digital signal processing fundamentals

40
Digital Signal Processing (DSP) Fundamentals

Upload: elaine-malabana

Post on 21-Dec-2014

1.063 views

Category:

Technology


5 download

DESCRIPTION

 

TRANSCRIPT

Page 1: Digital signal processing fundamentals

Digital Signal Processing(DSP)

Fundamentals

Page 2: Digital signal processing fundamentals

Overview

• What is DSP?

• Converting Analog into Digital– Electronically– Computationally

• How Does It Work?– Faithful Duplication– Resolution Trade-offs

Page 3: Digital signal processing fundamentals

What is DSP?

• Converting a continuously changing waveform (analog) into a series of discrete levels (digital)

Page 4: Digital signal processing fundamentals

What is DSP?

• The analog waveform is sliced into equal segments and the waveform amplitude is measured in the middle of each segment

• The collection of measurements make up the digital representation of the waveform

Page 5: Digital signal processing fundamentals

What is DSP?0

0.22 0.

44 0.64 0.

82 0.98 1.

11 1.2

1.24

1.27

1.24

1.2

1.11

0.98

0.82

0.64

0.44

0.22

0-0

.22

-0.4

4-0

.64

-0.8

2-0

.98

-1.1

1-1

.2-1

.26

-1.2

8-1

.26

-1.2

-1.1

1-0

.98

-0.8

2 -0.6

4 -0.4

4 -0.2

20

-2

-1.5

-1

-0.5

0

0.5

1

1.5

21 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

Page 6: Digital signal processing fundamentals

Converting Analog into DigitalElectronically

• The device that does the conversion is called an Analog to Digital Converter (ADC)

• There is a device that converts digital to analog that is called a Digital to Analog Converter (DAC)

Page 7: Digital signal processing fundamentals

Converting Analog into DigitalElectronically

• The simplest form of ADC uses a resistance ladder to switch in the appropriate number of resistors in series to create the desired voltage that is compared to the input (unknown) voltage

V-7

V-6

V-low

V-1

V-2

V-3

V-4

V-5

V-high

SW-8

SW-7

SW-6

SW-5

SW-4

SW-3

SW-2

SW-1

Output

Page 8: Digital signal processing fundamentals

Converting Analog into DigitalElectronically

• The output of the resistance ladder is compared to the analog voltage in a comparator

• When there is a match, the digital equivalent (switch configuration) is captured

Analog Voltage

ResistanceLadder Voltage

ComparatorOutput Higher

EqualLower

Page 9: Digital signal processing fundamentals

Converting Analog into DigitalComputationally

• The analog voltage can now be compared with the digitally generated voltage in the comparator

• Through a technique called binary search, the digitally generated voltage is adjusted in steps until it is equal (within tolerances) to the analog voltage

• When the two are equal, the digital value of the voltage is the outcome

Page 10: Digital signal processing fundamentals

Converting Analog into DigitalComputationally

• The binary search is a mathematical technique that uses an initial guess, the expected high, and the expected low in a simple computation to refine a new guess

• The computation continues until the refined guess matches the actual value (or until the maximum number of calculations is reached)

• The following sequence takes you through a binary search computation

Page 11: Digital signal processing fundamentals

Binary Search

• Initial conditions– Expected high 5-volts

– Expected low 0-volts

– 5-volts 256-binary

– 0-volts 0-binary

• Voltage to be converted– 3.42-volts

– Equates to 175 binary

Analog Digital

5-volts 256

0-volts 0

2.5-volts 128

3.42-volts Unknown (175)

Page 12: Digital signal processing fundamentals

Binary Search

• Binary search algorithm:

• First Guess:

Analog Digital

5-volts 256

0-volts 0

128

3.42-volts unknownNewGuessLow

LowHigh

2

12802

0256

Guess is Low

Page 13: Digital signal processing fundamentals

Binary Search

• New Guess (2):Analog Digital

5-volts 256

0-volts 0

1923.42-volts unknown

1921282

128256

Guess is High

Page 14: Digital signal processing fundamentals

Binary Search

• New Guess (3):Analog Digital

5-volts 256

0-volts 0

1603.42-volts unknown

1601282

128192

Guess is Low

Page 15: Digital signal processing fundamentals

Binary Search

• New Guess (4):Analog Digital

5-volts 256

0-volts 0

1763.42-voltsunknown176160

2

160192

Guess is High

Page 16: Digital signal processing fundamentals

Binary Search

• New Guess (5): Analog Digital

5-volts 256

0-volts 0

1683.42-volts unknown

1681602

160176

Guess is Low

Page 17: Digital signal processing fundamentals

Binary Search

• New Guess (6): Analog Digital

5-volts 256

0-volts 0

1723.42-volts unknown

1721682

168176

Guess is Low

(but getting close)

Page 18: Digital signal processing fundamentals

Binary Search

• New Guess (7):Analog Digital

5-volts 256

0-volts 0

1743.42-volts unknown

1741722

172176

Guess is Low

(but getting really, really, close)

Page 19: Digital signal processing fundamentals

Binary Search

• New Guess (8):Analog Digital

5-volts 256

0-volts 0

3.42-volts 175!175174

2

174176

Guess is Right On

Page 20: Digital signal processing fundamentals

Binary Search

• The speed the binary search is accomplished depends on:– The clock speed of the ADC– The number of bits resolution– Can be shortened by a good guess (but usually

is not worth the effort)

Page 21: Digital signal processing fundamentals

How Does It Work?Faithful Duplication

• Now that we can slice up a waveform and convert it into digital form, let’s take a look at how it is used in DSP

• Draw a simple waveform on graph paper– Scale appropriately

• “Gather” digital data points to represent the waveform

Page 22: Digital signal processing fundamentals

Starting Waveform Used to Create Digital Data

Page 23: Digital signal processing fundamentals

How Does It Work?Faithful Duplication

• Swap your waveform data with a partner

• Using the data, recreate the waveform on a sheet of graph paper

Page 24: Digital signal processing fundamentals

Waveform Created from Digital Data

Page 25: Digital signal processing fundamentals

How Does It Work?Faithful Duplication

• Compare the original with the recreating, note similarities and differences

Page 26: Digital signal processing fundamentals

How Does It Work?Faithful Duplication

• Once the waveform is in digital form, the real power of DSP can be realized by mathematical manipulation of the data

• Using EXCEL spreadsheet software can assist in manipulating the data and making graphs quickly

• Let’s first do a little filtering of noise

Page 27: Digital signal processing fundamentals

How Does It Work?Faithful Duplication

• Using your raw digital data, create a new table of data that averages three data points– Average the point before and the point after

with the point in the middle– Enter all data in EXCEL to help with graphing

Page 28: Digital signal processing fundamentals

Noise Filtering Using Averaging

Raw

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

Ave before/after

-150

-100

-50

0

50

100

150

0 10 20 30 40

TimeAmplitude

Page 29: Digital signal processing fundamentals

How Does It Work?Faithful Duplication

• Let’s take care of some static crashes that cause some interference

• Using your raw digital data, create a new table of data that replaces extreme high and low values:– Replace values greater than 100 with 100– Replace values less than -100 with -100

Page 30: Digital signal processing fundamentals

Clipping of Static Crashes

Raw

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

eliminate extremes (100/-100)

-150

-100

-50

0

50

100

150

0 10 20 30 40

TimeAmplitude

Page 31: Digital signal processing fundamentals

How Does It Work?Resolution Trade-offs

• Now let’s take a look at how sampling rates affect the faithful duplication of the waveform

• Using your raw digital data, create a new table of data and delete every other data point

• This is the same as sampling at half the rate

Page 32: Digital signal processing fundamentals

Half Sample Rate

Raw

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

every 2nd

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

Page 33: Digital signal processing fundamentals

How Does It Work?Resolution Trade-offs

• Using your raw digital data, create a new table of data and delete every second and third data point

• This is the same as sampling at one-third the rate

Page 34: Digital signal processing fundamentals

1/2 Sample Rate

Raw

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

every 3rd

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

Page 35: Digital signal processing fundamentals

How Does It Work?Resolution Trade-offs

• Using your raw digital data, create a new table of data and delete all but every sixth data point

• This is the same as sampling at one-sixth the rate

Page 36: Digital signal processing fundamentals

1/6 Sample Rate

Raw

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

every 6th

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

Page 37: Digital signal processing fundamentals

How Does It Work?Resolution Trade-offs

• Using your raw digital data, create a new table of data and delete all but every twelfth data point

• This is the same as sampling at one-twelfth the rate

Page 38: Digital signal processing fundamentals

1/12 Sample Rate

Raw

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

every 12th

-150

-100

-50

0

50

100

150

0 10 20 30 40

Time

Amplitude

Page 39: Digital signal processing fundamentals

How Does It Work?Resolution Trade-offs

• What conclusions can you draw from the changes in sampling rate?

• At what point does the waveform get too corrupted by the reduced number of samples?

• Is there a point where more samples does not appear to improve the quality of the duplication?

Page 40: Digital signal processing fundamentals

How Does It Work?Resolution Trade-offs

Bit Resolution

High Bit Count

Good Duplication

Slow

Low Bit Count

Poor Duplication

Fast

Sample Rate High Sample Rate

Good Duplication

Slow

Low Sample Rate

Poor Duplication

Fast