1. Signals

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

3. Binary Basics
All computer files are “binary”, that is composed of 0’s and1’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

4. 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

5. 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
“uint64” is an unsiqned integer saved in 64 bits
“double” is a double

6. 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

7. 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 CIS404!

8. 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

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

10. Fourier Analysis f=(k-1)/N 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

11. Fourier Analysis
f=8
s1(t)
s2(t)
f=1/2
0.5*s1(t)
+s2(t)

12. 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

13. 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;
s2=cos(F)*a(:)+sin(F)*b(:); %original signal

14. 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

15. 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!