Digital implementation of RC low pass filter
Thanks to the nice article from Xilinx TechXclusives [XLNX-TECH], let us try to understand the probable digital implementation of resistor-capacitor based low pass filter. Consider a simple RC filter shown in the figure below. Assuming that there is no load across the capacitor, the capacitor charges and discharges through the resistor path. Figure: RC low…
BER for BPSK in ISI channel with MMSE equalization
In the past, we had discussed BER for BPSK in flat fading Rayleigh channel and BER for BPSK in a frequency selective channel using Zero Forcing Equalization. In this post, lets discuss a frequency selective channel with the use of Minimum Mean Square Error (MMSE) equalization to compensate for the inter symbol interference (ISI). For…
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 model all the values in the training set is given equal importance. Let us consider the case where it is known…
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 of Understanding Digital Signal Processing, Richard Lyons and is also available online at Digital Signal Processing Tricks – High-speed vector…
Symbol Error Rate (SER) for 16-QAM
Given that we have went over the symbol error probability for 4-PAM and symbol error rate for 4-QAM , let us extend the understanding to find the symbol error probability for 16-QAM (16 Quadrature Amplitude Modulation). Consider a typical 16-QAM modulation scheme where the alphabets (Refer example 5-37 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]). are used.
GATE-2012 ECE Q25 (math)
Question 25 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q25. If , then the value of is, (a) (b) (c) (d) 1
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.
Viterbi with finite survivor state memory
In the post on Viterbi decoder and soft input Viterbi decoder, we discussed a convolutional encoding scheme with rate 1/2, constraint length and having generator polynomial and having generator polynomial . If the number of uncoded bits is , then the number of coded bits at the output of the convolutional encoder is . Decoding…
Binary to Gray code for 16QAM
In the previous post on Binary to Gray code conversion for PSK, I had claimed that “for a general M-QAM modulation the binary to Gray code conversion is bit more complicated“. However following a closer look, I realize that this is not so complicated. 🙂 The QAM scenario can be treated as independent PAM modulation…
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) code, and quantify the bounds in the performance gain.
GATE-2012 ECE Q46 (math)
Question 46 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q46. The maximum value of in the interval [1, 6] is (A) 21 (B) 25 (C) 41 (D) 46 Solution Let us start by finding the critical points of the function . The first derivative is, . Solving by…
Convolutional code
Coding is a technique where redundancy is added to original bit sequence to increase the reliability of the communication. In this article, lets discuss a simple binary convolutional coding scheme at the transmitter and the associated Viterbi (maximum likelihood) decoding scheme at the receiver. Update: For some reason, the blog is unable to display the…
Matlab or C for Viterbi Decoder?
Are you bothered by speed of the speed of the simulations which you develop in Matlab/Octave? I was not bothered much, till I ran into the Viterbi decoder. If you recall, the Matlab/Octave simulation script for BER computation with hard soft decision Viterbi algorithm provided in post Viterbi with finite survivor state memory took around…