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? Let there be independent and identically distributed Gaussian random variables with mean and variance and we form a new random…
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 frequency of oscillation with no frequency components else where. However the spectrum of practical oscillators do have spectrum skirts around…
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,…
Wishing all the readers of dsplog.com a great year 2010 ! Its been a mixed year for dsplog. Some key milestones a) Crossing 1000 subscribers with 1100+ comments in March 2009 b) Crossing 100 posts with 2200 subscribers and 2600+ comments in October 2009 c) As I write this, we have 102 posts with 2603…
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…
In a classification problem, the output (also called the label or class) takes a small number of discrete values rather than continuous values. For a simple binary classification problem, where output takes only two discrete values : 0 or 1, the sigmoid function can be used to transform the output of a linear regression model…
In a post on Minimum Shift Keying (MSK), we had discussed that MSK uses two frequencies which are separated by and phase discontinuity is avoided in symbol boundaries. In that post, we had discussed MSK as a continuous phase transmit signal and showed that phase changes through 0, 90, 180 and 270 degrees. In this…
In an earlier post, it was mentioned that delta modulator without the quantizer is identical to convolving an input sequence with . Let us first try to validate that thought using a small MATLAB example and using the delta modulator circuit shown in Figure 9.13a of DSP-Proakis [1]. % delta modulation xn = sin(2*pi*1/64*[0:63]); xhatn…
I happened to visit ‘The Digital Signal Processing Blog’, maintained by Mr. Andres Kwasinski, Ph. D. In the blog one can find details about the upcoming IEEE conferences pertaining to communication and multimedia processing. Further, in some of the posts, author shares his thoughts on topics like fixed point arithmetic (here) and wavelets (here) etc….
IEEE 802.11ac Very High Throughput (for <6GHz band) is an upcoming standard which is development by IEEE standardization committee. The mandate of Task Group AC is supposed to enhance the High Throughput rates achieved by 802.11n. As described in the document VHT below 6GHz PAR plus 5C’s (802.11-08/0807r4) the group has the following objectives :
In the previous post on I-Q modulator and de-modulator, we had briefly mentioned that the a baseband PAM transmission can be modelled as , where is the symbol period, is the symbol to transmit, is the transmit filter, is the symbol index and is the output waveform. In this post, the objective is to understand…
Question 38 on Communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q38. A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X=0)=9/10, then the probability of error for an optimum receiver will be (A) 7/80 (B) 63/80 (C)…
In problem 9.14 of DSP-Proakis, the objective is to analyze the effect of zero-order interpolation and first-order interpolation to double the number of samples in the sinusoidal while keeping the sampling frequency unchanged. My take: The first part of the problem (a) is to generate the sequence having half the frequency of . For zero-order…
In previous posts, we had discussed equalization of a 2×2 MIMO channel with Zero Forcing (ZF) equalization and later, Zero Forcing equalization with successive interference cancellation (ZF-SIC). In this post, we will explore a variant of ZF-SIC called Zero Forcing Successive Interference Cancellation with optimal ordering. We will assume that the channel is a flat…