Problem 8: There are digital filtering schemes that use the process conceptually

Question

Problem 8: There are digital filtering schemes that use the process conceptually shown in Figure (a) below, where the filter may be comprised of two parallel paths. xn) x(n)+2x(n-2) +x(n-4) w(n) Time-synchronization delay line Delay Delay..-Delay x(n) y(n) w(n) x(n)+2x(n-2)+x(n-4) The actual implementation, however, will typically need a delay line as shown in Figure (b). The delay-line in the upper path is needed to compensate for the delay of the FIR filter in the bottom path. How many unit-delay elements do you have to insert in the upper path for its delay to match that of the lower path?

Explanation / Answer

The Wn filter output requires a delay of 4 time units to get x(n-4) term. 2x(n-2) and x(n) terms will be avaible much before that. x(n-2) will be avaible 2 time units before x(n-4) and x(n) will be immediately availabe. So the time-synchronisation delay line will require atleast 4 unit delay elements to compensate the delay by the FIR filter Wn.

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