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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.
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Lecture 5: Signal Processing II EEN 112: Introduction to Electrical and Computer Engineering Professor Eric Rozier, 2/20/13
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)
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
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
Hertz • Instances per second • kHz, MHz, GHz – standard SI-prefixes for hertz
Rate and Time • If 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 concept
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?
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?
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.
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)
Acoustic Signals • Acoustic signals are audible up to 24 kHz • What is the corresponding Nyquist sampling rate?
Acoustic Signals • Industrial standards • 6000 Hz • 8000 Hz • 11025 Hz • 16000 Hz • 22050 Hz • 32000 Hz • 32075 Hz • 44100 Hz • 48000 Hz
Spoken Sentence • 16000 Hz • 11025 Hz • 8000 Hz • 6000 Hz
Spoken Sentence • 16000 Hz • 11025 Hz • 8000 Hz • 6000 Hz
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.
Spectrogram Frequency vs Time Color or height mapped to dB
A2D: Analog to Digital • Two steps • Sampling (which we just covered) • Quantization
Quantization • Analog signals take any value between some minimum and maximum • Infinite possible values • We need a finite set of values
State in Digital Logic • Flip-flops store state for sequential logic (vscombinatorical 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
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
How to quantize • Simple algorithm, assume 2-bits, how many states?
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
How to quantize • What do we do with data in between these values? • Let’s refine our algorithm
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
QuantizationClassification Rule • A general classification rule
QuantizationReconstruction Rule • A general reconstruction rule