Signals and Systems

Signals and Systems. Introduction- -I.

Digital Control System. Digital Controller DAC ADC Plant Sensor + -.

Continuous and Discrete. T he inputs and outputs of electrical, mechanical, chemical and biological processes are measured as functions of time with amplitudes expressed in terms of voltage, current, torque, pressure, etc. These functions are called continuous-time signals , and to process them with a computer they must be converted into binary sequences—or a string of ones and zeros that is understood by the computer . In a digital computer, differentiation and integration can be done only approximately, and the solution of ordinary differential equations requires a discretization process..

Signal Representation. 4.

5.

6. Simulink Model. Ts=O.1s t sin 10 ZOH Ts = 0.05s ZOHI.

Derivative and Forward Finite Difference. Derivative operator:  Forward finite difference operator:.

Check-1. The forward finite difference is Coinciding with the derivative..

Check-2. The forward finite difference is The derivative is.

Check-3. The forward finite difference is The derivative is.

Conclusion. 11. Number of samples, n. Number of samples, n.

12. Simulink Model. Is Sample Time 0.01 Au Ts = 0.01s 0.02 Scope 0.01.

Derivative and Backward Finite Difference. 13.

Check-4. 14.

15. Matlab Program. Matlab Program. Ts = 0.1 ; %% forward finite difference for n=0:N-1, x1 = 4*cos(2*pi*(n+1)* Ts ); x2 = 4*cos(2*pi*n* Ts ); del_x1(n+1) = x1-x2; end yf = del_x1/ Ts ; %% backward finite difference for n=0:N-1, x1 = 4*cos(2*pi*n* Ts ); x2 = 4*cos(2*pi*(n-1)* Ts ); del_x2(n+1) = x1-x2; end yb = del_x2/ Ts ;.

Integration and Summation. 16. n=0. n=1. n=9. high base.

17. Check-5. Check-5. abstract. Upper bound approximation.