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…
The definition of Toeplitz matrix from [1] is: A matrix is said to be Toeplitz if the elements are determined completely by the difference .
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 to understand how we can use CORDIC for finding the phase and magnitude of a complex number. Basics The CORDIC…
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…
In the past, we had discussed BER for BPSK in flat fading Rayleigh channel. In this post, lets discuss a frequency selective channel with the use of Zero Forcing (ZF) equalization to compensate for the inter symbol interference (ISI). For simplifying the discussion, we will assume that there is no pulse shaping at the transmitter….
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 the given training set. However, how does the least square error criterion work when the training set is corrupted by…
We have installed Google FriendConnect on dspLog.com. With Google Friend Connect, you can: (a) You can interact with other members who have similiar interests. You will come to know the list of other sites (apart from dspLog.com) where the members have joined. You can add a member as a friend and so on. (b) You…
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 variables. The magnitude which has the probability density, is called a Rayleigh random variable. Further, the phase is uniformly distributed from…
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…
This is a guest post by Jose Antonio Urigüen who is an Electrical and Electronic Engineer currently studying an MSc in Communications and Signal Processing at Imperial College in London. This guest post has been created due to his own curiosity when reviewing some concepts of BER for BPSK in Rayleigh channnel published in the…
In this post, let us try to understand Gray codes and their usage in digital communication. Quoting from Wiki entry on Gray code [Gray-Wiki], The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one digit. In a digital communication system,…
Question 34 on signals from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q34. Consider the differential equation with and The numerical value of is (A) -2 (B) -1 (C) 0 (D) 1
Following the request by Siti Naimah, this post discuss the bit error probability for coherent demodulation of binary Frequency Shift Keying (BFSK) along with a small Matlab code snippet. Using the definition provided in Sec 4.4.4 of [DIG-COMM-SKLAR]), in binary Frequency shift keying (BFSK), the bits 0’s and 1’s are represented by signals and having…