Homework 2

ADSP 2004

Notes for all Homeworks:

  • You have to save the programs that you generate, because their output will be used in further assignments.

  • While submitting the homework attach all programs and plots that you think are necessary to evaluate it.

  • Unless otherwise specified, you are allowed to discuss the homework with anybody. You should write up your own solutions, and do all your own programming.

  • If you submit homework later than the specified date, you lose marks at the rate of 20% per day, compounded daily. If you cannot submit in class, you can submit either in Codito, or with any teacher in the department. (Get them to sign and date it.)

Spread the Spectrum

Suppose X is a stationary random process. Suppose P is a zero mean white noise sequence of +1s and -1s. What can you say of the process XP i.e., the pointwise multiplication of X and P. (If you conclude it is stationary, also give the autocorrelation function. If you conclude it is not, why not?)

Take two voice signals x1 and x2, and two independantly generated modulating keys p1 and p2, both being random sequences of +1s and -1s. Let y = x1p1 + x2p2. y is the spread sprectrum encoded bitstream. Suppose at the decoder, we know p1 but not p2. A rough estimate of x1 is q = p1y. Calculate the SNR in this estimate. Improve the estimate by Weiner filtering q to reduce the effect of x2. What is the improved SNR? (You should assume local stationarity for the voice signals.)