Video Lectures

14 thoughts on “Video Lectures”

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

   • I have not written on this topic. Please refer to the following Matlab support page
     http://www.mathworks.com/help/matlab/matlab_prog/vectorization.html

     • I need to find loglikelihood ratio. I ll generate normally distributed random numbers using ‘normrnd’ command in matlab. but it’s giving negative values and when i take log, it shows complex numbers. please help

       • Two posts related to your question. Hope this helps
         https://www.gaussianwaves.com/2012/10/likelihood-function-and-maximum-likelihood-estimation-mle/
         https://www.gaussianwaves.com/2010/01/maximum-likelihood-estimation-2/

         • thank you, I got the basics I needed

2. 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 :
     Rayleigh fading: https://www.gaussianwaves.com/2010/02/fading-channels-rayleigh-fading-2/
     Rician Fading: https://www.gaussianwaves.com/2012/07/ebn0-vs-ber-for-bpsk-over-rician-fading-channel/
     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/

     • Thank you ,
       That was very much informative

     • 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)

3. 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

4. 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

5. hi Mathuranathan sir,
   I am vineeth.
   I need help in generating CP-OFDM waveform in Matlab. Can you help me with that sir.

   • CP-OFDM related posts are available here.
     https://www.gaussianwaves.com/tag/ofdm/

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