How Do You Design a Digital FIR Filter to Remove a 70Hz Disturbance?

[BriWel]

I have a question which is to design a filter of the form:

y(n) = a(0)x(n) + a(1)x(n-1) + a(2)x(n-2) to remove a narrowband disturbance with frequency f0 = 70Hz.
The sampling frequency, fs is 280Hz.

I've made an attempt at answering it, but don't think my result is correct:

w0 = (2*pi)* (f0/fs) = pi/2

I then calculate the zeros of the filter from the definition of w

z1 = exp^(i*(pi/2))[
z2 = exp^(-i*(pi/z))
where i = sqrt(-1)

The transfer function of the filter is therefore;

Z²H(z) = (z - exp^(i*(pi/2))[ )(z - exp^(-i*(pi/z)) )

When expanded and simplified this gives

H(z) = z² + 1, so the filter function

y(n) = x(n) + x(n - 2),
giving
a(0) = 1
a(1) = 0
a(2) = 1

Which I'm pretty sure is wrong. Can anyone tell me where I have gone wrong?

 

[dsprao]

You did wrong while expanding and simplifying