Elec. Forensics & Failure
Elec. Forensics & Failure ECE 5960
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This 14 page Class Notes was uploaded by Shyanne Lubowitz on Monday October 26, 2015. The Class Notes belongs to ECE 5960 at University of Utah taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/230010/ece-5960-university-of-utah in ELECTRICAL AND COMPUTER ENGINEERING at University of Utah.
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Date Created: 10/26/15
Please complete this code and answer the questions designated QlQ22 clear rand 39state39 7654 randn 39state39 7654 Suppose we want a 7 4 Hamming code n 2Am l k n m Produce the parity check matrix H hammgenm G gen2parH39 Q2 How do H and G differ from the ones discussed on the wikipedia page Q3 Is the code still systematic How can you tell Generate some data N target 80 le6 N7 k floor Nitargetk data round rand N l d reshape data k Nk Encode the data with the generator matrix c rem G d 2 Q4 Can you see the encoded data in the coded data stream Map to antipodal signaling 1 l l 2c for ii llength EbNos EbNoidB EbNosiiL add noise to the coded data EbNo 10A EbNoidBlO Q5 what is the code rate Rifec in terms of k and n and Rifec Es l O l centered around 05 sigma sqrt Es EsNo 2 sigmaA2 NO2 noise sigma randn size x y x noise Do hard decision decoding Q8 what decision rule will give a hard decoding oo Q7 Do you think this signal should make any hard decision errors Q8 Compute syndromes from the parity matrix syn rem H hd 2 Convert syndromes from binary to decimal to easily use the lookup ble ta syn2dec 2A m l lO syngloc syn2dec syn o 6 Create a look up table to convert syndromes to correction vectors correction syndtableH39 o 6 Apply the correction vectors via modulo 2 addition decoded rem hd correction lsyn7loc 2 errors decodedmlend errorsiuc hdmlend errorsihamm decoded N c display some of the decoding steps for small data sets if N lt 81 d d c c hd hd syniloc syniloc decoded decoded errors errors errorsihamm errorsihamm end BERii sum errors N BERgncii sum errorsiuc N theoryii berawgn EbNoidB 39psk39 2 39nondiff39 end EbNos EbNos BER BER BER uc BERiuc theory theory figurem semilogy EbNos theory 39b39 EbNos BERiuc 39r39 EbNos BER 39k39 legend 39theory39 39symbol error rate39 39hamming BER39 grid on axis EbNosl EbNosend le 6 01 o0 Now set Nitarget le6 o o Then uncomment lines of code that fall between lines of 0 Run the code for m 3 4 5 o o o o Q9 What is the code rate in each case 39 quotI o0 102 Assuming an uncoded data rate of Rbit 1 Mbps what symbol rate does each of these choices represent nu o0 112 Assuming the uncoded signal required 1 MHZ of bandwidth what signalling bandwidth does each of these choices require l39l39l39l39l39 o0 o0 Q12 What is the coding gain you can measure at BER le S for each of these choices oo theory symbol error rate BER 06 dB coding gain m 3 theory symbol error rate theory symbol error rate 15 dB coding gain m 5 theory symbol error rate BER 16 dB coding gain m 6 o o o0 o0 o0 o0 o o0 o0 o0 o0 o o Q o0 o o o theory symbol error rate BER 17 dB coding gain m 7 4 6 8 10 12 Q13 Does Hamming code performance coding gain increase with block size n NOTE this is representative of most FEC approaches Q14 Does Hamming code performance coding gain increase with coding rate kn NOTE this behavior is opposite that of most FEC approaches Q15 Would you expect improved performance if a decoding algorithm worked with soft decision data rather than hard decision as used above Q16 Suppose you had the following received data sequence Which three recieved values are least reliable and most reasonable for a decision algorithm to invert 13 04 11 08 09 soft Suppose you have the following data Q17 if exactly four consecutive bits are inverted by noise in the channel would the Hamming codes examined above be able to correct all our bit inversions Q18 Could they correct any of them under certain conditions 9 o 9 o Q19 Give matlab code to represent feeding this data into a 10 x 10 interleaver and reading it back out interleaved Q20 What are the first twenty values of the interleaved sequence oo Assume the data is l interleaved after coding 2 sent through the channel which caused exactly four consecutive bit inversions deinterleaved and 4 passed through the Hamming decoder Q21 Will the hamming code be able to correct all o0 o0 o0 oo Q22 What is the maximum length of a consecutive string of bit inversions that could be corrected through using this interleaver together with a single error correcting Hamming code o0 o0 o0 u E ECE 5325 Wireless Communications Vocoders quantization and compression Q1 Which of the following consonants are voiced P t S l p I ch sh mm mm Go to lthttpwwwspsctugrazaUcoursesscldownloadgt and download Vocoderzip Extract it to a local directory and open indexhtml Read the text in the lefthand panel Q2 Which excitation method in Figure 4b righthand panel in the browser is used to produce a d tone generator or noise generator How is that excitation expressed in Figure 5 Read the instructions for using the vocoder simulation program in section 4 of the left hand panel Then do the following 0 Load the prerecorded text He caught them at your house 0 Click on Analyze Click on Synthesize Switch the view mode to the leftmost choice Q3 Do the original and synthesized images look identical m Q4 Do they sound the same Click the Audio speaker button Q5 How would you rate the quality according to Table 82 in Rappaport Switch the view mode to the colored middle button Q6 What are the redbars Q9 What does this tell you about which LPC vocoder approach is used from Section 87 in Rappaport 1 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S Central Campus Dr Salt Lake City UT 841129206 Phone 801 5816941 Fax 801 5815281 wwweceutahedu ECE 5325 Wireless Communications Now do the following 0 Switch to the rightmost view mode and do the following 0 Click the pencil button at the far left of the synthesis panel 0 Click the down arrow at the far right 0 Click Synthesize 0 Play the signal Q9 Why did the pitch bars disappear Q10 How does the speech differ with this setting What is the model doing to achieve this sound mime ml huha ca 39imfmii r Q11 Is it still intelligible Now do the following 0 Click the undo arrow at the far right Select the updown arrow button Move the pitches to 200 Hz Click Synthesize Play the signal Q12 How does the speech differ with this setting What is the model doing to achieve this sound Q13 Is it still intelligible Q14 Assuming speech covers a dynamic range of up to 40 dB how many bits of quantization are required to reproduce speech Rely on your textbook section 83 2 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S Central Campus Dr Salt Lake City UT 841129206 Phone 801 5816941 Fax 801 5815281 wwweceutahedu ECE 5325 Wireless Communications Q15 If compact discs CDs use 16bit quantization what dynamic range can they reconstruct Suppose that you wanted to transmit a sequence b of ones and zeros where pb 0 pb 1 05 Rely on the MacKay textbook Q16 What is the entropy of this signal Q18 How much can this signal be compressed according to the Entropy law Source coding theorem see MacKay textbook Suppose you wanted to transmit a sequence b of ones and zeros where pb 0 01 and pb 1 09 Q19 What is the entropy of this signal Q22 What does the Entropy law tell you about how much an LPC coder can compress speech 3 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S Central Campus Dr Salt Lake City UT 841129206 Phone 801 5816941 Fax 801 5815281 Wwweceutahedu ECE 5325 Wireless Communications 4 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S Central Campus Dr Salt Lake City UT 841129206 Phone 801 5816941 Fax 801 5815281 Wwweceutahedu Pulse shaping notes Digital modulation most often looks like either discrete phase or frequency shifts in a signal Frequency shifts keying FSK compares fairly well to FM except that the data is not an analog signal imposed on a carrier Instead it consists of a limited number of discrete frequency shifts Section 64 Digital modulation offers significant benefits over analog modulation AM amp FM It offers 1 greater noise immunity you just have to get close to one of a limited set of discrete states 2 greater security public key encryption 3 compression 4 FEC 5 equalization Digital modulation quality is generally measured in terms of two efficiencies that are readily compared in terms of higher order modulation Higher order modulation involves subdividing the average available amplifier power into more than just two choices l As an example one could send three bits of information at a time with 2 energy levels but they d have to be closer together than with just two for the same average power Thus they re more susceptible to noise 1 power efficiency EbN0 We ve seen this a lot with our BER curves a Higherorder mod is predictably more susceptible to noise and less power efficient than lowerorder modulation b We ve seen power efficiency a lot and will return to it again later 2 bandwidth efficiency RbB a Higher order modulation passes multiple bits per symbol say 3 bits at a time when there are 23 available levels per symbol Thus the symbol rate goes down by a factor of three and the modulation uses less 3X less bandwidth But bandwidth is an elusive term If you use the nulltonull definition p 281 the bandwidth of BPSK is 2Rb But adjacent sidelobes are only down 13 dB and leaves little room for margin in cell systems The FCC uses 99 power confinement To get that low requires 05 on either side of bandwidth edges or 23 dB This is near 13 6 6 or about three nulls on either side of the center frequency Thus the bandwidth could also be called 6Rb or more That really eats into the number of users that you can support in a bandwidth Section 66 A natural way to limit bandwidth is to lter a signal If you lter a signal it looks like the smearing you get in a channel This generally leads to 181 Nyquist found the criteria a lter must satisfy to avoid adding 181 Basically you need the lter to have a response of zero at all symbol times except the center of the lter where you pass the data Many lters are Nyquist lters but certain ones are especially good ones First lters that limit bandwidth approximate an ideal lowpass lter in the frequency domain and look somewhat like a sinc function in the time domain The goal is spectral con nement so you want your lter to mimic a lowpass lter Second good lters should decay rapidly away from zero so that you can truncate them to a reasonable length for practical realizability You also want them to decay quickly to minimize the impact of timing jitter Third you want the combined ltering at TX and RX sides to be a Nyquist pulse Since optimal ltering involves matched ltering at the RX side the Root Raised Cosine RRC lter is a real favorite You can compute it in matlab as follows h rcosine l samples per symbol sqrt R alpha delay 12 num symbols in the lter With a RRC the bandwidth is limited to 1alpha Rb Thus with an RRC and alpha 03 a typical value the bandwidth is B l3Rb or 136 022 times the bandwidth of unshaped BPSK This allows you to cram almost ve times the number of users into a cellprovider bandwidth Very valuable and no ISI
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