Question

Given the following equation:

H(z)= 2+5z⁻¹-9z⁻²+5z⁻³+3z⁻⁴/5+25z⁻¹+2z⁻²^-z⁻³+z⁻⁴
a. Plot the magnitude

Answer 1

To plot the magnitude of the given equation H(z), we need to evaluate its absolute value. Use the given values of z to calculate the real and imaginary parts, square them, sum them together, and take the square root to find the magnitude at each point.

Step-by-step explanation:

To plot the magnitude of the given equation H(z), we need to evaluate its absolute value. The magnitude of a complex number can be found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the real part is 2+5z⁻¹-9z⁻²+5z⁻³+3z⁻⁴ and the imaginary part is 5+25z⁻¹+2z⁻²^-z⁻³+z⁻⁴.

Using the given values of z, we can substitute them into the equation and calculate the real and imaginary parts. Then, we can square each part and sum them together. Finally, we take the square root of the sum to get the magnitude at each point.

For example, if we substitute z = 2.78, we get a real part of 44.3438 and an imaginary part of 16.2477. The magnitude can be calculated as
`sqrt(44.3438^2 + 16.2477^2)`, which is approximately 47.0841.