Oscillator phase noise


Oscillators are used in typical radio circuits to drive the mixer used for the up-conversion or down-conversion of the passband transmission. Ideally, the spectrum of the oscillator is expected to have an impulse at the [...]

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Thermal noise of RC low pass filter


  This post discuss about the thermal noise in RC low pass filter. Using the noise equivalent model using resistor with a voltage source, which gets passed through a no noise RC low pass filter. [...]

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Noise Figure of cascaded stages


Following the discussion on thermal noise and it’s modeling and noise figure computation for a simple resistor network, in this article let us discuss the Noise Figure of cascaded stages.

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Noise Figure of resistor network


The post on thermal noise described the noise produced by resistor  ohms over bandwidth  at temperature Kelvin. In this post, let us define the noise voltage at the input and output of a resistor network and further use it to [...]

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SOLVED the Rubik’s cube !!!   After 6 months, 2 cube’s and countless twists and turns, extremely glad to reach here. Will enjoy the beauty of the solved cube for couple of days before breaking [...]

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Thermal Noise and AWGN


A friend called me up couple of days back with the question – How white is AWGN? I gave him an answer over phone, which he was not too happy about. That got me thinking [...]

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Hamming (7,4) code with soft and hard decoding


An earlier post we discussed hard decision decoding for a Hamming (7,4) code and simulated the the bit error rate. In this post, let us focus on the soft decision decoding for the Hamming (7,4) [...]

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ADC SNR with clock jitter and quantization noise


My friend and colleague Mr. Vineet Srivastava pointed me to a nice article on  clock jitter - Clock Jitter Effects on Sampling : A tutorial – by Carlos Azeredo-Leme, IEEE Circuits and Systems Magazine, Third Quarter [...]

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Weighted Least Squares and locally weighted linear regression


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

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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Symbol Error rate for QAM (16, 64, 256,.., M-QAM)


In May 2008, we derived the theoretical symbol error rate for a general M-QAM modulation (in  Embedded.com, DSPDesignLine.com and dsplog.com) under Additive White Gaussian Noise. While re-reading that post, felt that the article is nice and warrants a [...]

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Newton’s method to find square root, inverse


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

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

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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