of the ECG, until recently readouts of test data like that which we used were examined by eye and results were determined by estimation. Methods like this are not standardized and not very repeatable. The EMD may provide efficient handling of natural data. LPF filtering is a must to filter out the noise, the efficiency for noise removal is very poor in this case. We have used a 5th Oder Butterworth filter to get the best response possible. Least mean square (LMS) algorithm is a very efficient method for noise minimization in communication systems. The adaptive nature of the algorithm provides the best output among LPF, EMD and LMS. In emerging 4G technology in wireless communication OFDMA is the access scheme for speed and efficiency to provide error free communication using a OFDM channel. We have designed a code for addition of noise and its removal in an OFDM channel.

FUTURE SCOPE OF WORK

Noise minimization in video signals Analysis of variety of noise in image and their implementation into the codes designed. Hardware implementation of the study done To design an algorithm based on the study in Oder to publish the research

REFERENCES

The lists of references for the project are:-1. Freesound.org - 'avalanche.wav' by mystiscool_files2. Reuter_Schweizer_Sound_triggering_ISSW093. A20_PhysRevLett_93_2380014. acoustic-wave-technology-sensors-9365. Chanchal De PhD Thesis6. TA_Radio waves_EN7. Basics of wireless communication by Theodore.s.rappaport.8. Analog and digital communication by B.P.Lathi.9. Analog communication by milliman halkias.10. Digital signal processing by Oppenheim.

BIBLIOGRAPHYwww.wikipedia.comwww.mecanum.com/fileswww.cdbaby.com/cd/ChuckWilson

www.treemangathering.com/hollowvoicesnewcd.htmlwww.ias.ac.in/sadhana/Pdf2007Jun/155.PDFHouston Chronicle Archives http://hdl.handle.net/2115/20232www.sciencedirect.comwww2.imm.dtu.dk/~pch/Projekter/acoustic.htmlwww.mpl.ucsd.edu/people/pgerstoft/asa/neumann.pdfwww.iitd.ac.in/

44

Documents

NOISE MINIMIZATION IN IMAGES AND COMMUNICATION