INTRODUCTION TO 18 491 FUNDAMENTALS OF SIGNAL PROCESSING

INTRODUCTION TO 18 -491 FUNDAMENTALS OF SIGNAL PROCESSING Richard M. Stern 18 -491 lecture January 13, 2020 Department of Electrical and Computer Engineering Carnegie Mellon University Pittsburgh, Pennsylvania 15213

Welcome to 18 -491 Fundamentals of Signal Processing (DSP)! n Today will – Review mechanics of course – Review course content – Preview material in 18 -491 (DSP) Slide 2 ECE Department

Important people (for this course at least) n Instructor: Richard Stern – PH B 24, 8 -2535, rms@cs. cmu. edu n Course management assistant: Valeria Mc. Crary – HH 1112, 8 -4951, vmccrary@andrew. cmu. edu Slide 3 ECE Department

More important people n Teaching interns: n Vishrab Jade Commuri Traiger Slide 4 ECE Department

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

Does our work get graded? n Yes! n Grades based on: – Homework (including MATLAB problems) (33%) – Three exams (67%) » Two midterms (March 4 and April 8), and final exam » Plan on attending the exams! Slide 6 ECE Department

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

Other support sources n Office hours: – Two hours per week for instructor and each TA, times TBA – You can schedule additional times with me as needed n Course home page: – http: //www. ece. cmu. edu/~ece 491 n Canvas to be used for: – Grades: – discussions (on Piazza): – turning in homework (using Gradescope) Slide 8 ECE Department

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

Academic integrity (i. e. cheating and plagiarism) n CMU’s take on academic integrity: – http: //www. cmu. edu/policies/documents/Cheating. html n ECE’s take on academic integrity: – http: //www. ece. cmu. edu/programs-admissions/masters/academicintegrity. html n Most important rule: Don’t cheat! n 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 is NOT OK – “Collaborating” on exams is REALLY NOT OK! Slide 10 ECE Department

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

Complementary signal representations n Unit sample response n Discrete-time Fourier transforms n Z-transforms n Difference equations n Poles and zeros of an LSI system Slide 12 ECE Department

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

Signal representation: why perform signal processing? n A speech waveform in time: Slide 15 “Welcome to DSP I” ECE Department

A time-frequency representation of “welcome” is much more informative Slide 16 ECE Department

Downsampling the waveform by factor of 2: Slide 17 ECE Department

Consequences of downsampling by 2 Original: Downsampled: Slide 18 ECE Department

Upsampling the waveform Upsampling by a factor of 2: Slide 19 ECE Department

Consequences of upsampling by 2 Original: Upsampled: Slide 20 ECE Department

Linear filtering the waveform y[n] x[n] Filter 1: y[n] = 3. 6 y[n– 1]+5. 0 y[n– 2]– 3. 2 y[n– 3]+. 82 y[n– 4] +. 013 x[n]–. 032 x[n– 1]+. 044 x[n– 2]–. 033 x[n– 3]+. 013 x[n– 4] Filter 2: y[n] = 2. 7 y[n– 1]– 3. 3 y[n– 2]+2. 0 y[n– 3]–. 57 y[n– 4] +. 35 x[n]– 1. 3 x[n– 1]+2. 0 x[n– 2]– 1. 3 x[n– 3]+. 35 x[n– 4] Slide 21 ECE Department

Filter 1 in the time domain Slide 22 ECE Department

Output of Filter 1 in the frequency domain Original: Lowpass: Slide 23 ECE Department

Filter 2 in the time domain Slide 24 ECE Department

Output of Filter 2 in the frequency domain Original: Highpass: Slide 25 ECE Department

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. 6 y[n– 1]+5. 0 y[n– 2]– 3. 2 y[n– 3]+. 82 y[n– 4] +. 013 x[n]–. 032 x[n– 1]+. 044 x[n– 2]–. 033 x[n– 3]+. 013 x[n– 4] Slide 26 ECE Department

Lowpass filtering in the time domain: the unit sample response Slide 27 ECE Department

Lowpass filtering in the frequency domain: magnitude and phase of the DTFT Slide 28 ECE Department

The z-transform representation… y[n] x[n] Difference equation for Lowpass Filter 1: The corresponding z-transform of the system: Slide 29 ECE Department

The poles and zeros of the lowpass filter Slide 30 ECE Department

Lowpass filtering in the frequency domain: magnitude and phase of the DTFT Slide 31 ECE Department

Another type of modeling: the source-filter model of speech A useful model for representing the generation of speech sounds: Pitch Amplitude Pulse train source p[n] Vocal tract model Noise source Slide 32 ECE Department

Signal modeling: let’s consider the “uh” in “welcome: ” Slide 33 ECE Department

The raw spectrum Slide 34 ECE Department

All-pole modeling: the LPC spectrum Slide 35 ECE Department

An application of LPC modeling: separating the vocal tract excitation 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 Slide 36 ECE Department

Classical signal enhancement: compensation of speech for noise and filtering n Approach of Acero, Liu, Moreno, et al. (1990 -1997)… “Clean” speech x[m] Degraded speech h[m] Linear filtering z[m] n[m] Additive noise n Compensation achieved by estimating parameters of noise and filter and applying inverse operations Slide 37 ECE Department

“Classical” combined compensation improves accuracy in stationary environments Complete retraining – 7 d. B 13 d. B Clean VTS (1997) Original CDCN (1990) “Recovered” CMN (baseline) n Threshold shifts by ~7 d. B n Accuracy still poor for low SNRs Slide 38 ECE Department

Another type of signal enhancement: adaptive noise cancellation n Speech + noise enters primary channel, correlated noise enters reference channel n Adaptive filter attempts to convert noise in secondary channel to best resemble noise in primary channel and subtracts n Performance degrades when speech leaks into reference channel and in reverberation Slide 39 ECE Department

Simulation of noise cancellation for a PDA using two mics in “endfire” configuration n Speech in cafeteria noise, no noise cancellation n Speech with noise cancellation n But …. simulation assumed no reverb Slide 40 ECE Department

Signal separation: speech is quite intelligible, even when presented only in fragments n Procedure: – Determine which time-frequency components appear to be dominated by the desired signal – Reconstruct signal based on “good” components n A Monaural example: – Mixed signals – Separated signals - Slide 41 ECE Department

Practical signal separation: Audio samples using selective reconstruction based on ITD RT 60 (ms) 0 300 No Proc Delay-sum ZCAE-bin ZCAE-cont Slide 42 ECE Department

Phase vocoding: changing time scale and pitch n Changing the time scale: – Original speech – Faster by 4: 3 – Slower by 1: 2 n 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 Slide 43 ECE Department

Summary n Lots of interesting topics that teach us how to understand signals and design filters n An emphasis on developing a solid understanding of fundamentals n Will introduce selected applications to demonstrate utility of techniques n I hope that you have as much fun in signal processing as I have had! Slide 44 ECE Department

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