5. Given a finite sequence x = {x,k=0,1,2,...,N-1} the spectrum of the sequence can be estimated...

 

Transcribed Image Text:

5. Given a finite sequence x = {x,k=0,1,2,...,N-1} the spectrum of the sequence can be estimated using the periodogram formula == e N k-0 (a) Show that samples of the periodogram at frequencies f = (2/N)n can be computed (efficiently) by the FFT algorithm. (b) Show that the periodogram can be computed from the autocorrelation using the formula N-1 P (ex)=(m)e-12m N m--(N-1) (c) Modify the program you wrote in Problem 4 to compute and plot both the autocorrelation and the periodogram of a finite sequence. 5. Given a finite sequence x = {x,k=0,1,2,...,N-1} the spectrum of the sequence can be estimated using the periodogram formula == e N k-0 (a) Show that samples of the periodogram at frequencies f = (2/N)n can be computed (efficiently) by the FFT algorithm. (b) Show that the periodogram can be computed from the autocorrelation using the formula N-1 P (ex)=(m)e-12m N m--(N-1) (c) Modify the program you wrote in Problem 4 to compute and plot both the autocorrelation and the periodogram of a finite sequence.