INTRODUCTION TO 18-491 FUNDAMENTALS OF SIGNAL PROCESSING

1. INTRODUCTION TO 18-491FUNDAMENTALS OF SIGNAL PROCESSING Richard M. Stern 18-491 lecture January 14, 2019 Department of Electrical and Computer Engineering Carnegie Mellon University Pittsburgh, Pennsylvania 15213

2. Welcome to 18-491 Fundamentals of Signal Processing (DSP)! • Today will • Review mechanics of course • Review course content • Preview material in 18-491 (DSP)

3. Important people (for this course at least) • Instructor: Richard Stern • PH B24, 8-2535, rms@cs.cmu.edu • Course management assistant: Michelle Mahouski • HH 1112, 8-4951, mmahousk@andrew.cmu.edu

4. More important people • Teaching interns: • Tyler Supradeep VuongRangarajan

5. Some course details • Meeting time and place: • Lectures here and now • Recitations Friday 10:30 – 12:20, 12:30 – 2:20, SH 214 • Pre-requisites (you really need these!): • Signals and Systems 18-290 • Some MATLAB or background (presumably from 18-290)

6. Does our work get graded? • Yes! • Grades based on: • Homework (including MATLAB problems) (33%) • Three exams (67%) • Two midterms (March 6 and April 3), and final exam • Plan on attending the exams!

7. Textbooks • Major text: • Oppenheim, Schafer, Yoder, and Padgett: Discrete-Time Signal Processing • Plan on purchasing a hard copy new or used • Material to be supplemented by class notes at end of course • Some other texts listed in syllabus

8. Other support sources • Office hours: • Two hours per week for instructor and each TA, times TBA • You can schedule additional times with me as needed • Course home page: • http://www.ece.cmu.edu/~ece491 • Canvas to be used for grades (but probably not much else) • Piazza to be used for class discussions

9. Academic stress and sources of help • This is a hard course • Take good care of yourself • If you are having trouble, seek help • Teaching staff • CMU Counseling and Psychological Services (CaPS) • We are here to help!

10. Academic integrity (i.e. cheating and plagiarism) • CMU’s take on academic integrity: • http://www.cmu.edu/policies/documents/Cheating.html • ECE’s take on academic integrity: • http://www.ece.cmu.edu/programs-admissions/masters/academic-integrity.html • Most important rule: Don’t cheat! • But what do we mean by that? • Discussing general strategies on homework with other students is OK • Solving homework together is NOT OK • Accessing material from previous years isNOT OK • “Collaborating” on exams is REALLY REALLYNOT OK!

11. 18-491: major topic areas • Signal processing in the time domain: convolution • Frequency-domain processing: • The DTFT and the Z-transform • Complementary signal representations • Sampling and change of sampling rate • The DFT and the FFT • Digital filter implementation • Digital filter design • Selected applications

12. Complementary signal representations • Unit sample response • Discrete-time Fourier transforms • Z-transforms • Difference equations • Poles and zeros of an LSI system

13. Some application areas (we may not get to all of these) • Linear prediction and lattice filters • Adaptive filtering • Optimal Wiener filtering • Two-dimensional DSP (image processing) • Short-time Fourier analysis • Speech processing

14. Signal representation: why perform signal processing? • A speech waveform in time: “Welcome to DSP I”

15. A time-frequency representation of “welcome” is much more informative

16. Downsampling the waveform Downsampling the waveform by factor of 2:

17. Consequences of downsampling by 2 Original: Downsampled:

18. Upsampling the waveform Upsampling by a factor of 2:

19. Consequences of upsampling by 2 Original: Upsampled:

20. Linear filtering the waveform y[n] x[n] Filter 1: y[n] = 3.6y[n–1]+5.0y[n–2]–3.2y[n–3]+.82y[n–4] +.013x[n]–.032x[n–1]+.044x[n–2]–.033x[n–3]+.013x[n–4] Filter 2: y[n] = 2.7y[n–1]–3.3y[n–2]+2.0y[n–3]–.57y[n–4] +.35x[n]–1.3x[n–1]+2.0x[n–2]–1.3x[n–3]+.35x[n–4]

21. Filter 1 in the time domain

22. Output of Filter 1 in the frequency domain Original: Lowpass:

23. Filter 2 in the time domain

24. Output of Filter 2 in the frequency domain Original: Highpass:

25. Let’s look at the lowpass filter from different points of view … y[n] x[n] Difference equation for Lowpass Filter 1: y[n] = 3.6y[n–1]+5.0y[n–2]–3.2y[n–3]+.82y[n–4] +.013x[n]–.032x[n–1]+.044x[n–2]–.033x[n–3]+.013x[n–4]

26. Lowpass filtering in the time domain: the unit sample response

27. Lowpass filtering in the frequency domain: magnitude and phase of the DTFT

28. Pitch Pulse train source Vocal tract model Noise source Another type of modeling: the source-filter model of speech A useful model for representing the generation of speech sounds: Amplitude p[n]

29. The poles and zeros of the lowpass filter

30. Signal modeling: let’s consider the “uh” in “welcome:”

31. The raw spectrum

32. All-pole modeling: the LPC spectrum

33. An application of LPC modeling: separating the vocal tract excitation and and filter Original speech: Speech with 75-Hz excitation: Speech with 150 Hz excitation: Speech with noise excitation: Comment: this is a major techniques used in speech coding

34. Classical signal enhancement: compensation of speech for noise and filtering • Approach of Acero, Liu, Moreno, et al. (1990-1997)… • Compensation achieved by estimating parameters of noise and filter and applying inverse operations “Clean” speech Degraded speech x[m] h[m] z[m] Linear filtering n[m] Additive noise

35. “Classical” combined compensation improves accuracy in stationary environments • Threshold shifts by ~7 dB • Accuracy still poor for low SNRs Complete retraining –7 dB 13 dB Clean VTS (1997) Original CDCN (1990) “Recovered” CMN (baseline)

36. Another type of signal enhancement: adaptive noise cancellation • Speech + noise enters primary channel, correlated noise enters reference channel • Adaptive filter attempts to convert noise in secondary channel to best resemble noise in primary channel and subtracts • Performance degrades when speech leaks into reference channel and in reverberation

37. Simulation of noise cancellation for a PDA using two mics in “endfire” configuration • Speech in cafeteria noise, no noise cancellation • Speech with noise cancellation • But…. simulation assumed no reverb

38. Signal separation: speech is quite intelligible, even when presented only in fragments • Procedure: • Determine which time-frequency time-frequency components appear to be dominated by the desired signal • Reconstruct signal based on “good” components • A Monaural example: • Mixed signals - • Separated signals -

39. Practical signal separation: Audio samples using selective reconstruction based on ITD RT60 (ms) 0 300 No Proc Delay-sum ZCAE-bin ZCAE-cont

40. Phase vocoding: changing time scale and pitch • Changing the time scale: • Original speech • Faster by 4:3 • Slower by 1:2 • Transposing pitch: • Original music • After phase vocoding • Transposing up by a major third • Transposing down by a major third Comment: this is one of several techniques used to perform autotuning

41. Summary • Lots of interesting topics that teach us how to understand signals and design filters • An emphasis on developing a solid understanding of fundamentals • Will introduce selected applications to demonstrate utility of techniques • I hope that you have as much fun in signal processing as I have had!