ps1_fall09

# ps1_fall09 - Department of Electrical and Computer...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Department of Electrical and Computer Engineering Digital Speech Processing Problem Set No. 1 Problem 1 Consider the sequence of values described by the difference equation: y [ n ] = 2 y [ n- 1]- . 5 y [ n- 2] with initial conditions: y [- 1] = 0 (1) y [- 2] =- 2 (a) Solve for y [0] ,y [1] ,y [2] ,y [3] (b) Determine an analytic solution for y [ n ] for all n (c) If the limit of sequential terms is given by the factor G , i.e., lim n →∞ y [ n ] y [ n- 1] = G determine G . Problem 2 An input signal, x [ n ], defined over the region-∞ < n < ∞ , is passed through a cubic non-linearity yielding the output signal y [ n ] = ( x [ n ]) 3 (a) If the input to the system is of the form x 1 [ n ] = cos( ω n ) ,-∞ < n < ∞ determine the output spectrum, Y 1 ( e jω ), and plot the magnitude of Y 1 ( e jω ) (assuming ω << ω S , the radian sampling frequency of the digital system). Hint: recall the trigonometric relationships cos 2 ( x ) = 1 2 + cos(2 x ) 2 cos 3 ( x ) = cos(3 x ) 4 +...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

ps1_fall09 - Department of Electrical and Computer...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online