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?
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
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Spectrogram Speech 8000 Hz
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Spectrogram Speech 6000 Hz
Slide 35
Spectrogram Piano 16000 Hz
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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.