analog and digital signals ad/da conversion bme 1008 introduction to biomedical engineering fiu,...

Analog and Digital SignalsAD/DA conversion

BME 1008 Introduction to Biomedical EngineeringFIU, Spring 2015

Feb 5Lesson 3

http://commons.wikimedia.org/wiki/File:A-D-A_Flow.svg

Analog signal

Voltage changescontinuously withpressure.

Digital signal

Voltage has discrete values.

Analog signal

Analog signalsSmooth and continuous.

Most physical and biological signals, e.g. sound, temperature, blood pressure, pH.

Many sensors produce an analog signal; temperature, pressure, pH, light intensity etc.

Used typically by some older electronic devices, e.g. radio, TV, tape recorders, vinyl records.

time

Digital signalsDiscrete and discontinuous.

Used by digital computers, i.e. most modern computers, including PC and supercomupters.

Used by many modern electronic devices, e.g. satellite radio, digital TV, digital cameras, scientific instruments etc.

Advantages over analog signals: immune to noise, flexible hardware, easy computing, robust storing, transmission, compression.

0 1 0 1 0 1 0 1 0 1 0

time

amplitude

Analog-to-digital conversion(ADC)Modern telecommunication technology.Music recording, CD recordings. Hearing aids with digital signal processing.Scientific instruments, medical devices, e.g. ECG, EEG, pH-meters etc.

Digital imaging systems commonly use analog-to-digital converters in digitizing pixels.

Digital ECG

Analog or Digital?

• 100 billion (1011) neurons.• 100 trillion (1014) synapses.• peaks are the firing of the cells.• the analog looking signals at the bottom represent sub-threshold activity.

McCulloch and Pitts & The Binary Neuron

• Neurons first studied in the 40’s• Only two states were known, firing and not firing.

•Artificial neural networks can be trained to recognize complex input patterns, e.g. sounds, images, faces etc.

•Biological brain and its theoretical models work entirely different than the modern digital computers.

Modern Digital Computer

"Von Neumann Architecture" http://commons.wikimedia.org/wiki/File:Von_Neumann_Architecture.svg#mediaviewer/File:Von_Neumann_Architecture.svg

10110000 01100001.....

inc ecxjne .loop...

Machine Assembler C/C++ Matlab code

Abstraction from the details of the hardware

main() { printf("hello"); }

y = 1:10plot(y.^2)

low high

Analog-to-digital Converter ADC

Sampling rate of ADC

Quiz 3 - Sampling%Write the script in Matlab editor:clearsamplingInterval=1; %secondstime=0:samplingInterval:4; %secondssignalPeriod = 0.27; %secondssignal = sin(2*pi*time/signalPeriod);figure; plot(time,signal,'.-')

1) Adjust 'samplingInterval' to obtain proper plot of sin(). 2) What is the maximum 'samplingInterval'

for which the shape of sin() is preserved?

0 1 2 3 4-1

-0.5

0

0.5

1

undersampled

Quiz 3 Answer

samplingInterval= 0.1; 0.01; 0.001;% ok % good % oversampled

General rule: (sampling Interval) < (signal period)/2or (sampling frequency) > 2×(signal frequency),where (sampling frequency) = 1/(sampling Interval).

0 1 2 3 4-1

-0.5

0

0.5

1

0 1 2 3 4-1

-0.5

0

0.5

1

0 1 2 3 4-1

-0.5

0

0.5

1

Audio in Matlab[Y,FS,NBITS]=wavread('fileName.wav');% reads a WAVE audio file and returnsY -sampled data, FS - sample rate in Hertz, NBITS the number of bits per sample.

wavplay(Y,FS);% plays the signal in vector Y with sample frequency of FS Hertz% alternatively try audioplayer()>> help audioplayer

Matlab script to read and play a WAV file:

clearfileName = 'THE_MICROSOFT_SOUND.WAV';[Y,FS,NBITS] = wavread(fileName);plot(Y)wavplay(Y,FS)whosFSNBITS

0 2 4 6 8 10 12 14

x 104

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

3.852 3.854 3.856 3.858 3.86 3.862 3.864 3.866 3.868 3.87

x 104

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

THE_MICROSOFT_SOUND.WAV

FS = 22050 %Hz

NBITS = 8

length(Y)ans = 135005

%number of elements

Addition of sine signal to the original sound

time = (1:length(Y))/FS; % length(Y) - returns number of elements

sine = 0.2*sin(2*pi*FS/50*time)'; % ' - transpose to column vector

wavplay(sine,FS);pause(2)wavplay(Y+sine,FS);figure; plot(time,sine,'g-.',time,Y,'b--',... time,sine+Y,'r:')

% ... - line continuation

Quiz 4- Sounds clearFS = 5000; %sample frequency of 5kHztime = [0:25000]/FS; y1 = 0.25*sin(2*pi*FS/5*time);wavplay(y1,FS)pause(2)y2 = 0.25*sin(2*pi*FS/25*time);wavplay(y2,FS)pause(2)wavplay(y1+y2,FS)plot(time,y1,time,y2,time,y1+y2)

Quiz 5- WAV files Search Windows or Google for a '*.wav' file, and

copy the file to Matlab current folder. Import the file into Matlab with wavread() or

Menu/File/Import.Plot the samples. Play sound with wavplay() (or audioplayer() ).

Modify the sound to fade out.Hint: Multiply the audio samples by a decaying functionY2=Y.*exp(-(1:length(Y))/(length(Y)/5))';

Note:wavplay() and audioplayer() may be unavailable or not

working in some Matlab configurations, e.g. Matlab on Citrix, Mac OS.