References 237 show that the resulting filtering function is periodic, with a period given by the least common multiple of f 1 and f 2 . For example, if periods of the two filters are 500 GHz and 600 GHz, then the cascaded structure will be periodic with a period of 3000 GHz. Now suppose the period of each filter can be tuned by 10%. For the numbers given above, the first filter's period can be tuned to 500 ± 25 GHz and the sec- ond filter's to 600 ± 30 GHz. Note that the two combs overlap at a frequency of 193,000 GHz. To get an idea of the tuning range of the cascaded structure, determine the nearest frequency to this initial frequency at which the two combs overlap when periods of the individual filters are tuned to (1) 525 GHz and 630 GHz, (2) 475 GHz and 630 GHz, (3) 475 GHz and 570 GHz, and (4) 525 GHz and 570 GHz. To get an idea of how complex it is to tune this structure, also determine the periods of each filter to obtain an overlap at 193,100 GHz. 3.29 Consider the Clos switch architecture described in Section 3.7.1. Show that if p 2m - 1, the switch is strictly nonblocking.