DSP

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Modeling phase noise (frequency domain approach)

by Krishna Sankar on September 30, 2012

plot_simulated_phase_noise_profile

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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Weighted Least Squares and locally weighted linear regression

by Krishna Sankar on February 5, 2012

weight_function

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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Least Squares in Gaussian Noise – Maximum Likelihood

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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Newton’s method to find square root, inverse

by Krishna Sankar on December 25, 2011

function_tangent_slope

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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Closed form solution for linear regression

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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Stochastic Gradient Descent

by Krishna Sankar on November 15, 2011

Convergence Batch Stochastic Gradient Descent

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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Batch Gradient Descent

by Krishna Sankar on October 29, 2011

Measured and predicted  pageviews per article sep2011 dsplog.com

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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Approximate Vector Magnitude Computation

by Krishna Sankar on February 8, 2009

plot_approximate_vector_magnitude_computation

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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Linear to log conversion

by Krishna Sankar on November 20, 2008

linear to log using LUT

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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Negative Frequency

by Krishna Sankar on August 8, 2008

Negative Frequency Real Complex Sinusoidal

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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Chi Square Random Variable

by Krishna Sankar on July 28, 2008

PDF of chi square random variable

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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Deriving PDF of Rayleigh random variable

by Krishna Sankar on July 17, 2008

Plot of simulated/theoretical PDF of Rayleigh random variable

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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Update: Correction in Matlab code for raised cosine filter

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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Using CORDIC for phase and magnitude computation

by Krishna Sankar on December 16, 2007

Flow chart for the operations involved when CORDIC is used for phase and magnitude computation

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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