Slide 1

Lecture 5: Signal Processing IIEEN 112: Introduction to Electrical and Computer EngineeringProfessor Eric Rozier, 2/20/131SOME DEFINITIONS2DecibelsLogarithmic unit that indicates the ratio of a physical quantity relative to a specified level.

10x change is 10 dB change. 2x change ~3dB change.RememberL_dB = 10 log_10 (P1/P0) for powerL_db = 20 log_10 (A1/A0) for amplitude(Power ~ Amplitude^2)

PeriodA measurement of a time interval

A periodic signal that repeats every 10s

Periodic observation, count the number of students who are asleep every 1 minuteRate1/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 HertzHertzInstances per secondkHz, MHz, GHz standard SI-prefixes for hertzRate and TimeIf a period is 10s, the rates is 1/10s.Hertz is cycles per second

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 conceptSAMPLING CONTINUOUS SIGNALS9SamplingConversion 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?SamplingAffects 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?Digital Sampling

Sampling Issues

Sampling Issues

The Problem

Fixing the Problem

SamplingNyquist 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.Nyquist in PracticeTelephone speech has a bandwidth of 3500 HzAt what rate should it be sampled?

7000 HzIn practice it is sampled at 8000 Hz, to avoid conversion factors(Once every 124 microseconds)Acoustic SignalsAcoustic signals are audible up to 24 kHzWhat is the corresponding Nyquist sampling rate?Acoustic SignalsIndustrial standards6000 Hz8000 Hz11025 Hz16000 Hz22050 Hz32000 Hz32075 Hz44100 Hz48000 HzSpoken Sentence

Spoken Sentence

Spoken Sentence16000 Hz

11025 Hz

8000 Hz

6000 Hz

Piano

Piano

Spoken Sentence16000 Hz

11025 Hz

8000 Hz

6000 Hz

SPECTROGRAMS27Spectrogram

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.Spectrogram

Frequency vs TimeColor or height mapped to dBSpectrogram Speech16000 Hz

Spectrogram Speech11025 Hz

Spectrogram Speech8000 Hz

Spectrogram Speech6000 Hz

Spectrogram Piano16000 Hz

Spectrogram Piano11025 Hz

Spectrogram Piano8000 Hz

Spectrogram Piano6000 Hz

ANALOG TO DIGITAL CONVERSION38A2D: Analog to DigitalTwo stepsSampling (which we just covered)QuantizationQuantizationAnalog signals take any value between some minimum and maximumInfinite possible valuesWe need a finite set of valuesWhy do we need finite values?

State in Digital LogicFlip-flops store state for sequential logic (vs combinatorical logic)Each one can hold a 0 or 1, one bitPut X together and we have X bits worth of state we can storeHow do we get this?

How to quantizeInformallyIf 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

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

How to quantizeSimple 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 Min01 Min + (Max Min)/310 Min + 2(Max Min)/311 Min + 3(Max Min)/3 = Max

How to quantizeWhat do we do with data in between these values?

Lets refine our algorithmQuantizationClassification ruleTells us which state of our bit vector the value corresponds toReconstruction ruleTells us how to interpret a state of the bit vectorQuantizationClassification RuleA general classification rule

QuantizationReconstruction RuleA general reconstruction rule

Putting it all TogetherFrom 5 to 12, 2-bits

HomeworkSee course website for this weeks signals homework.