Signals Outline Announcements Homework III due Today by

Signals

Outline • Announcements: – Homework III: due Today by 5, by e-mail • for P. 4: n can be anything you want – HW IV available soon. • Binary Files • Signals, signals

Binary Basics • All computer files are “binary”, that is composed of 0’s and 1’s • When the computer reads ASCII files, it takes chunks of 8 bits (1 byte) and looks up the character • To save pi to 16 digits takes 18 bytes in ASCII • If you save the 1’s and 0’s that correspond to the double precision value of pi, that takes only 8 bytes

Problem with Binary Files • You can’t just look at them • You must know exactly how they were created – integers vs. floating point – single precision vs. double precision – signed vs. unsigned

Reading Binary files • fid=fopen(fname, ’r’); %’r’ = read binary • A=fread(fid, N, precision) – N=number of data points, use Inf to read everything – precision is how the file was created • “uint 64” is an unsiqned integer saved in 64 bits • “double” is a double

Free advice (you get what you pay for) • The only reasons to use binary files are – someone gives you one – you enjoy frustration and pain – you’re too poor (or cheap) to buy a new hard drive

Writing. mat files outside Matlab • . mat files are a great format for storing data – easy to use with Matlab – multiple variables / file – compact • It is possible to save data to. mat files from C/C++ programs using Matlab C/C++ library • For more info: – See Lecture 09 notes – Take CIS 404!

Signals • Signals are time series – Examples: • Sound (pressure vs. time) • Earthquake (displacement vs. time) • S&P 500 ($/share vs. time) • Signals are usually continuous, but we sample them at discrete times – regular vs. irregular sampling – Sampling frequency

Signal Basics • Simplest signal: s(t)=A*sin(2*pi/f*(t-phi)) – A=amplitude – f=frequency – phi=phase A • A, f, phi summarize signal phi 1/f

Fourier Analysis • Real signals are more complicated • Fourier proved that any function can be represented as sum of sines & cosines of various frequencies: f=(k-1)/N

Fourier Analysis s 1(t) f=8 s 2(t) f=1/2 0. 5*s 1(t) +s 2(t)

Signals in MATLAB • In MATLAB, a signal is a vector of numbers s • Matlab’s signal processing functions assume – s was sampled regularly – s is complete (no missing data, nans, -999’s etc. ) • You must know sampling frequency f

Fourier Analysis • Fourier transform (fft) – Finds amplitudes over a range of frequencies • amp=fft(s); – If s is n-by-1, amp will be n-by-1 and complex • – First half of amp contains info: • a=real([amp(1), 2*amp(2: n/2)])/n; %cos coefs. • b=imag([0, -2*amp(2: n/2)])/n; %sin coefs. • f= (0: (n/2 -1))/n/(t(2)-t(1)); %frequencies • F=2*pi*t(: )*f; • s 2=cos(F)*a(: )+sin(F)*b(: ); %original signal

Fourier Analysis • What’s the point? – fft transforms from time-domain to frequency domain • • Energy at frequency j = sqrt(a(j). ^2+b(j). ^2) Plot energy vs. f Peaks are important f’s Could remove energy at some frequencies

Signal Processing Toolbox • Matlab’s Signal Processing Toolbox contains lots of functions for working with digital signals – transforms beyond fft – filter design, implementation – spectral analysis – Check on-line help for more info – Need to understand theory better than I do!