Discrete Cosine Transform

Y = 81x-x⁴

n=32;

i = [0:1/n:1-1/n];

f = 81*i - i.^4;

h = hadamard(n);

c = 1./n*f*h;

F = c*h;

Figure 4. Original function graph, transformed by Hadamar’s matrix and reconstructed function graph

5. 
   Y=x/(2*x^2+1)
   

N=128;

i = [0:1/N:1-1/N];

f = i./(2*i.*i+1);

plot(f);

H=hadamard(N);

C = 1./N*f*H;

F=C*H;

subplot(311)

plot(f)

subplot(312)

plot(C)

subplot(313)

plot(F)



Xulosa

Xulosa qilib shuni aytish mumkinki, men ushbu topshiriqni bajarish davomida signallarni filtrlash algoritmlaridan ayrimlari, ya’ni diskret kosinus almashtirish, tezkor Fur’ye almashtirish, Adamar matritsalarini hosil qilish va uning yordamida signallarga ishlov berish usullarini o’rgandim. Xususan, Diskret kosinus almashtirishlardan korrelyatsiya va svertka (o‘ram)ni hisoblashni tezlashtirishda va spektr tahlilida va bundan tashqari ma’lumotlarni siqish, misol uchun ovozni (tovush) yoki tasvirni uzatish, elektrokardiogramma va elektroensenogramma kabi meditsina signallarini yozish uchun foydalanilishini bilib oldim.