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by Krishna Sankar on September 30, 2012

In typical wireless system simulations, there is a need to model the phase noise profile of the local oscillator. For eg, the phase noise profile of the oscillator can be of the shape described in [...]

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by Krishna Sankar on February 5, 2012

From the post on Closed Form Solution for Linear regression, we computed the parameter vector which minimizes the square of the error between the predicted value and the actual output for all values in the training set. In that [...]

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by Krishna Sankar on January 15, 2012

From the previous posts on Linear Regression (using Batch Gradient descent, Stochastic Gradient Descent, Closed form solution), we discussed couple of different ways to estimate the parameter vector in the least square error sense for [...]

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by Krishna Sankar on December 25, 2011

Some of us would have used Newton’s method (also known as Newton-Raphson method) in some form or other. The method has quite a bit of history, starting with the Babylonian way of finding the square [...]

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by Krishna Sankar on December 4, 2011

In the previous post on Batch Gradient Descent and Stochastic Gradient Descent, we looked at two iterative methods for finding the parameter vector which minimizes the square of the error between the predicted value and the actual [...]

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by Krishna Sankar on November 15, 2011

For curve fitting using linear regression, there exists a minor variant of Batch Gradient Descent algorithm, called Stochastic Gradient Descent. In the Batch Gradient Descent, the parameter vector is updated as, . (loop over all [...]

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by Krishna Sankar on October 29, 2011

I happened to stumble on Prof. Andrew Ng’s Machine Learning classes which are available online as part of Stanford Center for Professional Development. The first lecture in the series discuss the topic of fitting parameters [...]

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by Krishna Sankar on February 8, 2009

In this post, let us discuss a simple implementation friendly scheme for computing the absolute value of a complex number . The technique called (alpha Max + beta Min) algorithm is discussed in Chapter 13.2 [...]

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by Krishna Sankar on November 20, 2008

In signal processing blocks like power estimation used in digital communication, it may be required to represent the estimate in log scale. This post explains a simple linear to log conversion scheme proposed in the [...]

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by Krishna Sankar on August 8, 2008

Last week, I received an email from Mr. Kishore. He was wondering about the physical significance of negative frequency. Does negative frequency really exist? Though I have seen conflicting views on the net (thread in [...]

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by Krishna Sankar on July 28, 2008

While trying to derive the theoretical bit error rate (BER) for BPSK modulation in a Rayleigh fading channel, I realized that I need to discuss chi square random variable prior. What is chi-square random variable? [...]

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by Krishna Sankar on July 17, 2008

In the post on Rayleigh channel model, we stated that a circularly symmetric random variable is of the form , where real and imaginary parts are zero mean independent and identically distributed (iid) Gaussian random [...]

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by Krishna Sankar on May 25, 2008

Thanks to the keen observation by Mr. Phan Minh Hoang, I was notified that the Matlab/Octave scripts provided along with the topic raised cosine filtering was not behaving properly. Reason: I was not taking care [...]

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by Krishna Sankar on December 16, 2007

In a previous post (here), we looked at using CORDIC (Co-ordinate Rotation by DIgital Computer) for understanding how a complex number can be rotated by an angle without using actual multipliers. Let us know try [...]

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