0.

Analogy between vector and signal

Analogy between vector and signalVector is one which has magnitude and direction. consider two vectors v1 and v2. component of vector v1 along v2 is obtained by drawing perpendicular from the end of vector v1.

Where c12 co-efficient ve error vectorv1v2vec12v2

Analogy between vector and signalThe co-efficient is selected such that the error vector is minimum.Component of v1 along v2 is given by c12v2 v1 =c12v2+veIf the angle between the vector is there dot product is v1.v2= |v1||v2| cos Component of v1 along v2 =| v1 | cos c12 v2 =|v1| cos =v1.v2/|v2|

Analogy between vector and signalIf vectors v1 and v2 are orthogonal dot product of v1 and v2 is zero so as c12. v1.v2C12= |v2| 2

Analogy between vector and signalConsider two signals f1(t) and f2(t)Component signal of f1(t) along f2(t)=c12f2(t)f1(t)=c12f2(t)+fe(t)fe(t)=f1(t)-c12f2(t)

C12 co-efficientfe(t) error function

Analogy between vector and signalTo find the value of co-efficient c12 the error signal should be minimum for the error to be minimum the mean of error of signal is taken E mean

Where E= 1 fe2(t) dt t2-t1dE/dc12=0

t2t1

Analogy between vector and signald ( 1 (f1 (t)-c12f2(t)) 2 dt)=0dt t2-t1

f1(t)f2(t) dtC12= f22(t) dt

If the fn f1(t) & f2(t) is orthogonal c12=0t2t2t1t1t2t1