Определение системных характеристик цепи. Определение сигнала на выходе цепи. Расчет масштабного множителя на входе цепи, страница 3

= -0.5*0.045664 + 0.16*0.1016 = -0.022832 + 0.016256  = -0.006576;

n=6:

y(6T) = - 0,5y(6T – T) + 0,16y(6T – 2T) - 0,1x(6T) + 0,5x(6T – 2T) =

= - 0,5y(5T) + 0,16y(4T) - 0,1x(6T) + 0,5x(4T) =

= -0.5*-0.006576 + 0.16*0.045664 = 0.003288 + 0.007306 = 0.010594;

n=7:

y(7T) = - 0,5y(7T – T) + 0,16y(7T – 2T) - 0,1x(7T) + 0,5x(7T – 2T) =

= - 0,5y(6T) + 0,16y(5T) - 0,1x(7T) + 0,5x(5T) =

= -0.5*0.010594 + 0.16*-0.006576 = -0.005297 + -0.001052 = -0.006349;

n=8:

y(8T) = - 0,5y(8T – T) + 0,16y(8T – 2T) - 0,1x(8T) + 0,5x(8T – 2T) =

= - 0,5y(7T) + 0,16y(6T) - 0,1x(8T) + 0,5x(6T) =

= -0.5*-0.006349 + 0.16*0.010594 = 0.003175 + 0.001695 = 0.00487;

n=9:

y(9T) = - 0,5y(9T – T) + 0,16y(9T – 2T) - 0,1x(9T) + 0,5x(9T – 2T) =

= - 0,5y(8T) + 0,16y(7T) - 0,1x(9T) + 0,5x(7T) =

= -0.5*0.00487 + 0.16*-0.006349 = -0.002435 + -0.001016 = -0.003451;

n=10:

y(10T) = - 0,5y(10T – T) + 0,16y(10T – 2T) - 0,1x(10T) + 0,5x(10T – 2T) =

= - 0,5y(9T) + 0,16y(8T) - 0,1x(10T) + 0,5x(8T) =

= -0.5*-0.003451 + 0.16*0.004870 = 0.001725 + 0.000779 = 0.002505;

n=11:

y(11T) = - 0,5y(11T – T) + 0,16y(11T – 2T) - 0,1x(11T) + 0,5x(11T – 2T) =

= - 0,5y(10T) + 0,16y(9T) - 0,1x(11T) + 0,5x(9T) =

= -0.5*0.002505 + 0.16*-0.003451 = -0.001252 + -0.000552 = -0.001804;

n=12:

y(12T) = - 0,5y(12T – T) + 0,16y(12T – 2T) - 0,1x(12T) + 0,5x(12T – 2T) =

= - 0,5y(11T) + 0,16y(10T) - 0,1x(12T) + 0,5x(10T) =

= -0.5*-0.001804 + 0.16*0.002505 = 0.000902 + 0.000401 = 0.001303;

n=13:

y(13T) = - 0,5y(13T – T) + 0,16y(13T – 2T) - 0,1x(13T) + 0,5x(13T – 2T) =

= - 0,5y(12T) + 0,16y(11T) - 0,1x(13T) + 0,5x(11T) =

= -0.5*0.001303 + 0.16*-0.001804 = -0.000651 + -0.000289 = -0.00094;

n=14:

y(14T) = - 0,5y(14T – T) + 0,16y(14T – 2T) - 0,1x(14T) + 0,5x(14T – 2T) =

= - 0,5y(13T) + 0,16y(12T) - 0,1x(14T) + 0,5x(12T) =

= -0.5*-0.00094 + 0.16*0.001303 = 0.000470 + 0.000208 = 0.000679;

n=15:

y(15T) = - 0,5y(15T – T) + 0,16y(15T – 2T) - 0,1x(15T) + 0,5x(15T – 2T) =

= - 0,5y(14T) + 0,16y(13T) - 0,1x(15T) + 0,5x(13T) =

= -0.5*0.000679 + 0.16*-0.00094 = -0.000339 + -0.00015 = -0.00049;

n=16:

y(16T) = - 0,5y(16T – T) + 0,16y(16T – 2T) - 0,1x(16T) + 0,5x(16T – 2T) =

= - 0,5y(15T) + 0,16y(14T) - 0,1x(16T) + 0,5x(14T) =

= -0.5*-0.00049 + 0.16*0.000679 = 0.000245 + 0.000109 = 0.000353;

n=17:

y(17T) = - 0,5y(17T – T) + 0,16y(17T – 2T) - 0,1x(17T) + 0,5x(17T – 2T) =

= - 0,5y(16T) + 0,16y(15T) - 0,1x(17T) + 0,5x(15T) =

= -0.5*0.000353 + 0.16*-0.00049 = -0.000177 + -0.000078 = -0.000255;

n=18:

y(18T) = - 0,5y(18T – T) + 0,16y(18T – 2T) - 0,1x(18T) + 0,5x(18T – 2T) =

= - 0,5y(17T) + 0,16y(16T) - 0,1x(18T) + 0,5x(16T) =

= -0.5*-0.000255 + 0.16*0.000353 = 0.000128 + 0.000057 = 0.000184;

n=19:

y(19T) = - 0,5y(19T – T) + 0,16y(19T – 2T) - 0,1x(19T) + 0,5x(19T – 2T) =

= - 0,5y(18T) + 0,16y(17T) - 0,1x(19T) + 0,5x(17T) =

= -0.5*0.000184 + 0.16*-0.000255 = -0.000092 + -0.000041 = -0.000133;

Сигнал на выходе:

y(nT) = {-0.06; -0.02; 0.2904; 0.1016; 0.045664; -0.006576; 0.010594; -0.006349; 0.00487; -0.003451; 0.002505; -0.001804; 0.001303; -0.00094; 0.000679; -0.00049; 0.000353; -0.000255; 0.000184; -0.000133}

б) По формуле свертки (линейной и круговой).

По формуле линейной свертки.

 - формула линейной свертки.

n=0:

y(0T) = x(0T)*h(0T-0T) = 0.6*-0.1 = -0.06;

n=1:

y(1T) = x(0T)*h(1T-0T) + x(1T)*h(1T-1T) = 0.6*0.05 + 0.5*-0.1 = 0.03 - 0.05 = -0.02;

n=2:

y(2T) = x(0T)*h(2T-0T) + x(1T)*h(2T-1T) + x(2T)*h(2T-2T) =

= 0.6*0.459 + 0.5*0.05 + 0.1*-0.1 = 0.2754 + 0.025 - 0.01 = 0.2904;

n=3:

y(3T) = x(0T)*h(3T-0T) + x(1T)*h(3T-1T) + x(2T)*h(3T-2T)  =