7/25/2019 answ.doc

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Write the mean value formula of the signal ( )y t .1

0

1 N

i

i

y yN

=

= (1)

Here,Number of samples isN .

Since, there are 11samples. The value of N is eual to 11.

!o"if# euation (1) for the mean value of signal ( )1y t .

[ ]

1

1

0

0 1 $ % & ' ( ) * + 10

1

1

11

N

i

i

y yN

y y y y y y y y y y y

=

=

= + + + + + + + + + +

Substitute 0 for 0y , 11. for 1y , 1+.0$ for $y , 1+.0$ for %y , 11. for &y , 0 for 'y ,

11. for (y , 1+.0$ for )y , 1+.0$ for *y , 11. for +y an" 0 for 10y .

[ ]1 0 11. 1+.0$ 1+.0$ 11. 0 11. 1+.0$1

11

0

1+.0$ 11. 0y + + + + + +=

=

Substitute 0 for 0y , 1'.$+ for 1y , $&.% for $y , $&.%for %y , 1'.$+ for &y , 0 for 'y ,

1'.$+ for (y , $&.% for )y , $&.% for *y , 1'.$+ for +y an" 0 for 10y .

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

$ $ $ $

$ rms$ $ $ $

0 1'.$+ $&.% $&.% 1'.$+ 01

11 1'.$+ $&.% $&.% 1'.$+ 0

%%*1.&$*

11

1.'%

y + + + + + = + + + + +

=

=

Hence, the rms value for the signal ( )$y t $ rmsy is 1.'% .

Thus, the rms value of a signal having ero mean is a statistical measure of the

fluctuations in the signal.