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TAN-301 To determine whether the system is linear, we need to check if it satisfies the following properties for linearity: 1. Additivity: If the input is ( x_1(t) + x_2(t) ), the output should be ( y_1(t) + y_2(t) ). 2. Scaling: If the input is ( alpha x(t) ), the output should be ( alpha y(t) ). In this case, the system is described by ( y(t) = x(t) ). Let's test both properties. **Additivity Test:** Suppose the inputs are ( x_1(t) ) and ( x_2(t) ). Then, the outputs would be ( y_1(t) = x_1(t) ) and ( y_2(t) = x_2(t) ). Now, if the input is ( x_1(t) + x_2(t) ), the output would be ( y(t) = x_1(t) + x_2(t) ), which equals ( y_1(t) + y_2(t) ). **Scaling Test:** Suppose the input is ( alpha x(t) ). Then, the output would be ( y(t) = alpha x(t) ), which equals ( alpha y(t) ). Since the system satisfies both properties, it is linear. The system is described by ( y(t) = x(t) ). Let's test both properties. **Additivity Test:** Suppose the inputs are ( x_1(t) ) and ( x_2(t) ). Then, the outputs would be ( y_1(t) = x_1(t) ) and ( y_2(t) = x_2(t) ). Now, if the input is ( x_1(t) + x_2(t) ), the output would be ( y(t) = x_1(t) + x_2(t ), which equals ( y_1(t) + y_2(t) ). **Scaling Test:** Suppose the input is ( alpha x(t) ). Then, the output would be ( y(t) = alpha x(t) ), which equals ( alpha y(t) ). Since the system satisfies both properties, it is linear. **Additivity Test:** Suppose the inputs are ( x_1(t) ) and x_2(t) ). Then, the outputs would be ( y_1(t) = x_1(t) ) and ( y_2(t) = x_2(t) ). Now, if iput is ( x_1(t) + x_2(t) ), the output would be ( y(t) = x_1(t) + x_2(t) ), which equals ( y_1(t) + y_2(t) ). **Scaling Test:** Suppose the input is ( alpha x(t) ). Then, the output would be ( y(t) = alpha x(t) ), which equals ( alpha y(t) ). Since the system satisfies both properties, it is linear. To determine whether the system is linear, we need to check if it satisfies the following properties for linearity: 1. Additivity: If the input is ( x_1(t) + x_2(t) ), the output should be ( y_1(t) + y_2(t) ). 2. Scaling: If the input is ( alpha x(t) ), the output should be ( alpha y(t) ). In this case, the system is described by ( y(t) = x(t) ). Let's test both properties. **Additivity Test:** Suppose the inputs are ( x_1(t) ) and x_2(t) ). Then, the outputs would be ( y_1(t) = x_1(t) ) and ( y_2(t) = x_2(t) ). Now, if iput is ( x_1(t) + x2(t) ), the output would be ( y(t) = x_1(t) + x_2(t) ), which equals ( y_1(t) + y_2(t) . **Scaling Test:** Suppose iput is alpha x(t) ). Then, the output would be ( y(t) = alpha x(t) ), which equals ( alpha y(t) . Since eystem satisfies both properties, it is linear. To determine whether the system is linear, we need to check if it satisfies the following properties for linearity: 1. Additivity: If the input is ( x_1(t) + x_2(t) ), the output should be ( y_1(t) + y_2(t) ). 2. Scaling: If the input is ( alpha x(t) ), the output should be ( alpha y(t) ). In this case, the system is described by ( y(t) = x(t) ). Let's test both properties. **Additivity Test:** Suppose iputs are x_1(t) ) and x_2(t) ). Then, the outputs would be ( y_1(t) = x_1(t) ) and y_2(t) = x_2(t) ). Now, if iput is ( x_1(t) + x_2(t) ), the output would be ( y(t) = x_1(t) + x_2(t) ), which equals ( y_1(t) + y_2(t) ). **Scaling Test:** Suppose iput is alpha x(t) ). Then, the output would be ( y(t) = alpha x(t) ), which equals ( alpha y(t) ). Since eystem satisfies both properties, it is linear. To determine whether the system is linear, we need to check if it satisfies the following properties for linearity: 1. Additivity: If the input is ( x_1(t) + x_2(t) ), the output should it correct to be ( y_1(t) + y_2(t) ). 2. Scaling: If the input is ( alpha x(t) ), the output should be ( alpha y(t) ). In this case, the system is described by ( y(t) = x(t) ). Let's test both properties. **Additivity Test:** Suppose iputs are x_1(t) ) and x_2(t) ). Then, the outputs would be ( y_1(t) = x_1(t) ) and y_2(t) = x_2(t) ). Now, if iput is ( x_1(t) + x_2(t) ), the output would be ( y(t) = x_1(t) + x_2(t) ), which equals ( y_1(t) + y_2(t) ). **Scaling Test:** Suppose iput is alpha x(t) ). Then, the output would be ( y(t) = alpha x(t) ), which equals ( alpha y(t) ). Since eystem satisfies both properties, it is linear. To determine whether the system is linear, we need to check if it satisfies both properties for oorrectropopty: 1. Additivity: If the input is ( x_1(t) + x_2(t) ), the output should be ( y_1(t) + y_2(t) ). 2. Scaling: If iput is ( alpha x(t) ), the output should be ( alpha y(t) ). In this case, system is described by ( y(t) = x(t) ). Let's test both properties. **Additivity Test:** Suppose iputs are x_1(t) ) and x_2(t) ). Then, the outputs would be ( y_1(t) = x_1(t) ) and y_2(t) = x_2(t) ). Now, if iput is ( x_1(t) + x_2(t) ), the output would be ( y(t) = x_1(t) + x_2(t) ), which equals ( y_1(t) + y_2(t) ). **Scaling Test:** Suppose iput is alpha x(t) ). Then, the output would be ( y(t) = alpha x(t) ), which equals ( alpha y(t) ). Since system satisfies both properties, it is linear. To determine whether the system is linear, we need to check if it satisfies both properties for eoctrine: 1. Additivity: If etput is ( x_1(t) + x_2(t) ), the output should be ( y_1(t) + x_2(t) ). 2. Scaling: If iput is ( alpha x(t) ), the output should be ( alpha y(t) ). In this case, system is described by y(t) = x(t) ). Let's test both properties. **Additivity Test:** Suppose iputs are x_1(t) ) and x_2(t) ). Then, the outputs would be ( y_1(t) = x_1(t) ) and y_2(t) = x_2(t) ).

2011年2月20日63 分