Sunday, April 15, 2012

Preparations for exam

1. s- , z- domains
2. Laplace , z- and DFT properties
3. z-transform calculations for functions.
4. Butterfly diagram
5. FIR, IIR filter design concepts
6. Problems based on methods used to convert analog filter into a digital filter
7. Windowing.

Good Day !

Monday, March 26, 2012

Homework - 13

Q1. Realise the following second order system by using direct form - I
          y[n]  =  y[n-1]  -0.5y[n-3]  +  0.5x[n-1]

Q2. Determine the direct form - II realisation for the following system:
          y[n]  =  -0.1y[n-1]  +  0.72y[n-2]  +0.7x[n]  - 0.252x[n-2]

Q3. Determine the transposed structure for the system given by the difference equation :
         y[n] = 0.5 y[n-1]  - 0.25 y[n-2]  +  x[n]  + x[n-1]

Q4. Realise the FIR system H(z) = ( 1 + 0.5z^-1)(1 + 0.5z^-1 + 0.25 z^-2) in
       Direct form and Cascade  form.

Q5. Let the coefficients of a three stage FIR lattice structure be K1 = 0.1, K2 = 0.2, and K3 = 0.3.
       Find the  coefficients of direct form - I FIR filter and draw its block diagram.

Q6. An FIR filter is given by y[n] = x[n] + (2/5) x[n-1] + (3/4)x[n-2] + (1/3) x[n-3].
       Draw the lattice structure.

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Good Day !

Sunday, March 25, 2012

Review

We shall now FOCUS on complete understanding of Digital Filter Design. While we do this, it is advised to review all topics covered till now with stress on :

  1. Sampling and Nyquist criterion
  2. Difference Equation
  3. Z-Transform
  4. Impulse response
  5. Convolution
  6. Discrete Fourier Transform
  7. Fast Fourier Transform
  8. FIR filter design techniques
  9. IIR filter techniques
I will upload a quiz and assignment tonight.

Good Day !

Tuesday, March 13, 2012

Homework - 12

Look at the two figures given below and explain their significance in your own words.

Figure 1 a to f



Figure 2 a to d



Thursday, March 8, 2012

Homework - 11

Dear ALL !

If you find time, do study additional material without worrying too much in case you do not understand something.

You will be doing a GREAT FAVOUR to the class by sharing all your doubts with me.
This will help me in preparing for the next class better.

Collect the following graphic representations before next week :

1. Time-domain and frequency domain representation of a rectangular waveform with a time-period of T.
    (Hint : Fourier Series).

Observe : What happens in the frequency domain as T tends to infinity in the time-domain ?

2. Time-domain and frequency domain representation of a pulse (width/duration = Tp). A pulse can be thought of as a rectangular waveform with a time-period of T = Infinity. (Hint : Fourier Transform.)

3. Time-domain and frequency domain representation of a periodic train of  unit impulses with a frequency of fs( = 1/T). (Hint : See chapter on Sampling). Assume fs is the Nyquist rate.

Now, take a signal which is band-limited (No frequencies above the highest frequency say +W/2.) Note : If W/2 is the highest frequency, Nyquist rate fs will be W.

4. What will be the plot in the frequency domain when the above band-limited signal is sampled at its Nyquist rate fs ? Sketch it.

5.What will be the plot in the frequency domain when the above band-limited signal is sampled at LESS THAN the  Nyquist rate fs ? Sketch it.

6. What will be the plot in the frequency domain when the above band-limited signal is sampled at GREATER THAN Nyquist rate fs ? Sketch it.

You will find all the answers in the  text books.
You are encouraged to discuss this with your colleagues to get  a clear picture of signals and their spectra (frequency domain representation).

I will give you some more hints tonight.

I will post the solutions on Sunday.

Good Day.

Wednesday, March 7, 2012

DSP_Quiz_01

Holi Greetings to ALL !


I have posted a NEW quiz today.
Please checkout.

Good Day

Tuesday, March 6, 2012

Homework - 10

Find the Discrete Fourier Transform of the following sequences :
Assume N = 4 and the samples taken for a duration T = 2pi
1.  x[k] = {1, 1, 0, 0}.
     Ans :  {2, 1-j, 0, 1+j}

2. x[k] = {1, 2, 1, 2}
    Ans :  {6, 0, -2, 0}

3. x[k] = {6, 0, -2, 0}
    Ans : {4, 8, 4, 8}

4. x[k] = {4, 8, 4, 8}
    Ans : {24, 0, -8, 0}

Good Day