Signal to quantization noise in quantized sinusoidal
In problem 4.37 of DSP-Proakis [1], the task is to analyze the total harmonic distortion in quantized sinusoidal, where .
Read More
Gray code to Binary conversion for PSK and PAM
Given that we have discussed Binary to Gray code conversion, let us discuss the Gray to BInary conversion. Conversion from Gray code to natural Binary Let be the equivalent Gray code for an bit binary number with representing the index of the bit. 1. For , i.e, the most significant bit (MSB) of the Gray…
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 output for all values in the training set. A closed form solution for finding the parameter vector is possible, and in this post…
Trying out PAPR reduction for OFDM by multiplication with j
In this post, we will explore a probable way of reducing PAPR (peak to average power ratio) in OFDM by changing the phase of some of the subcarriers. This is in response to the comment to post on Peak to Average power ratio for OFDM, where Mr. Elibom suggested to reduce the PAPR by cyclically…
MIMO with MMSE SIC and optimal ordering
This post attempts to build further on the MIMO equalization schemes which we have discussed – (a) Minimum Mean Square Error (MMSE) equalization, (b) Zero Forcing equalization with Successive Interference Cancellation (ZF-SIC) and (c) ZF-SIC with optimal ordering. We have learned that successive interference cancellation with optimal ordering improves the performance with Zero Forcing equalization….
Understanding Shannon’s capacity equation
Let us try to understand the formula for Channel Capacity with an Average Power Limitation, described in Section 25 of the landmark paper A Mathematical Theory for Communication, by Mr. Claude Shannon. Further, the following writeup is based on Section 12.5.1 from Fundamentals of Communication Systems by John G. Proakis, Masoud Salehi
Linear to log conversion
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 DSP Guru column on DSP Trick: Quick-and-Dirty Logarithms. The scheme makes implementation of a linear to log conversion simple and…
GATE-2012 ECE Q11 (signals)
Question 11 on signals from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q11. The unilateral Laplace transform of is . The unilateral Laplace transform ofis (A) (B) (C) (D) Solution From the definition of Laplace transform for a function defined for all real numbers is, , where with real numbers and . To find the Laplace…
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. The noise power at the output is computed by integrating the output voltage spectral density over all frequencies.
Alamouti STBC
In the recent past, we have discussed three receive diversity schemes – Selection combining, Equal Gain Combining and Maximal Ratio Combining. All the three approaches used the antenna array at the receiver to improve the demodulation performance, albeit with different levels of complexity. Time to move on to a transmit diversity scheme where the information…
BER for BPSK in OFDM with Rayleigh multipath channel
Mr. Lealem Tamirat, in a comment on BER for BPSK in Rayleigh channel, wondered about the performance of an OFDM modulated system in a frequency selective Rayeligh fading channel. My response was that, Though the total channel is a frequency selective channel, the channel experienced by each subcarrier in an OFDM system is a flat…
GATE-2012 ECE Q47 (math)
Question 47 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q47. Given that and , the value of is (A) (B) (C) (D) Solution To answer this question, we need to refer to Cayley Hamilton Theorem. This is discussed briefly in Pages 310-311 of Introduction to Linear Algebra, Glibert Strang (buy…
Solved!
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 it and going over the whole journey again…. (Thanks dear Kunju for introducing me to the cube) Disclosure : After solving…
MIMO with Zero Forcing Successive Interference Cancellation equalizer
The post on MIMO with Zero Forcing equalizer discussed a probable way of equalizing a 2×2 MIMO channel. The simulated results with the 2×2 MIMO system with zero forcing equalizer showed matching results as obtained in for a 1×1 system for BPSK modulation in Rayleigh channel. In this post, we will try to improve the…