Following discussion of bit error rate (BER) for BPSK and bit error rate for FSK, it may be interesting to move on to discuss a higher order constellation such as Pulse Amplitude Modulation (PAM). Consider that the alphabets used for a 4-PAM is (Refer example 5-34 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]).
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…
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…
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,…
In the post on transmit pulse shaping filter, we had discussed pulse shaping using rectangular and sinc. In this post we will discuss about optimal receiver structure when pulse shaping is used at the transmitter. The receiver structure is also called as matched filter. For the discussion, we will assume rectangular pulse shaping, the channel…
My friend Mr. Balaji volunteers for Vibha, a non-profit organization whose mission is to ensure that every underprivileged child attains his or her right to education, health and opportunity. Vibha, which was founded in 1991 has a volunteer network of 825 members spread across Atlanta, Austin, Bay Area, Boston, Chicago, Dallas, Houston, Jacksonville, Los Angeles,…
In a multi class classification problem, the output (also called the label or class) takes a finite set of discrete values . In this post, system model for a multi class classification with a linear layer followed by softmax layer is defined. The softmax function transforms the output of a linear layer into values lying…
In DSP-Proakis, I found the problem 2.56 interesting as it provides insight into delta modulation. The task is to show that, where is any discrete time signal and is the unit step function.
In a previous post (here), we discussed in brief, Orthogonal Frequency Division Multiplexing (OFDM) transmission. Let us know probe bit more into the motivation of cyclic prefix (aka guard interval) associated with each OFDM symbol. What is cyclic prefix? Let us consider one subcarrier (subcarrier +1 specified in IEEE 802.11a specification) alone. In the figure…
Let us try to understand simulation of a typical Orthogonal Frequency Division Multiplexing (OFDM) transmission defined per IEEE 802.11a specification. Orthogonal pulses In a previous post (here ), we have understood that the minimum frequency separation for two sinusoidals with arbitrary phases to be orthogonal is , where is the symbol period. In Orthogonal Frequency…
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 re-run, using OFDM as the underlying physical layer. This post discuss the derivation of symbol error rate for a general…
Two points suffice for drawing a straight line. However we may be presented with a set of data points (more than two?) presumably forming a straight line. How can one use the available set of data points to draw a straight line? A probable approach is to draw a straight line which hopefully minimizes the…
Question 52 on electromagnetics from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. An infinitely long uniform solid wire of radius carries a uniform dc current of density . Q52. The magnetic field at a distance from the center of the wire is proportional to (A) for and for (B) for and for (C) for and for (D) for and for Solution…