Answer the following questions about the time-domain response of FIR digital fil

Question

Answer the following questions about the time-domain response of FIR digital filters: picture above!

Answer the following questions about the time-domain response of FIR digital filters: y[n] = E M k = 0 bk x[n - k] When tested with an input signal that is an impulse, x[n] = delta [n], the observed output from the filter is the signal h[n] shown below: delta [n] = {1 for n = 0 0 for n = 0 rightarrow Determine the filter coefficients {bk} of the difference equation for the FIR filter, If the filter coefficients are {bk} = {13, -13, 13} and the input signal is x[n] = {0 for n even 1 for n odd determine the output signal y[n] for all n. Give your answer as either a plot or a formula.

Explanation / Answer

a) time domain response of fir filter= b0x(n)+b1x(n-1)+b2x(n-2)+.......................+bmx(n-m).

since we can write output in above fir response form=3*d(n)+7*d(n-1)+13*d(n-2)+9*d(n-3)+5*d(n-4) :where x(n)=d(n),impulse funtion

so comparing with fir filter response

we get (bk)=(3,7,13,9,5)

b)from figure,

we can write output in fir response form

y(n)=13*x(n)-13*x(n-1)+13*x(n-2)

we know that x(n)=0 for n=even and x(n)=1 for n=odd

after putting value of 1, 2 ,3 in above y(n), we get result like this

y(n)=-13 , n=even

y(n)=26 , n=odd

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