INTRO TO DIG SIG PRO
INTRO TO DIG SIG PRO E C E 467
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This 10 page Class Notes was uploaded by Eloy Ferry on Saturday September 26, 2015. The Class Notes belongs to E C E 467 at Clemson University taught by John Gowdy in Fall. Since its upload, it has received 69 views. For similar materials see /class/214305/e-c-e-467-clemson-university in ELECTRICAL AND COMPUTER ENGINEERING at Clemson University.
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Date Created: 09/26/15
ECE 467667 Introduction to Digital Signal Processing LECTURE1 Introduction to Diqitgl Siqnal Processigq Signal A physical phenomena whbse variations represent information EXAMPLE Speech Signal W I I AU jl M AV I V V IV U V t I l Pitch Period EXAMPLE Electrocardiogram ECG Signal Vt Vt vquot v lt gt Pulse Period ECE T467667 Introduction to Digital Signal Processing Other Siqnals Radar 39 Biomedical Sonar Music 0 Seismic 0 Digital Communications Digital Discrete in time and in amplitude 3A 2A l l 0T 2T 3T 4T t Processing One or more of improve qualityeg remove noise Extract informationeg estimate pitch period of a speech signal Convert to a more useful formeg apply the Fourier Transform Generate a useful signaleg speech synthesis music synthesis Example of analoq signal accessing Filtering to remove noise 1 Let xt stnt Low frequency signal high frequency signal ECE T467667 Introduction to Digital Signal Processing Use quotlow passquot filter to remove the noise Xt L m t Want to be as close as possible to st Svstem Function of the above system 1 s q R HSR sRLS Frequency Response R 39 HJQ HS ism 19 We can write Xj 2lj 2 s1s2 NomiH09 Si9HiQNiQHi9 ECE T467667 Introduction to Digital Signal Processing Ideaycase example N09 HUQ 4 Ideal Low Pass Fllterquot I Q In general we can write Hug H39 aim Y 39J 1 Phase Response Magnitude response where Hie JReHJ39Q2 mHJ3922 ECE T467 667 Introduction to Digital Signal Processing and arg Hj 2f tan1W R9HJS2 When I luGQXeJaTQUUQ H S2 39 J lvUQXelargvh M19 arguum argvunn mm meJ M191 Then Hui L091 W091 And arg H1sz arg U09 arg v09 Now go back to the example quotCrudequot Low J lt Pass Filter E L Q 5 ECE 14676657 Introduction to Digital Signal Processing arg HjQ arg R arg R jLQ tanquot tan391L39 g 2 R R J 0 NITi General timedomain expression for linear shiftinvariant LSI analog system xt ht gm is t xt ht Convolution Where ht is thelimpulse response of the system and where ht Hs the System Function ECE T467 667 Introduction to Digital Signal Processmg Analyze our analog lowpass filter xt L 4W As input frequency gt O inductor gtshortcirCUit impedance Ls LjQ gt t xt gain 1 As input frequency ace inductor gt0pen circuitzcurrent through RO gt t 0 gain 0 Dig Ital Filter A linear shiftinvariant LSl digital system Most general form yn xnhn where hn is the unit sample response ie the response to the input xn6n 5n 1 321o123 yn i xk1n Jk xn hn convolution kz oo ECE T467 667 Introduction to Digital Signal Processing For frequency domain analysis use ztransforms YzXzHz 39 xv system function where Hz arm ih nz39n n oo When 2 ej Yej Xe Hequot Frequency Response He5 is also the Discrete Time Fourier TransformDTFT of hn Heilt innel n Ts co Most digital filters can39be represented as a linear difference equation mm bkxn k ajyn l i1 If all of the a1 terms are 0 the filter is finite impulse response FIR Otherwise the filter is infinite impulse response IIR Example FIR digital filter yltnquotgxltngt xltn 1gt vz xz 1xz l 2 Xz1 2 1 ECE T467 667 Introduction to Digital Signal Processing 39 arg Hejm z arglt1 e j Egg 0 1 arg 1cosmszinm tan1 Sinw 1cosm Another WELL to evaluate the phase for this example Go back to the expression 12 Helquot e 2 2 cod w e cos Z arg Hej arg eJEm arg cos 162 Note that arg e 2 002 and arg cos 0 when cod 2 0 7c when cod lt O J Therefore we can plot arg e 3as follows V arg He 0 7732 7t2 mu l0
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