Определение системных характеристик цепи. Определение сигнала на выходе цепи. Расчет масштабного множителя на входе цепи, страница 4

= 0.6*-0.2215 + 0.5*0.459 + 0.1*0.05 = -0.1329 + 0.2295 + 0.005  = 0.1016;

Так как входной сигнал состоит из 3-х значений, то x(3T) = x(4T) = x(4T) = … =  0 и далее эти значения при расчете опущены.

n=4:

y(4T) = x(0T)*h(4T-0T) + x(1T)*h(4T-1T) + x(2T)*h(4T-2T)  =

= 0.6*0.18419 + 0.5*-0.2215 + 0.1*0.459 = 0.110514 - 0.11075 + 0.0459 = 0.045664;

n=5:

y(5T) = x(0T)*h(5T-0T) + x(1T)*h(5T-1T) + x(2T)*h(5T-2T) = 

= 0.6*-0.127535 + 0.5*0.18419 + 0.1*-0.2215 = -0.076521 + 0.092095 - 0.02215 = -0.006576;

n=6:

y(6T) = x(0T)*h(6T-0T) + x(1T)*h(6T-1T) + x(2T)*h(6T-2T) = 

= 0.6*0.093238 + 0.5*-0.127535 + 0.1*0.18419  = 0.055943 - 0.063768 + 0.018419 = 0.010594;

n=7:

y(7T) = x(0T)*h(7T-0T) + x(1T)*h(7T-1T) + x(2T)*h(7T-2T) =

= 0.6*-0.067025 + 0.5*0.093238 + 0.1*-0.127535 =  - 0.040215 + 0.046619 - 0.012754 = -0.006349;

n=8:

y(8T) = x(0T)*h(8T-0T) + x(1T)*h(8T-1T) + x(2T)*h(8T-2T) =

= 0.6*0.04843 + 0.5*-0.067025 + 0.1*0.093238  = 0.029058 - 0.033512 + 0.009324 = 0.00487;

n=9:

y(9T) = x(0T)*h(9T-0T) + x(1T)*h(9T-1T) + x(2T)*h(9T-2T) =

= 0.6*-0.034939 + 0.5*0.048430 + 0.1*-0.067025 = - 0.020963 + 0.024215 - 0.006702 = -0.003451;

n=10:

y(10T) = x(0T)*h(10T-0T) + x(1T)*h(10T-1T) + x(2T)*h(10T-2T) =

= 0.6*0.025218 + 0.5*-0.034939 + 0.1*0.04843 = 0.015131 - 0.01747 + 0.004843 = 0.002505;

n=11:

y(11T) = x(0T)*h(11T-0T) + x(1T)*h(11T-1T) + x(2T)*h(11T-2T) =

= 0.6*-0.018199 + 0.5*0.025218 + 0.1*-0.034939 =  -0.010920 + 0.012609 - 0.003494 = -0.001804;

n=12:

y(12T) = x(0T)*h(12T-0T) + x(1T)*h(12T-1T) + x(2T)*h(12T-2T) = 

= 0.6*0.013135 + 0.5*-0.018199 + 0.1*0.025218 = 0.007881 - 0.0091 + 0.002522 = 0.001303;

n=13:

y(13T) = x(0T)*h(13T-0T) + x(1T)*h(13T-1T) + x(2T)*h(13T-2T) =

= 0.6*-0.009479 + 0.5*0.013135 + 0.1*-0.018199 =  -0.005688 + 0.006567 - 0.001820 = -0.00094;

n=14:

y(14T) = x(0T)*h(14T-0T) + x(1T)*h(14T-1T) + x(2T)*h(14T-2T) =

= 0.6*0.006841 + 0.5*-0.009479 + 0.1*0.013135 = 0.004105 - 0.004740 + 0.001313 = 0.000679;

n=15:

y(15T) = x(0T)*h(15T-0T) + x(1T)*h(15T-1T) + x(2T)*h(15T-2T) =

= 0.6*-0.004937 + 0.5*0.006841 + 0.1*-0.009479 = -0.002962 + 0.003421 - 0.000948 = -0.00049;

n=16:

y(16T) = x(0T)*h(16T-0T) + x(1T)*h(16T-1T) + x(2T)*h(16T-2T) =

= 0.6*0.003563 + 0.5*-0.004937 + 0.1*0.006841 = 0.002138 - 0.002469 + 0.000684 = 0.000353;

n=17:

y(17T) = x(0T)*h(17T-0T) + x(1T)*h(17T-1T) + x(2T)*h(17T-2T) = 

= 0.6*-0.002572 + 0.5*0.003563 + 0.1*-0.004937 =  -0.001543 + 0.001782 - 0.000494 = -0.000255;

n=18:

y(18T) = x(0T)*h(18T-0T) + x(1T)*h(18T-1T) + x(2T)*h(18T-2T) =

= 0.6*0.001856 + 0.5*-0.002572 + 0.1*0.003563 = 0.001114 - 0.001286 + 0.000356 = 0.000184;

n=19:

y(19T) = x(0T)*h(19T-0T) + x(1T)*h(19T-1T) + x(2T)*h(19T-2T) =

= 0.6*-0.001339 + 0.5*0.001856 + 0.1*-0.002572 = -0.000804 + 0.000928 - 0.000257 = -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}

По формуле круговой свертки.

 - формула круговой свертки.

где N₁ – число отчетов импульсной характеристики.

N₂ –  число отчетов входного воздействия.

N₁ = 20;

N₂ = 3;

N = N₁ + N₂ – 1 = 22;

n=0:

y(0T) = x(0T)h(0T - 0T) + x(1T)h(0T - 1T) + x(2T)h(0T - 2T) = 0.6*-0.1 = -0.06;

n=1:

y(1T) = x(0T)h(1T - 0T) + x(1T)h(1T - 1T) + x(2T)h(1T - 2T) = 0.6*0.05 + 0.5*-0.1 = -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 = 0.2904;

n=3:

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