We have found previously that a system with an impulse response that is symmetric by a...

 

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We have found previously that a system with an impulse response that is symmetric by a point has linear phase, namely h[2M – n] = h[n], 0 > U A 0=[u]y We can use this property to our advantage in terms of structure complexity We have 12M y[n] = >. h[k]x[n – k] k=0 Your homework is to solve for - A.) The final expanded form of y[n], suitable to implement a system block diagram • Hint 1: h[M – n] = h[n + M] Hint 2: As can be seen from the final expanded form of y[n] we can reduce the number of required MACS by a factor of 2 by utilizing the fact that linear phase FIR filters have symmetric coefficients. This type of structure is referred to as a folded FIR filter. - B.) Draw the block diagram for the folded FIR filter structure solved for in part A.) We have found previously that a system with an impulse response that is symmetric by a point has linear phase, namely h[2M – n] = h[n], 0 > U A 0=[u]y We can use this property to our advantage in terms of structure complexity We have 12M y[n] = >. h[k]x[n – k] k=0 Your homework is to solve for - A.) The final expanded form of y[n], suitable to implement a system block diagram • Hint 1: h[M – n] = h[n + M] Hint 2: As can be seen from the final expanded form of y[n] we can reduce the number of required MACS by a factor of 2 by utilizing the fact that linear phase FIR filters have symmetric coefficients. This type of structure is referred to as a folded FIR filter. - B.) Draw the block diagram for the folded FIR filter structure solved for in part A.)

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