# Video Lectures

### Video Lectures: Watch, Listen and Learn !!!

Serial #Topic Link to Video Lectures
2Digital CommunicationsView Lecture
3Digital Signal Processing by Alan V. OppenheimView Lecture
4Discrete Stochastic ProcessView Lecture
5Electromagnetics and Applications View Lecture
6Error Correcting CodesView Lecture
7Fourier Transforms and Applications – Stanford UniversityView Lecture
8GPS TechnologyView Lecture
9Information Theory, Entropy and InferenceView Lecture
10Linear AlgebraView Lecture
11Low Power VLSI Circuits and SystemsView Lecture
12Signals and Systems by Alan V. OppenheimView Lecture
13Stanford Class X - Interactive ClassesView Lectures
14Wireless CommunicationsView Lecture
15MIT Open CourseWareOnline Courses
16Bayes' Theorem for Everyone - By Nat NapoletanoView Video
17Introduction to Kalman FilterView Lecture

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• abhilash b

Hi Mathuranathan,
I have questions on ofdm,
what happens if the channel changes within symbol duration? still the orthogonality is retained?
what happens when channel response exceeds the cyclic prefix length?

-regards

• abhilash b

Hi Mathuranathan,
I need one help
Given z = max(X1, X2, …. Xn),
X1,X2,,,Xn are all random variables and unordered. how to find the pdf of z ?

-regards

• abhilash b

hi Mathuranathan,
I have one basic doubt.
Why do we consider complex normal distribution, instead we can go for real normal distribution?
Is the complex normal can be represented in matlab? If so how?

-regards

• When talking about real normal distribution, it is one dimensional. The same concept can be extended to multivariate case, where the distribution across multi-dimension are jointly Gaussian. Complex normal distribution is a subset of multivariate normal distribution, where the number of dimension considered is just 2 (also bivariate normal distribution). We name these two dimensions as real and imaginary parts.

There are many applications to complex normal distribution. For example, A QPSK modulation is a two dimensional modulation, where each transmitted symbol is represented on two basis function – sine and cosine. Thus these symbols are represented as complex number. Actually, you cannot transmit a complex number. What happens really is that you are modulating the input message on two basis function – sine and cosine with same frequency but are offset 90* with respect to each other interms of phase.

If I would like to introduce noise in the QPSK modulation system, where the transmitted symbols are represented as complex number in the form S = s1 + j s2, then I would need a complex gaussian noise of form N = n1+jn2. The received signal is represented as Y = S+N, where everything is complex.

Yes, it is possible to generate complex distributions in matlab. Example
N = randn(1,100) + i1 * randn(1,100); %gives complex normal distributed samples

More applications :
AWGN noise (Complex case) : https://www.gaussianwaves.com/2015/06/how-to-generate-awgn-noise-in-matlaboctave-without-using-in-built-awgn-function/
Simulating white noise as multivariate Gaussian random vector: https://www.gaussianwaves.com/2013/11/simulation-and-analysis-of-white-noise-in-matlab/

• abhilash b

Thank you ,
That was very much informative

• abhilash b

Hi Mathuranathan,
If i go for modulation using multiple basis functions (say 4), and if I introduce noise in them,
then the resulting noise will be N= n1 + jn2 + kn3 + ln4? Am I correct in representing the noise?
Or it should be N = n1+j(n2 + k(n3 + l n4))) ?

• Yes. The noise can be represented in four dimension as n1 + j n2 + k n3 + l n4.

To implement in Matlab or any programming language, each dimension is represented as a column vector in a Nx 4 matrix, where N represents the desired number of noise samples

Example:
To generate 10 I.I.D 4 dimensional noise samples that follow Gaussian distribution, each column represent a single dimension.

Noise = [randn(10,1) ; randn(10,1) ; randn(10,1) ; randn(10,1) ]

To understand, consider the case of 2 dimensional noise (complex noise)
Noise = [ randn(10,1) ; randn(10,1)] is equivalent to
Noise = randn(10,1) + i1* randn(10,1)

• abhilash b

how to vectorize the code(i.e. to reduce the number of for loops)