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…
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.
My friend and colleague Mr. Vineet Srivastava pointed me to a nice article on clock jitter – Clock Jitter Effects on Sampling : A tutorial – by Carlos Azeredo-Leme, IEEE Circuits and Systems Magazine, Third Quarter 2011. In this post, let us discuss the total Signal to Noise Ratio at the output of an analog to…
This is the third post in the series discussing receiver diversity in a wireless link. Receiver diversity is a form of space diversity, where there are multiple antennas at the receiver. The presence of receiver diversity poses an interesting problem – how do we use ‘effectively‘ the information from all the antennas to demodulate the…
Long back in time we discussed the BER (bit error rate) for BPSK modulation in a simple AWGN channel (time stamps states August 2007). Almost an year back! It high time we discuss the BER for BPSK in a Rayleigh multipath channel. In a brief discussion on Rayleigh channel, wherein we stated that a circularly…
In this post, let us evaluate the impact of frequency offset resulting in Inter Carrier Interference (ICI) while receiving an OFDM modulated symbol. We will first discuss the OFDM transmission and reception, the effect of frequency offset and later we will define the loss of orthogonality and resulting signal to noise ratio (SNR) loss due…
In this post, the objective is to figure out the minimum separation between two sinusoidals having frequencies , of duration each to be orthogonal. Let the phase difference between the sinusoidals is where can take any value from to (Refer Example 4.3 [DIG-COMM-SKLAR]). For the two sinuosidals to be orthogonal,
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…
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 :
Some among you will be aware that in a wireless link having multiple antenna’s at the receiver (aka receive diversity) improves the bit error rate (BER) performance. In this post, let us try to understand the BER improvement with receive diversity. And, since we are just getting started, let us limit ourselves to additive white…
Using the services of a new author ‘RV’, we are starting a new series of articles in the blog. Typically in India, many of the competitive examinations pertaining to Engineering (GATE, IES) and rectuitment by private and public sector companies (ISRO, BSNL, BEL, BHEL) uses examination with objective questions for the first level screening. We…
Question 7 on digital from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q7. The output Y of a 2-bit comparator is logic 1 whenever the 2 bit input A is greater than 2 bit input B. The number of combinations for which output is logic 1 is (A) 4 (B)…
Question 24 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q24. Two independent random variables X and Y are uniformly distributed in the interval [-1, 1]. The probability that max[X,Y] is less than 1/2 is (A) 3/4 (B) 9/16 (C) 1/4 (D) 2/3
Question 52 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q2. The power spectral density of a real process for positive frequencies is shown below. The values of and , respectively are (A) (B) (C) (D) Solution For a wide sense stationary function, the auto-correlation with delay is defined as,…