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Outcome Based Education

INDIA HAS BECOME A PERMANENT MEMBER OF THE WASHINGTON ACCORD. Outcome Based Education. Focus Learning , not teaching Students, not faculty Outcomes, not inputs or capacity . Components that contribute to Academic Abilities. Components that contribute to Transferable Skills.

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Outcome Based Education

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  1. INDIA HAS BECOME A PERMANENT MEMBER OF THE WASHINGTON ACCORD Outcome Based Education Focus Learning, not teaching Students, not faculty Outcomes, not inputs or capacity  Dr.P.Meena,Assoc.Prof., EEE

  2. Components that contribute to Academic Abilities

  3. Components that contribute to Transferable Skills

  4. The components of course delivery that contribute to the defined attributes of the course . Dr.P.Meena,Assoc.Prof.,EEE

  5. Digital Signal ProcessingIntroduction Inception:1975 with the development of Digital Hardware such as digital hardware. Personal computer revolution in 1980s and 1990s caused DSP explosion with new applications. Dr. P.Meena, Assoc.Prof(EE) BMSCE 5

  6. Advantages of DSP Technology High reliability Reproducibility Flexibility & Programmability Absence of Component Drift problem Compressed storage facility (especially in the case of speech signals which has a lot of redundancy). DSP hardware allows for programmable operations. Signal Processing functions to be performed by hardware can be easily modified through soft ware(efficient algorithms) Dr. P.Meena, Assoc.Prof(EE) BMSCE 6

  7. Advantages of DSP Technology High reliability Reproducibility Flexibility & Programmability Absence of Component Drift problem Compressed storage facility (especially in the case of speech signals which has a lot of redundancy). DSP hardware allows for programmable operations. Signal Processing functions to be performed by hardware can be easily modified through soft ware(efficient algorithms) Dr. P.Meena, Assoc.Prof(EE) BMSCE 7

  8. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  9. Digital Signal Processing with overlapping borders Dr. P.Meena, Assoc.Prof(EE) BMSCE

  10. A TYPICAL DIGITAL SIGNAL PROCESSING SYSTEM dB dB A/D CONVERTER D/A CONVERTER Dig.Signal Processor Analog prefilter or Antialiasing filter Low pass filtered signal Discrete time signal Discrete time signal Reconstruction filter same as the pre filter Sampling frequency Dr. P.Meena, Assoc.Prof(EE) BMSCE 10

  11. Course Outcomes CO1: Ability to apply the knowledge of mathematics, science and fundamentals of signals and systems to ascertain the behavior of complex engineering systems. CO2:Ability to Identify techniques, formulate representations and analyze responses of digital systems. CO3:Ability to Design digital system components and test their application using modern engineering tools, as solutions to engineering problems. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  12. Course Contents • Different operations on a signal in the digital domain • Different forms of realizations of a • Digital System. • Design Procedures for Digital Filters Dr. P.Meena, Assoc.Prof(EE) BMSCE

  13. Outcomes of this Course: • By The End Of The Course , • Distinguish The Digital and Analog Domains. • Analyse Signals, and reconstruct. • Develop Block Diagrams For Different System Representations,. • Design Analog And Digital Filters. • Ready to Take up Specialized Courses in Audio, speech, • image and Real-time Signal Processing, Further On Dr. P.Meena, Assoc.Prof(EE) BMSCE 13

  14. Course Outline Course Delivery: Lecture,handouts,videos,animations,discussions,activities Course Assessment: Marks: Tests: 20 (T1 & T2) Quiz; 05 Tutorials: 10 Lab: 15 Dr. P.Meena, Assoc.Prof(EE) BMSCE

  15. Review of Signals & Systems Dr. P.Meena, Assoc.Prof(EE) BMSCE 15

  16. Audio • Video (Represented as a function of 3 variables.) • Speech- • Continuous-represented as a function of a single (time) variable). • Discrete-as a one dimensional sequence which is a function of a discrete variable. • Image: Represented as a function of two spatial variables • Electrical - Signals Dr. P.Meena, Assoc.Prof(EE) BMSCE 16

  17. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  18. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  19. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  20. Relation between analog frequency and digital frequency Dr. P.Meena, Assoc.Prof(EE) BMSCE 20

  21. -Fs -Fs/2 -Fs/4 Fs/4 Fs/2 Fs 3/2Fs -3/2Fs f in Hertz(analog) Ω in radians/sample Digital Ω=-3∏ Ω=-2∏ Ω=-∏ Ω=-∏/2 Ω=0 Ω=∏ Ω=2∏ Ω=3∏ Ω=∏/2 Nyquist interval Ω=∏/2,f=Fs/4 Ω=∏,f=Fs/2 f=0,Ω=0 Ω=-∏,f=-Fs/2 0 Ω= -∏/2,f=-Fs/4 Diagrammatic Representation of relation between analog frequency and digital frequency:+ve angle counter clock wise Dr. P.Meena, Assoc.Prof(EE) BMSCE

  22. Sampling of continuous time signals The Fourier transform pair for continuous-time signals is defined by If is sampled uniformly at times T seconds apart from a discrete- time signal x[n] is obtained. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  23. The Fourier transform of the resulting sequence x[n] can be shown to be is the sum of an infinite number of amplitude-scaled, frequency-scaled, and translated versions of Thus The Fourier transform of the continuous-time signal is illustrated in the following figure.. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  24. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  25. From the figure it is easy to see that the triangles of Will not overlap if <π This inequality can be re arranged to give, If we let,Ω0 equal 2πf0 where f0 is in Hertz, the above inequality becomes, Therefore, if the sampling rate I/T is greater than 2 f0 no overlap occurs. If there is no overlap, the spectrum Can be found and by the inverse transform can be reconstructed. If however, >π The triangles will overlap and the spectrum of the continuous signal cannot be reconstructed Dr. P.Meena, Assoc.Prof(EE) BMSCE

  26. The Sampling Theorem • A signal xa(t) can be reconstructed from its sample values xa(nT) if the sampling rate 1/T is greater than twice the highest frequency (f0 in Hertz ) present in xa(t). • The sampling rate 2f0 for an analog band limited signal is referred to as the Nyquist Rate. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  27. Effect of Variation of Sampling frequency on the sampling of a sine wave of frequency 50Hz. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  28. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  29. What is the equation to this sequence ??? Periodic Signals Dr. P.Meena, Assoc.Prof(EE) BMSCE 29

  30. APeriodic Signals Extract from cnx.org Dr. P.Meena, Assoc.Prof(EE) BMSCE 30

  31. The two signals shown though of different digital frequencies have the same sampled sequence . Dr. P.Meena, Assoc.Prof(EE) BMSCE

  32. Therefore we find that a sampled sine wave of frequency f is indistinguishable from a sine wave of frequency fs-f, fs+f,2fs-f,2fs+f…. • Or in general kfs±f for any integer k. • These set of frequencies that are indistinguishable from one another are called aliases and the phenomenon is called “Aliasing” Dr. P.Meena, Assoc.Prof(EE) BMSCE

  33. Linear Shift Invariant System Is the frequency response of the system is recognized as the Fourier transform of the system’s impulse response Dr. P.Meena, Assoc.Prof(EE) BMSCE

  34. Frequency spectrum of a 100Hz sine wave sampled at 500Hz Frequency spectrum of a 100Hz sine wave sampled at 80Hz Under Sampling Dr. P.Meena, Assoc.Prof(EE) BMSCE

  35. Alias during under sampling Dr. P.Meena, Assoc.Prof(EE) BMSCE

  36. Effect of Aliasing Dr. P.Meena, Assoc.Prof(EE) BMSCE 36

  37. Real &Imag parts of Dr. P.Meena, Assoc.Prof(EE) BMSCE 37

  38. Representation of a Complex Exponential Function Extract from cnx.org Dr. P.Meena, Assoc.Prof(EE) BMSCE 38

  39. Two dimensional plot of Dr. P.Meena, Assoc.Prof(EE) BMSCE 39

  40. Frequency content of a signal Continuous time : Periodic - Fourier series Non-periodic- Fourier transform Discrete time: Discrete Time Fourier Transform-DTFT Discrete Fourier Transform -DFT Dr. P.Meena, Assoc.Prof(EE) BMSCE 40

  41. THE DISCRETE TIME FOURIER TRANSFORM The discrete time Fourier transform of a sequence: The discrete time Fourier transform of a system: It seen that the discrete time Fourier transform of a system is 2π periodic and continuous in Ω Dr. P.Meena, Assoc.Prof(EE) BMSCE

  42. Inverse Discrete Time Fourier Transform (iDTFT) Dr. P.Meena, Assoc.Prof(EE) BMSCE

  43. DTFT of a Sinusoidal signal of analog frequency 50Hz 43

  44. Dr. P.Meena, Assoc.Prof(EE) BMSCE

  45. DTFT of a Discrete Impulse Dr. P.Meena, Assoc.Prof(EE) BMSCE

  46. Discrete Unit Step Function • Magnitude of the DTFT Dr. P.Meena, Assoc.Prof(EE) BMSCE

  47. 1.The Transfer function is a function of the continuous variable Ω. 2. This needs computation of infinite sum at uncountable infinite frequencies. 3.Hence the above transform is not numerically computable. 4.The transform is defined for aperiodic sequences. Disadvantage of DTFT Dr. P.Meena, Assoc.Prof(EE) BMSCE 47

  48. x[n]=0 for n<0 and >N; ≠0 otherwise A repeated sequence of finite length N Dr. P.Meena, Assoc.Prof(EE) BMSCE

  49. Discrete Fourier Transform, DFT Dr. P.Meena, Assoc.Prof(EE) BMSCE

  50. Dr. P.Meena, Assoc.Prof(EE) BMSCE

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