Ministry of development of information technologies and telecommunications tashkent university of information technologies named after muhammad al-khorezmi

MINISTRY OF DEVELOPMENT OF INFORMATION TECHNOLOGIES AND TELECOMMUNICATIONS
TASHKENT UNIVERSITY OF INFORMATION TECHNOLOGIES NAMED AFTER MUHAMMAD AL-KHOREZMI

Practical work No. 3

Checked: Дадажонова З.

Fulfilled: Абдурасулов З.

Ташкент – 2022

Theoretical part


Transformation Wavelet
In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function. is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space. of square integrable functions.

An operation in functional analysis that is applied to two functions and returns a third function is called convolution.

Correlation is the ratio of two or more signals. In our case, this is the ratio of data1 and data2.


1.Implementation of the Wavelet transformation in the matlab environment


Compress:

2. Свертка речевого сигнала

clear all;
[data fs] = audioread('Zohirjon.m4a');
x = -3:0.01:1;
z = 3*x.^4-16*x.^3+2;

%convolution

data2 = conv(data, z, 'same');
figure(1),
plot(data2);
title('convulation')

clear all;
[data fs] = audioread('Zohirjon.m4a');
x = -3:0.01:1;
z = 3*x.^4-16*x.^3+2;

%convolution

data2 = conv(data, z, 'same');
figure(1),
plot(data2);
title('convulation')
figure(2),
plot(data);
title('Voice Zohirjon');

3. Корреляция речевого сигнала.
%correlation
n = length(data);
s1 = 0;
s2 = 0;
s3 = 0;
a = sum(data)/n;
b = sum(data2)/n;
for z = 1:n
s1 = s1+(data(z)-a)*(data2(z)-b);
s2 = s2+(data(z)-a)*(data(z)-a);
s3 = s3+(data2(z)-b)*(data2(z)-b);
end
r1 = abs(s1/sqrt(s2*s3))*100

4. Дискретное косинусное преобразование
clear all;
[data fs] = audioread('Zohirjon.m4a');
x = -3:0.01:1;
z = 3*x.^4-16*x.^3+2;
%% DCT
a_dct=dct(a);
b_dct=idct(a_dct);
subplot(411);plot(data);title("основной сигнал");
subplot(412);plot(a_dct);title("Спектер");
subplot(413);stem(a_dct);title("Дискретный значение");
subplot(414);plot(b_dct);title("Востановление сигнала");



Conclusion: In this practical work, I performed 4 operations: Wavelet transform implementation in matlab environment, speech signal convolution, speech signal correlation, discrete cosine transform. I learned how to remove noise from the signal, I found a convolution. Performed a correlation of two signals data1 and data2. And found the Discrete Cosine Transformation of Signals.