Page 66 - Applied Numerical Methods Using MATLAB

PROBLEMS 55
4
output analog input
2 digital
output
0

−2
input time
−4
−4 −2 0 2 4 0 2 4 6 8
(a) The input-output relationship of an ADC (b) The output of an ADC to a sinusoidal input
Figure P1.10 The characteristic of an ADC (analog-to-digital converter).

(b) Make a program that uses two ADC routines to find the output d for
the analog input data a = 3*sin(t) with t = [0:200]/100*pi and
plots a and d versus t to see how the analog input is converted into the
digital output by the ADC. The graphic result is supposed to be like
Fig. P1.10b.
1.11 Playing with Polynomials
(a) Polynomial Evaluation: polyval()
Write a MATLAB statement to compute
8
p(x) = x − 1 for x = 1 (P1.11.1)
(b) Polynomial Addition/Subtraction by Using Compatible Vector Addi-
tion/Subtraction
Write a MATLAB statement to add the following two polynomials:

2
4
3
p 1 (x) = x + 1, p 2 (x) = x − 2x + 1 (P1.11.2)
(c) Polynomial Multiplication: conv()
Write a MATLAB statement to get the following product of polynomials:
4 2
p(x) = (x + 1)(x + 1)(x + 1)(x − 1) (P1.11.3)
(d) Polynomial Division: deconv()
Write a MATLAB statement to get the quotient and the remainder of
the following polynomial division:
8
2
p(x) = x /(x − 1) (P1.11.4)
(e) Routine for Differentiation/Integration of a Polynomial
What you see in the below box is the routine “poly_der(p)”, which
gets a polynomial coefficient vector p (in the descending order) and
outputs the coefficient vector pd of its derivative polynomial. Likewise,
you can make a routine “poly_int(p)”, which outputs the coefficient