A causal 4th order FIR digital filter, where its impulse response is symmetrical about its mid-point, has the following 3 values of the step response (i. e., the input is a step u(n)): y(n)=box(n)+b1x(n-1)+b2x(n-2), b3 x(n-3)+b4x(n-4), bo=0.02840647, b1=0.23700868, b2=0.469170166, b3=-.734585316, b4=0 y(0) = 0.02840647, y(1) = 0.26541468, and y(2) = 0.734585316. M) Determine the impulse response h(n). Is the filter stable?
N) Write an expression for the frequency response H(ejw). Hence, plot the magnitude and phase response. Identify the type of filter it represents?
0) Determine the difference equation of the system?
P) Draw the block diagram of the difference equation of the filter. How many multiplications and additions do we need for each sample?
Q) Determine the steady-state output yss(n) if the input signal is given by: x(n) = 10u(n) + 5 cos(0.5tn)u(n).