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 !
Digital Signal Processing
Quote : "If egg is broken by outside force, life ends. If broken by inside force, life begins. Great things always begin from inside force, trust yourself."
Sunday, April 15, 2012
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 !
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.
------------
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 :
- Sampling and Nyquist criterion
- Difference Equation
- Z-Transform
- Impulse response
- Convolution
- Discrete Fourier Transform
- Fast Fourier Transform
- FIR filter design techniques
- 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
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.
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
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
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
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