In Problem 6.61, we considered one method for using a basic filter module repetitively t...

In Problem 6.61, we considered one method for using a basic filter module repetitively to implement a new filter with improved characteristics. Let us now consider an alternative approach, proposed by J. W. Tukey in the book, Exploratory Data Analysis (Reading, MA: Addison-Wesley Publishing Co., Inc., 1976). The procedure is shown in block, diagram form in Figure P6.62(a).

where is real and M is an integer. Show how to modify the system in Figure P6.62(a) so that the overall system will approximate a lowpass filter.