MATLAB MATRIX LABORATORY

1
??? ?????? ????? ?MATLAB
??? ??? ?????? ????????
2

• Course Syllabus
• First Day
• About Signal Processing Toolbox Signals and
  Filters Fourier Transforms Individual
  Practicing
• Second Day
• Introduction to Graphical User Interface of the
  Signal Processing ToolboxlSignal BrowserFilter
  ViewerDesigneSpectrum ViewerIndividual
  Practicing
• Literature
• A.Biran, M.Breiner.Matlab 5 for Engineers,
  Addison-Wesley, Reading, MA, 1999.

• Course Destination
• Course is destined for non-programmers engineers
  and scientists who whish to gain primary skills
  in using Signal Processing Toolbox of Matlab.
• Prerequisites
• Primary skill in Matlab is required.
• Course organization
• Two morning sessions in three academic hours
  each, including individual practicing. Examples
  will be performed in real time by the lecturer
  and by the students.
• Bonus Those who wish can receive home task or
  propose and solve any problem which would check
  by lecturer.
• Minor modifications may take place.

3
1.????? ????? ?MATLAB

• ????? ??????
• 1. ????? ????? ?MATLAB
• - Signal Processing Toolbox
• - ????? ????????
• - ????? ?????? ????? ??????
• 2. ???? ?Signal Processing GUI - sptool
• - Signal Browser
• - Filter ViewerDesigner
• - Spectrum Viewer
• 3. ????? ?????? ??? ?SPTool
• - ????? ???
• - ???? ????? ?????? ??? ?????
• - ????? ?????? ????? ?? ??????

4
1.1 Signal Processing Toolbox

• SPT ?? ???? ?200 ???????? ?GUI ????
• ????? ????? ???????? ? ?????????
• ????? ??????????? ?? ????? ??????????
• ???? ?????? FIR ?IIR
• ????? ????
• ???? ?????? ??? 5.1
• (???? ???? 20.12.2001)

5
1.1 ????? ????????

• ????? ?? ????? ????? (??) ?Matlab ??????
• ???? ????? ???? ???? ??? ??
• ???? ?????? m ?????? ???? m ??????
• ????? ??????? ?? sinusoid , unit impulse ,
• unit step , and unit
  ramp
• ???????
• t(00.0011)'ynsin(2pi50t)0.5randn(size(
  t))
• plot(t(150),yn(150)),grid on, , siniusoid
  at 50 Hz
• y1zeros(99,1) plot(t(110),y(110)), unit
  impuls
• yones(100,1)plot(t(1100),y(1100)), unit
  step (filter assumes 0 initial cond.)
• yt unit ramp
• yt.2 try to plot
• ysquare(4t)plot(t(11000),y(11000)) try to
  plot

6
1.1 ????? ???????? (????)

• ?? ??? ???? ??? ??? ?? ????? ????. ?????? ????
  ?MATLAB ????? ??????? filter
• filter(B,A,x) ?? filter(B,A,x,Zi)
• ???? B,A ?? ?????? ?????? ??????? ?????
• Ynb1/a1x1 bnb/anbx?-a2/a1yn-1-ana/a1yn-na
  1
• ? Zi ????? ?? initial conditions ?? ?
• Yn Zib1/a1x1 bnb/anbx1-a2/a1yn-1-ana/a1y
  n-na1
• ??????
• signal x consists of two sinusoids, one at 50
  Hz and one at 120 Hz
• Fs100t01/Fs1xsin(2pit50).25sin(2pi
  t120)
• signal has white noise normally distributed
• xnx0.5randn(size(t))
• yfilter(0.5,1,-0.25,-0.25,x) non-init
  cond. filter with b0.5
• and a1,a2,a3 are 1, -0.25 and -0.25
  
• plot(t,x,t,y,'--'),grid on

7
1.1 ????? ???????? (????2)

• Digital Filter Difference Equation
• Y(z) b1 b2z-1 bn z-(n-1) /a1 a2 z-1
  an z -(n-1) X(z),
• X - input signal
• Y - output signal
• z ejwT
• T- period
• a,b - coefficients
• (denominator, numerator)
• n - order of filter
• If a2, a3, ,an 0 the filter is called
• FIR (finite impulse response)
• Otherwise - IIR (infinite impulse response)

8
1.1 ????? ???????? (????3)

• Digital Filter Specifications

Passband ripple,Rp
Stopband ripple,Rs
A,dB20log10A
9
1.1 ????? ???????? (????4)

• ??????? ???????
• ???? ?????? ?DSP ??? - ????? ????? ??
• ????? m ????? f???????
• ?????? IIR ?FIR ??????? ?????? ???????? MATLAB
  ??????? ?????? ???? ???????
• ????? y ??? ???????
• ??????
• b,aYulewalk(n,f,m) IIR, least square fit in
  time domain
• bFirls(n,f,m) least square linear phase
  FIR
• Y,wFreqz(b,a,n) frequency response Y and
  frequencies w for after filtering
• ???? n ??? ?? ?????
• ??????? ???? ???

10
1.1 ????? ???????? (????5)

• ?????(????)
• desired filter characteristics
• fHz0 100 150 200 225 250m1 1 .5 .5 1 1
  n6
• fs500b,ayulewalk(n,fHz/(fs/2),m) b and
  a to IIR, fs/2-the Nyquist f
• y1,w1freqz(b,a,128) signal after filtering
• plot(fHz/(fs/2),m,w1/pi,abs(y1))
• bbfirls(n,fHz/(fs/2),m) b to FIR
• y2,w2freqz(bb) signal after filtering
• plot(fHz/(fs/2),m,w1/pi,abs(y1), w2/pi,abs(y2))

11
1.1 ????? ???????? (????6)

• ???????
• ???? ????? ???? ???? ??? FIR ???? 8 ?????? ????
  ?????, ??? ?????? ??? ??? ?? ????????
• ???? ????? ???? ???? ??? IIR ???? 8 ?????? ????
  ?????, ??? ?????? ??? ??? ?? ????????
• ??? ??? ????? ?? ??? ??????? ?? ????? 100 ?400
  Hz ,????? 0.1s...0,??? ????? 2000 Hz
• ??? low-pass ?high-pass ??????? , ????? ?
• ????? f00, 225, 275, 1000Hz
• ?????????? m1,1,0,0 ???? low-pass ?????
• ?m0,0,1,1 ???? high-pass ?????
• ???? ?????? ?? ?????
• ???? ????? ??????? yulewalk ?? n6 ?filter

12
1.2 ????? ?????? ????? ??????

• ????? ????? ???????? DFT ????? ??????? FFT
• Fast Fourier Transform- ?? ?????? ?? ?????
  ?????.
• ?????? ?????? ????? ??? ??? ???? x ????????????
  ??? X ???
• ?????? ?????? ????? ??? ??? ???? x ????????????
  ??? X ???

13
1.2 ????? ?????? ????? ?????? (????)

• ?????? fft ? ifft
• fft(x,n)
• Ifft(x,n),
• where x is vector or rectangular array
• n (optionally) is number of points for
  transform
• ??????
• ?? 1/99?? ???? ????? ??? xsin(2p15t)sin(2p40t
  )
• ????? ?????? ?????
• t(01/991)xsin(2pi15t)sin(2pi40t)
• yfft(x) f(0length(y)-1)99/length(y)
• plot(f,abs(real(y))),grid on
• ???? ???? ???

14
1.2 ????? ????? ????? ?????? (????2)

• ????? ?????? ????? ????? ?? ?????? ??????
• x1real(ifft(y))
• plot(t,x,t,x1,'o'),grid on

Reconstructed points
15
2. ???? ?Signal Processing GUI

• ?SPTOOLBOX GUI ?????
• ????? ????????????
• ????? ?????????? ???????
• ????? ?????? ????????
• ?????? (Transforms)
• ????? ?? ?????????
• ????? ???? ????? ??????

16
.2 ???? ?Signal Processing GUI (????)

• SPTool ????
• Signal Browser for viewing, measuring and
• analyzing the time-domain information
  of signals
• Filter ViewerDesigner for design and editing
  IIR and FIR filters with standard
  (lowpass, highpass, bandpass,)
  configurations for viewing the
  characteristics
• of designed or imported filters
• Spectrum Viewer for graphical analysis of
  frequency-domain data using of
  spectral estimation methods

17
2 ???? ?Signal Processing GUI (????2)

• ???? GUI ?? SPToolbox- ????? sptool
• sptool

18
2.1 Signal Browser

• ???? ? Import ?????? File ???? ???? ? Input to
  SPTool ?
• ???? ? ?Import As ???? Signal
• ???? ?? From Disk ??? ????? ?? ?? ???? ???????
  ,???? mtlb.mat

19
2.1 Signal Browser(????2)

• ?File Contents ?????? ??????
• mtlb (radio signal data) ?Fs (sampling
  frequencies)
• ??????? mtlb ?Data ?Fs ? Sampling Frequency
• ???? ??OK ????? ????? ????? sig1 ????? ?????
  ???? ????? View ????? SPTool

20
2. 2 Filter ViewerDesigner

• ??? ??New Design ????? SPTool ???? ???? Filter
  Designer
• ???? ???? Keiser Window ?Algorithm ?Bandpass
  ?Type
• ????? SPTool ??? Edit-gtSampling
  Frequences-gtFilt1-gtEnter Sampling Frequencies ???
  ??? ????? Hz 2000

21
2.2 Filter ViewerDesigner (????)

• ?????? ?Passband ??Stopband Fp175 Fp2110
  Fs150 Fs2130 Rp4 ?
  Rs30
• ??? Apply ???? ????, ??? ?????? ????

Pass Band Region
Passband
Stopband frequencies
22
2.2 Filter ViewerDesigner ????? ???? IIR ?????

• ???? 'Chebyshev type1' highpass????? ???? 7
• ??? ????? 2000 Hz
• fp700Hz fs800Hz Rp2.5DB Rs35DB
• ??? ???? ???? ????? ????? Pass ??? ?????? ??
  ?????

23
2.3.Spectrum Viewer

• ????View ??? ???? Spectra? SPTool
• ????? Spectrum Viewer ?? PSD(Power Spectral
  Density)
• ?? input data
• ??? ????? ????
• Spectrum Viewer
• ????? ????? Welch
• ?????? ?????? ????????

PSD Power Spectral Density
????? ????? ?????? ?????????
24
2.3.Spectrum Viewer (????)

• ??? ????? ???? ????? ?? ??????? ???? ????? ????
  ????? ?? ??? ????? ?????.
• ???????????? ??
• ??????? ???????
• ??????? ???????
• Revert
• ?????? ???????
• Apply
• ?????? ????????

25
3. ????? ?????? ??? ?SPTool

• ?????? ?????
• 1. ????? ???
• 2. ???? ????? ?????? ??? ?????
• 3. ????? ?????? ????? ?? ??????
• 4. ????? ????????? ?? ??? ??????

26
3.1 ????? ???

• ????? ??? ????? ?? ??? ?????
• xrandn(5000,1)
• ????? ?? ????? ?? SPTool ??? ?? File -gt Import
• ???? For Workspace ????? ?signal ?'Import As '
• X ? Data?500 ? Sampling Frequency
• ?? ?? noise ?Name
• OK

27
3.2 ???? ????? ?????? ??? ?????

• ???? ?? New Design ????? ?? Filter Designer ??
  ????? filt1
• ???? ?? ??? ?????? ?5000 SPTool -gt Edit -gt
  Frequency Sampling -gt 5000 -gt OK
• ?Filter Designer ???? Equiripple ?Algorithm
  ?Bandpass ?Type
• ?? 750 ? 1250 ?Pass 500 ?1500 ? Stopband?0.01
  ?75 ?Rp ? Rs

???? ???? ?????
?????? ?????
28
3.3 ????? ?????? ????? ?? ??????

• ????? ?????? ????? filt1 ?????? ??? noise ?????
  SPTool
• ???? noise ?filt1 ????? Apply ?????? Filters
  ?Apply Filter box ???? Output Signal ?????
  blnoise ?OK. ?????? ????? blnoise
• ??? ?????? ??? ????? shift-click filt1 blnoise
  ?View ?Signals
• ?Selection ???? blnoise ??Color ??? Green

?????
29
3.4 ?????? ????????? ?? ??? ??????

• ???? SPTool , ???? noise ?Signals ???? Create
  ?Spectra
• ?Spectrum Viewer ???? Apply, ?????? Spectra ?????
  ???? spect1 .
• ????? ???? ??????? ???? spect2 ???? ??? noise.
• ?Spectra ?? SPTool ?????? ?spect1 ?spect2 ??????
  ?? View

spect1
spect2
30
???? 1 ????? ???????? ???????? ??????

• abs
• grid on
• fft
• filter
• fir
• firls
• freqz
• gid on
• Ifft
• length
• ones
• plot

randn real sin size sptool yulewalk
31
???? 2 ????? (?????) ?? ???????? ?? Signal
Processing Toolbox

• Filter analysis
• abs - Magnitudeangle - Phase anglefreqs -
  Laplace transform frequency responsefreqspace -
  Frequency spacing for frequency responsefreqz -
  Z-transform frequency response
• FIR Filter Design
• fir1 - Window based FIR filter design - low,
  high, band, stop, multifir2 - FIR arbitrary
  shape filter design using the frequency sampling
  methodfirls - Optimal least-squares FIR filter
  design
• IIR Digital Filter Design
• butter - Butterworth filter designellip -
  Elliptic filter designyulewalk - Yule-Walker
  filter design
• IIR Filter Order Estimation
• buttord - Butterworth filter order estimation

32
???? 2 ????? (?????) ?? ???????? ?? Signal
Processing Toolbox

• Transforms
• fft - Fast Fourier transformfft2 - 2-D fast
  Fourier transformfftshift - Swap vector
  halvesifft - Inverse fast Fourier
  transformifft2 - Inverse 2-D fast Fourier
  transform
• Statistical Signal Processing and Spectral
  Analysis
• corrcoef - Correlation coefficientscsd -
  Cross Spectral Densitypburg - Power Spectral
  Density estimate via Burg's methodpcov - Power
  Spectral Density estimate via the Covariance
  methodrootmusic - Sinusoid frequency and power
  estimation via the MUSIC algorithm
• Graphical User Interfaces
• fdatool - Filter Design and Analysis
  Toolsptool - Signal Processing Tool