DynCont#5: Z transform, Phils Lab, DDorran

Phisl lab

1.  Z transform is better than Fourier transform because it can do 2 things:
1. Check the stability of the implemented difference equation
2. See the frequency response of the system, that the difference equation represents
2. Z transform based stability check: Simple, replace y[n-1] by z^-1 Y and form the Z transfer function and check the location of poles . Zeros can be out side the unit circle for stable system
3. Z transform based frequency response z^(-k) = e^(-j theta k), where theta  = 2*pi*f/fs. Maximum value f can take is fs/2 so maximum value theta can take is theta = pi. 
4. For DC gain, omega is zero so z = 1
5. For high frequency gain, z= -1

 DDorran

1. Z transform is used to detect the presence of exponentially increasing or decreasing components in the signal
2. By identifying the increasing or decreasing oscillations in the impulse response  of a system we can determine if that system is stable or unstable
3. x[n] is a signal with different values for different n. z^(-n) is also a signal for different values of z. Multiplying individual values of the 2 signals and adding them is basically taking correlation of 2 signals. Higher the correlation, more is one signal present in another signal
4. Correlation is the measure of presence of one signal in another signal.
   
5. When taking correlation of 2 signals, note that if second signal is constructed using z = 1, then we are basically taking the DC value of the first signal. Also see 4th point of previous stack.
6. Z is e^(-sT). Value of the z transform at z = 1 in the plot with z values as x axis is the DC value of the signal.
    

New things he did.

1.  Started saying 2 word sentences in the second week of July 2022
2.  Started saying 3 word sentences in the second week of July 2022, like "Mukesha Amma kupudranga!" to Mukesh who was playing inside.
3. Went to Priya office for full day without going to school so that me and mother can go to Vaniyambadi for Manju funeral. Next day, he asked mother to go to shop and me to go to office so that he and Priya will be alone in the morning and she will take him to office in Bus rather than go to school.
4. Started saying all options other than school. "Priya, Bus train auto polama?"
5. Started identifying a train when we cross a train track near BEML gate and started asking shall we go in train whenever we cross BEML gate.
6. Started adding his own words into conversations : When Priya told me to buy chocolate and cake from behind on the bike, I asked her to repeat as I could not hear what she told. Him, sitting, inbetween told, "Chocolate, ice cream, cake". 
7. When we go to drop Priya in the morning, he starts crying that he wants to take his bag too. So that he can take his bag and go to Priya office rather than school.
   

Notes Random

1. Best drill bits to buy, even if you are drilling rocks: PDC = poly crystaline diamond compacts
2. Why Tungsten Carbide drill bits are better than HSS drill bits?
1. Tungsten carbide drill bits have to be sharpened only by diamond wheels, so their sharpening is done on good machines whose angles are controlled precisely. So they make better drill bits
2. HSS drill bits are cut in normal grinding wheels, so their angles may not be as precise and process may not be strictly controlled. This results in poorer drill bits in the end
   
3. Both Cobalt and Nickel are used as binder in Tungsten Carbide drill bits. When nickel is used, the bit is slightly magnetic. When cobalt is used ?
   
4. Cobalt has higher thermal expansion and so when Cobalt binded Tungsten Carbide drill bits are used for long, due to thermal expansion, they may fail.
5. Always have UV seals next to the commutator brushes in the motor. Constant sparking of the commutator brushes give out UV light and the light damages the polymer cage of the bearing and the grease.
   

 

DynCont#4: SVD, 3Blue1Brown

1.  If determinant is zero, the transformation matrix collapses the input vector to a point in the output vector space
2. A span of the vector is a line , infinite passing through the vector in both the directions. A vector can be multiplied by a constant number and the head of the vector will be somewhere along the line for different constants 
3. Matrix multiplication:
1. Row wise picture, conventional computational approach
2. Column wise picture
3. Transformation from one vector space to another vector space approach
4. Will be edited after listening to the lec again.
   

Notes, random

1.  No point in anticipating and worrying.
2. Know the scenario as best as possible and then start worrying about it so that you can worry effectively.
3. If some one is coming to you, he wants something from you. It may be knowledge, but consider how that knowledge will be used.
4. Some people may not have points of contacts at all. Not interested in talking to you or getting information from you. Not all people are same.
5. Survival is not every thing?
   

Cosmic view points: Purpose of universe

1. The egg, short story by Andy Weir : Purpose of universe is to mature us.
   
2.  Actions of intelligent life are an unfortunate irrelevance in the majestic universe of stars and galaxies. It is bad manners to  give too much importance to intelligence/Love= Emotion
   
3.  Only purpose of universe is to produce intelligent sentient beings. Other astronomical phenomena is just dead matter.

 

 

DynCont#3: SVD, MIT 18.065 Strang you tube lecture video 6

1.  We are looking for a bunch of orthogonal vectors u, which when multiplied by A, give another set of orthogonal vectors v, scaled by sigma
2. Curse of Dimensionality =   A matrix is basically scaling and rotation. For a 2x2 matrix, there are 4 terms . it has 2 scaling values and 2 rotations. The rotations increase the time taken. not the scaling. For 3x3 matrix, there are 9 independent terms with 6 rotations and 3 scaling terms. Similarly, 4x4 matrix has 4 scaling terms and 12 rotations.
3. Rank= If A has rank r, there are r orthogonal vectors , which when multiplied by A give another r orthogonal vectors.
4. If U vectors are orthogonal in AU=sigma V, it can be proven that V vectors are orthogonal by simply substituting VV' = (AU/Sigma1)* (AU/Sigma1)'

DynCont#2: SVD, MIT 18.065 Strang you tube lecture video

1.  A * v = u * Sigma
2. Matrix A times an orthogonal vector matrix = another orthogonal vector matrix scaled by sigma
3. Sigma is diagonal matrix
4. Sigma is the square of eigen values of A A'
5. AA' is symmetric and positive semi definite 
6. If A is mxn, AA' = m x m . Then, it will have m eigen values.
7. If A is mxn, A'A = n x n . Then, it will have n eigen values. If m is greater than n, then m-n eigen values of AA' will be zero.
8. Use of SVD:?
9. SVD from lecture 29 in 18:06?
10. Use of SVD from Knuth?