Signals and Systems - Electrical Engineering

44 C H A P T E R 0: From the Ground Up! Derivatives and Differences The following script compares symbolic with numeric computat ...

0.5 Soft Introduction to MATLAB 45 0 1 2 3 4 5 6 − 1 −0.5 0 0.5 1 t cos (t^2 ) (a) (b) 0 1 2 3 4 5 6 − 10 − 5 0 5 10 t −2 sin (t ...

46 C H A P T E R 0: From the Ground Up! equal to 1. In the following script we are combining numeric and symbolic computations t ...

0.5 Soft Introduction to MATLAB 47 z = int(sinc(t)ˆ2, t, 0, k); % integral of sincˆ2 from 0 to k zz(k) = subs(2∗z); % substituti ...

48 C H A P T E R 0: From the Ground Up! − 1 0 1 −0.5 0 0.5 1 x y x=cos(2πt), y=cos(2πt) x=cos(2πt), y=cos(4πt) x=cos(2πt), y=cos ...

0.5 Soft Introduction to MATLAB 49 − 1 −0.5 0 0.5 1 −0.5 0 0.5 1 x y −0.5 0 0.5 1 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 x y x=cos(2πt), y ...

50 C H A P T E R 0: From the Ground Up! theta = k∗pi/4; % phase of output y = Aˆk∗cos(2∗pi∗t + theta); if k == 0,subplot(221) el ...

0.5 Soft Introduction to MATLAB 51 012345 0 0.05 0.1 0.15 Unit-step response 012345 0 0.05 0.1 0.15 Impulse response 012345 0 0. ...

52 C H A P T E R 0: From the Ground Up! Table 0.1Basic Numeric Matlab Special variables ans Default name for result pi πvalue in ...

Problems 53 Table 0.2Basic Symbolic Matlab Functions Function Operation Calculus diff differentiate int integrate limit limit ta ...

54 C H A P T E R 0: From the Ground Up! 0.1. Bits or bytes Just to get an idea of the number of bits or bytes generated and proc ...

Problems 55 0.4. Backward difference—MATLAB Another definition for the finite difference is the backward difference: 1 [x(nTs)]= ...

56 C H A P T E R 0: From the Ground Up! n Commutative law: ∑ k ak= ∑ p(k) ap(k) for any permutationp(k)of the set of integerskin ...

Problems 57 whereNTs= 1 (i.e., we segment the interval [0,1] intoNintervals of widthTs). Graphically show that the above equatio ...

58 C H A P T E R 0: From the Ground Up! (c) Give an expression of the above sum for all possible values ofα. (d) Suppose now tha ...

Problems 59 0.14. Euler’s identity and trigonometric identities Use Euler’s identity to find an expression forcos(α)cos(β), and ...

60 C H A P T E R 0: From the Ground Up! (b)Compute the derivativey(t)=dx(t)/dtand plot its real and imaginary parts. How do thes ...

Problems 61 0.20. De Moivre’s theorem for roots Consider the calculation of roots of an equation, zN=α whereN≥ 1 is an integer a ...

62 C H A P T E R 0: From the Ground Up! (c) Show that the hyperbolic cosine is always positive and bigger than 1 for all values ...

2 P A R T Theory and Application of Continuous-Time Signals and Systems ...