Question

Analog Signal Processing & Filter Design

Please answser problem 1 below for parts a, b, c, and d. Please show all work written out, and matlab code for checking the problems with matlab.

1. Find the roots of the following polynomials and
**write** them in factored form:

a. s^{2} + 4s + 4 (Use the quadratic equation and check
with Matlab)

b. s^{2} + 2s + 10 (Use the quadratic equation and check
with Matlab)

c. s^{3} + 3s^{2} + 3s + 1 (check with Matlab)

d. s^{5} + 5s^{4} + 5s^{3} + 5s^{2}
+ 5s + 5 (check with Matlab)

Answer #1

**Answer**:**Roots of quadrartic
equation**

**(a.)** s2 + 4s + 4

**( b.)** s2 + 2s + 10

**( c.)** s3 + 3s2 + 3s + 1

**(d )** s5 + 5s4 + 5s3 + 5s2 + 5s + 5

**Factored form**

**For irreducible expressions**

>> syms x

>> factor(x^2 + 2*x++10, x, 'FactorMode', 'complex')

ans =

[ x + 1.0 - 3.0i, x + 1.0 + 3.0i]

>> syms x

>> factor(x^5 + 5*x^4+5*x^3+5*x^2+5*x+5, x, 'FactorMode',
'complex')

ans =

[ x + 4.0048532978402229828370560613657, x +
0.85551861251863940993560935374244 +
0.67897350403368406304597156425586i, x -
0.35794526143875090135413738442528 -
0.95836154763395495528090502329203i, x -
0.35794526143875090135413738442528 +
0.95836154763395495528090502329203i, x +
0.85551861251863940993560935374244 -
0.67897350403368406304597156425586i]

Analog Signal Processing &
Filter Design
Instructions:
Please show how you arrived at the result.
Use 3 significant figures and scientific or engineering
notation.
Use standard rounding, >0.5 in the next significant
figure, round up & <0.5 round down.
Provide the numerical solution to problems (unless the
problem asks for a formula or equation). e.g. don't write
Ö79, write 8.89, don't write 127/9, write 14.1
For the problem below:
Please Use Matlab for plots. Label the Matlab plots,
then capture...

Design the "high pass filter" for the signal,
x(t) = 10 sin (10 t) + 1 sin (1000 t) by MATLAB
I have to submit MATLAB code which is written on A4 size
paper.
Please show me MATLAB code.
* I can't recognize cursive script....

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