Simple Functions Problem

1. Jan 2, 2009

1alph1

1. The problem statement, all variables and given/known data

The relationship between the input x(n) and the output y(n) for the discrete System A is described by the expression

y(n)=2x(n)-3x(n-1)+x(n-1)

What is
(i) the impulse response function h(n)?
(ii) the frequency response function H(f)?
(iii) the amplitude response function A(f)?
(iv) the phase response function θ(f)?

Assume that the sample time T = 1 (units). Note that the sample frequency is then one sample per second and this means that the Nyquist limit is 0.5 (units–1). As a consequence our input signals x(t), before sampling, is assumed to have no frequency above f = 0.5 (units–1). If we expect to have higher frequencies then we should increase the sample frequency.

2. Relevant equations

impulse response function h(n) aka delta function δ(t) is the derivative of the unit step function. not sure if the is relevant or not if even accurate.

3. The attempt at a solution

The frequency response H(f) is equal to

y(jω)/x(jω)

and that the modulus of H(f) is equal to the amplitude response function A(f)

and the phase response function θ(f) is equal to the angle of H(f)

Im not too sure where to start this question, any pointers would be greatly appericated. thanks