Line 9: | Line 9: | ||

==Question 2== | ==Question 2== | ||

− | This implies that the difference equation must has the form | + | (a) This implies that the difference equation must has the form |

<math> y[n]=\sum_{i=0}^{N-1} b_i x[n-i] -\sum_{k=1}^{M} a_k x[n-k] </math> | <math> y[n]=\sum_{i=0}^{N-1} b_i x[n-i] -\sum_{k=1}^{M} a_k x[n-k] </math> | ||

where M is the number of poles and M>0 | where M is the number of poles and M>0 | ||

+ | |||

+ | |||

+ | (b) No, it must be an IIR filter as it must have poles. As explained in (a), the difference equation | ||

==Question 3== | ==Question 3== | ||

+ | (a) It's likely to be female, as the pitch is 250Hz. | ||

+ | |||

+ | (b) The gender will not influence the location of the local maxima. It only affects the pitch frequency. | ||

+ | |||

+ | (c) | ||

+ | |||

+ | (d) | ||

[[ HW9ECE438F13|Back to HW9ECE438F13]] | [[ HW9ECE438F13|Back to HW9ECE438F13]] |

## Revision as of 11:41, 4 November 2013

# Hw9_ECE438F13sln

## Question 1

This is because real systems have transfer functions with real coefficients. If we write the transfer function H(z) as H(z)=P(z)/Q(z), where P(z) and Q(z) are polynomial, then the poles of the transfer function are the zeros of the polynomial Q(z). But Q(z) has real coefficients (Since the system can be written as a difference equation with real coefficients).

## Question 2

(a) This implies that the difference equation must has the form

$ y[n]=\sum_{i=0}^{N-1} b_i x[n-i] -\sum_{k=1}^{M} a_k x[n-k] $

where M is the number of poles and M>0

(b) No, it must be an IIR filter as it must have poles. As explained in (a), the difference equation

## Question 3

(a) It's likely to be female, as the pitch is 250Hz.

(b) The gender will not influence the location of the local maxima. It only affects the pitch frequency.

(c)

(d)