1. INTRODUCTION TO 18-491 FUNDAMENTALS OF SIGNAL PROCESSING
Richard M. Stern
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 (DSP)

3. Important people (for this course at least)
Instructor: Richard Stern
PH B24, ,
Course management assistant: Michelle Mahouski
HH 1112, ,

4. More important people Teaching interns: Tyler Supradeep
Vuong Rangarajan

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
Some MATLAB or background (presumably from )

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: Course home page:
Two hours per week for instructor and each TA, times TBA
You can schedule additional times with me as needed
Course home page:
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:
ECE’s take on academic integrity:
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 is NOT OK
“Collaborating” on exams is REALLY REALLY NOT 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
Orange headings refer to deterministic topics

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
Orange headings refer to deterministic topics

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
x[n]
y[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 …
x[n]
y[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. Another type of modeling: the source-filter model of speech
A useful model for representing the generation of speech sounds:
Pitch
Pulse train source
Noise source
Vocal tract model
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
Welcome16
Welcome 75
Welcome 150
Welcome 0

34. Classical signal enhancement: compensation of speech for noise and filtering
Approach of Acero, Liu, Moreno, et al. ( )…
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)
out_pre0_norm out_new_pre out
out_post0_norm out_new_post20

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
Push-to-talk will make life MUCH easier!!

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
ANC_base
ANC_cancel

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 -
5_spk
1st_spk 2nd_spk 3rd_spk 4th_spk 5th_spk

39. Practical signal separation: Audio samples using selective reconstruction based on ITD
RT60 (ms)
No Proc
Delay-sum
ZCAE-bin
ZCAE-cont
Brian-Ba-R0I0 Brian-Ba-R3I0
Brian-DS-R0I0 Brian-DS-R3I0
Brian-ZB-R0I0 Brian-ZB-R3I0
Brian-ZC-R0I0 Brian-ZC-R3I0

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
Welcome16
Welcome 75
Welcome 150
Welcome 0

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!