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Lecture 5: Signal Processing II. EEN 112: Introduction to Electrical and Computer Engineering. Professor Eric Rozier, 2/20/13. SOME DEFINITIONS. Decibels. Logarithmic unit that indicates the ratio of a physical quantity relative to a specified level. - PowerPoint PPT Presentation
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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.