In pattern recognition, it is sometimes useful to expand a signal using the desired pattern, or…

In pattern recognition, it is sometimes useful to expand a signal using the desired pattern, or template, and its shifts, as basis functions. For simplicity, consider a signal of length N, x[n], n = 0,…,N − 1, and a pattern p[n], n = 0,…,N − 1. Then, choose as basis functions

that is, circular shifts of p[n].

that is, circular shifts of p[n].

(b) Assuming the previous condition is met, give the coefficients αk of the expansion

Show that a linear, periodically time-varying system of period N can be implemented with a polyphase transform followed by upsampling by N, N filter operations and a summation

 

Need your ASSIGNMENT done? Use our paper writing service to score better and meet your deadline.


Click Here to Make an Order Click Here to Hire a Writer