Homework 1

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.)

Notes for Homework 1:

  • You may use MATLAB's least squares solver for problems 2, 3 and 4. You may not use any model parameter estimators that MATLAB has.

  • To be submitted by Sunday the 15th of January 2004.

  1. Cheating

    2. I gave an exam, where they told me to multiply to polynomials f(x) and g(x). f(x) was about 30 x2 + 10 x + 20. (I only remember the MSDs now, but I remember the order correctly.) My answer was about 100 x4 + 100 x3 + 300 x2 + 100 x + 100. (Again I remember only the MSDs, but it was an order 4 polynomial.) Estimate g(x).

  2. Win-Win Situation

    3. I have a causal FIR filter kernel [0.5, 0.125, 0.25, 0.125]. I want to design an inverse filter, but I am constrained to using FIR filters. Design the optimal FIR inverse filter of order q. Vary q between 1 and 20. Plot the squared sum error against q. Plot the impulse response of inverse filter and combined system for q = 1, 2, 3, 4, 5, 10 and 20.

  3. Bathroom Singer

    4. My bathroom got excited with input.wav and produced output.wav. Model my bathroom using optimal AR, MA and ARMA methods. Plot order-error plots using a training and validation set. (Divide the data into training and validation sets.) What is your best model? Sing into it.

    Also use Pade, Prony and Shanks methods for the same orders, and compare error with optimal ARMA method.

  4. Spying

    5. The bug you placed recorded snippet.wav. Unfortunately, due to bad placement of the bug the talking is being overshadowed by the music. You better not let your boss know that you placed the bug wrong. Your partner finds the original music, music.wav. Save your job: clean the recording of the music. What is being said?

    (Music credits: Lyrics - Indira Sant. Music - Udayan. Performed by - Praful (voice), Karthik (piano), Shrivardhan (bass).)