Slide 1

Slide 2

Lecture 5: Signal Processing II EEN 112: Introduction to Electrical and Computer Engineering Professor Eric Rozier, 2/20/13

Slide 3

SOME DEFINITIONS

Slide 4

Decibels Logarithmic unit that indicates the ratio of a physical quantity relative to a specified level. 10x change is 10 dB change. 2x change ~3dB change. Remember L_dB = 10 log_10 (P1/P0) for power L_db = 20 log_10 (A1/A0) for amplitude (Power ~ Amplitude^2)

Slide 5

Period A measurement of a time interval A periodic signal that repeats every 10s Periodic observation, count the number of students who are asleep every 1 minute

Slide 6

Rate 1/period If I count the number of students who are asleep every minute, I do so with the rate of 1/60s, or at a rate of 0.0166667 Hertz

Slide 7

Hertz Instances per second kHz, MHz, GHz standard SI-prefixes for hertz

Slide 8

Rate and Time If a period is 10s, the rates is 1/10s. Hertz is cycles per second

Slide 9

Bandwidth (signal processing) Difference between the upper and lower frequencies in a continuous set that carry information of interest. Not to be confused with data bandwidth, which while related is not the same concept

Slide 10

SAMPLING CONTINUOUS SIGNALS

Slide 11

Sampling Conversion of continuous time signals into discrete time signals. How frequently we record, witness, or store, some signal. Frame rates, movies typically play at 24 frames/second (rate) What is the period?

Slide 12

Sampling Affects how much data we have to store to represent a signal. The more we store, the more space it takes! The less we store, the more error is introduced! How do we know how much is enough?

Slide 13

Digital Sampling

Slide 14

Sampling Issues

Slide 15

Slide 16

The Problem

Slide 17

Fixing the Problem

Slide 18

Sampling Nyquist Theorem (sampling theorem) An analog signal of bandwidth B Hertz when sampled at least as often as once every 1/2B seconds (or at 2B Hertz), can be exactly converted back to the analog original signal without any distortion or loss of information. This rate is called the Nyquist sampling rate.

Slide 19

Nyquist in Practice Telephone speech has a bandwidth of 3500 Hz At what rate should it be sampled? 7000 Hz In practice it is sampled at 8000 Hz, to avoid conversion factors (Once every 124 microseconds)

Slide 20

Acoustic Signals Acoustic signals are audible up to 24 kHz What is the corresponding Nyquist sampling rate?

Slide 21

Acoustic Signals Industrial standards 6000 Hz 8000 Hz 11025 Hz 16000 Hz 22050 Hz 32000 Hz 32075 Hz 44100 Hz 48000 Hz

Slide 22

Spoken Sentence

Slide 23

Slide 24

16000 Hz 11025 Hz 8000 Hz 6000 Hz

Slide 25

Piano

Slide 26

Slide 27

Spoken Sentence 16000 Hz 11025 Hz 8000 Hz 6000 Hz

Slide 28

SPECTROGRAMS

Slide 29

Spectrogram Visual representation of frequencies in a signal. Sometimes called, spectral waterfalls, or voiceprints/voicegrams Can identify spoken words phonetically. Also used in sonor, radar, seismology, etc.

Slide 30

Spectrogram Frequency vs Time Color or height mapped to dB

Slide 31

Spectrogram Speech 16000 Hz

Slide 32

Spectrogram Speech 11025 Hz

Slide 33

Spectrogram Speech 8000 Hz

Slide 34

Spectrogram Speech 6000 Hz

Slide 35

Spectrogram Piano 16000 Hz

Slide 36

Spectrogram Piano 11025 Hz

Slide 37

Spectrogram Piano 8000 Hz

Slide 38

Spectrogram Piano 6000 Hz

Slide 39

ANALOG TO DIGITAL CONVERSION

Slide 40

A2D: Analog to Digital Two steps Sampling (which we just covered) Quantization

Slide 41

Quantization Analog signals take any value between some minimum and maximum Infinite possible values We need a finite set of values

Slide 42

Why do we need finite values?

Slide 43

State in Digital Logic Flip-flops store state for sequential logic (vs combinatorical logic) Each one can hold a 0 or 1, one bit Put X together and we have X bits worth of state we can store

Slide 44

How do we get this?

Slide 45

How to quantize Informally If we have N bits per value, we have how many states? Values from [min, max] (inclusive) Each state provided by our bit vector needs to cover of the range

Slide 46

How to quantize Simple algorithm, assume 2-bits, how many states?

Slide 47

How to quantize Simple algorithm, assume 2-bits, how many states? First state is min. We now have (4-1) = 3 states left to cover the range (Max Min) 00 Min 01 Min + (Max Min)/3 10 Min + 2(Max Min)/3 11 Min + 3(Max Min)/3 = Max

Slide 48

How to quantize What do we do with data in between these values? Lets refine our algorithm

Slide 49

Quantization Classification rule Tells us which state of our bit vector the value corresponds to Reconstruction rule Tells us how to interpret a state of the bit vector

Slide 50

Quantization Classification Rule A general classification rule

Slide 51

Quantization Reconstruction Rule A general reconstruction rule

Slide 52

Putting it all Together From 5 to 12, 2-bits

Slide 53

Homework See course website for this weeks signals homework.