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Current issues
 Office hours: Jacek Misiurewicz Mon 16:3017:00, room 454, Damian Gromek Thu 1012, room 449
 Lecture start: 22 Feb (Thu), 08:1510:00, room 121
 Lab starts with an introductory meeting on 26 Feb (Mon) 9:15, room CS202,
Regular labs will be on odd ("N_blue"group) or even ("P_green" group) Mondays/Fridays, 8:1512:00
Where is Lab CS202?

What to do after EDISP?
If you are interested, choose elective courses:
 ETASP  (En) Techniques for Advanced Signal Processing
 EASP  (En) Adaptive Signal Processing
or in Polish:
TRA  Techniki Realizacji Algorytmów CPS
PSYL  Przetwarzanie SYgnałów w Labview
SRMP  Sygnały Radiolokacyjne i Metody ich Przetwarzania
CCM  CzasowoCzęstotliwościowe Metody przetwarzania sygnałów
APSG  Adaptacyjne Przetwarzanie SyGnałów

Home page of EDISP
(English) DIgital
Signal Processing course
semester 2018L (summer of 2018 acad. year)
Schedule
The lectures are on Thursday, room 121
08:1510:00.
There are
lab exercises, 4 hours every second week, room CS202 (new wing C).
Labs will be on Mondays, 812 (N and P weeks) or Fridays 1014 (P weeks; Fri is only available if the group is LARGE) , in
subgroups of not more than 12 students.
For the
introductory lab (lab0) we ALL met on
Mon, 26 Feb , 9:15 in room CS202.
Next lab (lab1) will
be
 Oct 30th (8:1512) for P (Parity even) subgroup
 Nov 6th (8:1512) for N (Nonparity = parity odd) subgroup,
"N" subgroup will have labs on Mondays marked
as "N" in the official
elka calendar (and "P" or "A" subgroup  on "P" Mondays).
Note that
 In some weeks the weekdays are swapped to equalize the semester,
 In some semesters the notion of "odd" (N) and "even" (P) in
that calendar may be not as straightforward as taught within a basic
algebra course.
A printable schedule is here
Books
Book base
The course is based on selected chapters of the book:
A. V. Oppenheim, R. W. Schafer, DiscreteTime Signal Processing,
PrenticeHall 1989 (or II ed, 1999; also acceptable previous editions
entitled Digital Signal Processing).
Other books
 Steven W. Smith, The Scientist and Engineer's Guide to Digital
Signal Processing  it is a free textbook covering some of the
subjects, to be found here: http://www.dspguide.com/pdfbook.htm
The book is slightly superficial, but it can be valuable  at least as a quick reference.
 Edmund Lai, Practical Digital Signal
Processing for Engineers and Technicians, Newnes (Elsevier), 2003
seems also a simple but thoroughly written book.
 Vinay K. Ingle, John G. Proakis, Digital Signal Processing using MATLAB, Thomson 2007, Bookware Companion series
Supplementary books I found in our faculty library:
Additional books available in Poland:
 R.G. Lyons, Wprowadzenie do cyfrowego przetwarzania sygnałów
(WKiŁ 1999)
 Craig Marven, Gilian Ewers, Zarys cyfrowego przetwarzania sygnałów,
WKiŁ 1999 (simple, slightly too easy)
[en: A simple approach to digital signal processing, Wiley & Sons, 1996]
 Tomasz P. Zieliński, Od teorii do cyfrowego przetwarzania sygnałów,
WKiŁ 2002 (and next edition with slightly modified title)
Please remember:
 there are notation differences between lecture and "dspguide"
 The official book is Oppenheim & Schafer (though notation is
sometimes different too)
 no book is obligatory as it is hard to get O&S, and
other books do not cover the subject fully.
Probably the best choice is to buy a used copy of O&S.
It'll serve you for years, if you are interested in DSP. And it contains a lot of PROBLEMS to solve and learn!
Ingle/Proakis is also a good book (and you may be able to buy a new or almost new copy).
If you know LANG=PL_pl  you may prefer to buy/borrow a laboratory scriptbook for CYPS, which is in
Polish language (Cyfrowe Przetwarzanie Sygnałów, red. A Wojtkiewicz,
Wydawnictwa PW).
Supplementary material
In the course of the semester you may realize that your math knowledge
is pulling you back. This is normal. DSP is a practical math usage, so
you need maths. Go back to your math books and notes, and look for
knowledge in the web.
Wikipedia may be too formal, but try it. Then, there is a number of course notes. I appreciated very much Paul DAwson's page when I looked for a simple example of a h(n) which convereges to zero, yet doesn't provide stability.
Course aims
In other words  what I expect you to learn, or what I will check when it comes to grading.
A student who successfully completes the course will:
 know the mathematical fundamentals of discretetime (DT) signal
processing: DT signals, normalized frequency notion, DT systems, LTI
assumption, impulse response, stability of a system
 understand the DT Fourier transforms and know how to apply them to simple DT signal analysis
 know basic window types and their usage for FT and STFT
 understand the description of a DT system with a graph, difference
equation, transfer function, impulse response, frequency response
 be able to apply Ztransform in analysis of a simple DT system
 understand filtering operation and the process of DT filter design; be able to use computer tools for this task
 know the basic attributes of a Digital Signal Processor
(differences w.r.t. general purpose processor, ways of speeding up the
calculations, fundamentals of block diagram and programming)
 understand 2D signal processing basics: 2D convolution/filtering, 2D Fourier analysis
 be able to use a numerical computer tool (Matlab, Octave or similar) for simulating, analyzing and processing of DT signals
Lecture slides
(You may always expect handmade corrections and inserts at the
lecture....)
 Lecture 1 slides: (intro, signals)
newerlect1.pdf
 Lecture 2 slides: (sampling, frequency)
newerlect1.pdf (from slide 12)
and
newerlect2.pdf
 Lecture 3 slides (frequency, FT od periodic signals, DFT):
(idea of a transform, FT  Fourier Transform of L2 signals) newerlect2.pdf
 Lecture 4 slides  DFT: newerlect2.pdf (continued)
and windowing \& FFT newerlect3.pdf
 Lecture 5:
FFT  newerlect3.pdf
ShortTime Fourier Transform (STFT, instantaneous spectrum): newlect6.pdf
 Lecture 6
FFT  Fast Fourier Transform
STFT  ShortTime Fourier Transform (STFT, instantaneous spectrum): newlect6.pdf
LTI systems, convolution, ztransform
lect_lti_z.pdf
HOMEWORK1 (solve till 30.11)
 Lecture 7 ztransform
lect_lti_z.pdf continued
 13 Apr  holidays start...
 Lecture 8 (20 Apr 2017) filters, filter design:
lect_filt.pdf
Filters  advanced design, tips, tricks lect_filtadv.pdf
HOMEWORK1 (due in the middle break)
 Lecture 9 (27 Apr 2017): Test I
 One hour test I, 10pts worth: bring YOUR OWN notes (handwritten on paper or on printed
lecture slides). No books, no photocopies of other person
notes.
The test will cover the subjects which were in the Homework1 i.e. up
to (and including) LTI systems and comvolution/impulse response.
Example test:test1_078a.pdf
More examples w/solution: down in the page

Filters lecture  continued.
 4 May 2017: NO LECTURE
 Lecture 10 (11 May 2017):
Filters lecture  continued.
 Lecture 11 (18 May 2017):
Implementing DSP lect_implem.pdf
Homework2 start  please download from homew2_2008plus.pdf.
 Lecture 12 (25 May 2017):
2D signals: newlect13_2d.pdf
and
signal processing
for data compression
Homework 2 due today
 Lecture 14 (1 Jun 2017):
2D signals continued
signal processing
for data compression
Advanced techniques;
 Lecture 13 (8 Jun 2017):
test II
example test here; in problem 1a use M=6 or 4 (not 5, as it has to be even)
More test examples in test examples section.
 THE END OF SEMESTER
Old slides below  this marker will be moved with slide update
 Lecture 11 (22 Dec 2016):
More on implementation tricks
and 2D signals:
newlect13_2d.pdf
Homework2 start  please download from homew2_2008plus.pdf.
 Lecture 12 (05 Jan 2017):
2D signals continued: newlect13_2d.pdf
and
signal processing
for data compression
Homework 2 due today
 Lecture 13 (12 Jan 2017):
test II
example test here; in problem 1a use M=6 or 4 (not 5, as it has to be even)
More test examples in test examples section.
 Lecture 14 (19 Jan 2017):
Random DT signals;
 Lecture 15 (26 Jan 2017):
Advanced techniques;
 THE END OF SEMESTER
 When: Thu 23.06, 1114 (preliminary session schedule), where: 120 Exam 1
pen, pencil, calculator and your own notes
plus lecture slides.
Copies of solutions for homeworks/tests/exams
are NOT allowed.
The exam covers ALL the course matter. There are "Problems" (longer)
and "Questions" (shorter), for total of 90 minutes.
If you fail Ex1 you are still entitled to take Ex2.
Students who earned the "shortpath" grade may take the ex1 or ex2
without any risk  better grade counts
Just after Exam1 there will be a possibility to retake test1 and/or test2.
Please mail me to declare if you want it.
A retaken T1/T2 does NOT count towards shortpath
 When: Wed 29.06 1114 (preliminary session schedule), where: 120 Exam 2
Examples of tests
Use them for study. Learn methods, not solutions.
Tests 2016
SAMPLE TEST 1.
SOLVED TEST 1.
There is no guarantee that the current test be identical ;). It
will be similar (the lecture was similar), but I might also put
more focus on different subjects. The only base is the lecture content
(live one, not only the published slides ....).
The main rule: exam covers the whole course content (sampled),
including the T1(H1)+T2(H2) area and also the lectures after the
H2.
Exam tests 2009 w/solution discussion
Exam version A
Exam version B
 In both cases the signal was sampled correctly
(f_{s}>2f)
 To calculate N_{0} it was enough to count no. of
samples in period (or divide f_{s} over f). Answer was
10(A) or 6(B). For N_{0} samples in period,
θ_{0} was equal to 2π/N_{0}.
 Ksize DFT will have K discrete samples over <π, +π)
(we include π, and exclude +π , but
due to periodicity of spectrum it is only a
convention)
for a cosine, only two samples are nonzero: at k such that
θ_{k}=±θ_{signal}. Form the
definition of θ_{k} you will see that this is
for k=±4 (this is the result of taking K=4N_{0}).
 You may label frequency axis with
k=K/2,....1,0,1,...K/2 or with its periodic equivalent
KK/2,....K1,0,1,...K/2
to label with θ just use
the expression for θ_{k}.

 H(z)=Y(z)/X(z) is easily obtainable from the time equation. It
was
0.2(1+z^{1})/(10.8z^{1}) [A]
0.2(1z^{1})/(1+0.8z^{1}) [B]
 Zeros are roots of numerator: 1 [A] or +1 [B]
Poles are roots of denominator: +0.8 [A] or 0.8 [B]. They are
inside unit circle, so the system is stable (but I didn't
ask...)
 Example graph:  please
find a_0, b_0, b_1 by yourselves. If you are smart, you may save
one multiplication by 0.2 (this is left as exercise to you).
 For x(n)= shifted delta, (a limited energy signal)
you may take the impulse response
and shift it appropriately. To find h(n) it is easiest to split
H(z) into two fractions: (shown for [A], for [B] change some signs)
0.2(1/(10.8z^{1})+z^{1}/(10.8z^{1}))
and lookup the inv.Z of 1/(10.8z^{1}) in the
table. The final result is a sum of two identical exponentials
shifted by 1 in time. Then, you shift h(n) to proper position....
 For x(n) = 1(1)^{n} (a periodic signal) we see a DC
component and a periodic component exp(jπn) with frequency of
π. We find numerical values of
H(0)=(2 or 0) and H(π)= (0 or 2) by substituting exp(0) and exp(π) for z, and
finally
y(n)=H(0)H(π)·(1)^{n}
 The response was symmetrical around its midpoint (n= 2 or
4). Thus, it was a repsonse of a zerophase filter delayed by 2 or
4.
 phase is linear φ=(2 or 4)θ
delay is constant and equal to (2 or 4)
 The response of filter is a rectangle modulated by
exp(jπn). Thus, the characteristics is a
sin(θL/2)/sin(θ), shifted to π. You may find the
mainlobe width, you may plot exactly zeros of A(θ) etc.
 Time resolution is proportional to time duration of window,
frequency resolution  to mainlobe width (which is prop. to 1/K
....).
Rectangular window has narrowest mainlobe possible, but high
sidelobes; so it is good for resolving signals close in frequency,
but without large difference in amplitudes.
Any other window will have wider mainlobe (so poorer resolution in
f).

There was nonlinearity introcuced by product of two samples (linear is
multiplication by a constant only).
Saying "stable=yes because of BIBO" was not enough; "because FIR" was
enough; if you call BIBO, you have to prove it by finding relation
between bound of input B_{x} and output B_{y}.
 LP filter with passband of π/4 (see the "lecture 17").
 Many shorter is better: by averaging we reduce the variance
of estimate. (variance is huuuuuge with single FFT)
 β (some call it α) controls the shape of window 
effectively the sidelobes level (high β  low sidelobes). Is
high β better? yes, if you are concerned with sidelobe level;
but remember that you pay with wider mainlobe (There Ain't No
Such Thing As A Free Lunch)
 Inv FT is calculated by summation when the spectrum is
discrete ([B], periodic signal) and by integration when the
spectrum is continuous ([A], limited energy signal).
 3 buses are for opcode, data1 (signal), data2
(coefficient).
Any instruction with dual move uses all three,
e.g MAC instruction needs 2 data, so it is nice that we can load
data in the same cycle
in 56002 it can be coded as:
mac a,b x:(r0+),x0 y:(r4+),y0
 Trivial
 def: order of n^2, FFT: order of n log2(n)
 y(n) length is, maximally, (length of h(n))+(length of
x(n))1. K=M+N1. Here, we were asked to find M knowing K and
N. Answer is, as you may guess, M=K(N1)
 The clue is in word "maximally". It may happen that for
certain signal (e.g in the stopband....) the y(n) is shorter.....
Exam test 2012/13
Exam sheet
T1/T2 test examples
Please note that the solutions are NOT a model ones to copy and paste.
In some cases a "full score" student solution to the test needs a bit of
explanations, and in many cases my solution is too large  I wanted to show different possibilities or broaden an example.
To summarize  don't learn by heart. Learn by brain. Try to solve the missing versions of tests.
Test1 2010/11 ver.A problems
Test1 2010/11 ver.B problems
Test1 ver.B solutions
Test1 ver.A solutions
Test2 2016L ver A. solved
Test2 2016L ver B. (do it yourself)
Test2 (ver.A) and solutions
Test2 (ver.B) (do it yourself!)
Also, think first, act later.
 If you see a system  what type of system it is? LTI? What consequences arise from this?
 If you see a signal  is it limited energy? periodic?
 Which tool to use for LE? Which one for periodic? Which FT definition is appropriate?
 Is the plot you see in time or in frequency?
 Is the plot you have to sketch  in time or freq domain?
 Will the sketch requested be continuous or discrete?
periodic? Will it have some symmetry? Is the function realvalued or
complex? Maybe we are plotting abs()?
 maybe the function in freq can be expressed as "real times
exp(j n0 theta)" because in time it is "symmetrical but shifted by n0"?
How much is n0? (If in freq domain  shifted by θ0  how much is this? )
 Signal is causal? Don't forget u(n) then.
 See 1? Try exp(j pi) instead. See exp(j pi)? Try (1)....
When solving at home, you may use matlab or octave to do calculations
like (1j)/(1+j) (or to verify your calculations). You may also use
these tools to show plots. Then try to understand why it is like you see
 no Matlab at the exam, please :).
Test1 2013/14 ver.A problems
 Max score was 13, I assume 10 is OK, and +3 is a bonus.
 Typical errors as I commented by email on your homework still show up.
 Hints:
 Impulse response is useful if system is LTI (Linear AND TimeInvariant  you must verify both!)
Stability is verified by finding M such that By=M Bx; one way to find M
is to calculate ∑ h(n). Remember that h(n) → 0 is NOT enough (look here for an example)
 Remember that fn or N are UNITLESS (don't use units like Hertz or seconds)  they are ratios of f/fs or just number of samples
Common error  forgetting that there is N0 and N, and N must be an integer (N=19 [A] or 9 [B])
 FFT complexity calculation was simple (answer: [A] 48 ms, [B] 2 ms)
 DTFT was either 2cosθ or 2jsinθ. The task was to plot
AMPLITUDE X(θ), then to recall that DFT8 will be just 8 samples of
X(θ)
 Formula N+L1 is good as a maximum length of convolution if
we don't know exactly signals. In this case h(n) was a short rectangular
pulse, x(n)  two wellseparated deltas, so in the output we got just
two copies of h(n). ([A]:10, [B]:14, however I gave 1/2 score for
correct application of L+N1)
Put this code in Octave or Matlab:
x=zeros(1,100);
n=[1:100]10;
x(n==0)=1;
x(n==40)=1;
figure(1);
stem(n,x); title('x(n)');axis([20 100 0 1.2]);
h=ones(1,5);
figure(2);
stem(0:4,h); title('h(n)');axis([20 100 0 1.2]);
figure(3)
y=conv(x,h);
stem([1:length(y)]10,conv(x,h));axis([20 100 0 1.2]);
 xs(n) was a SUM of x(n) with manipulated x(n):
1. shifted by N → X(k)⋅ exp(j N θ_k) ; happily this factor is always =1;
2. inverted in time → X(k) (or X*(k) for real signals)
Some students applied linearity idea in the argument of X(k) (WRONG!!!! Do it only on X, not on k)
Test 2 (2013/14) solutions sketch
Computer plots:
Test 1 (2016z) solved
The labs will be taught by
Lab rules (do's/dont's, grading)
Disclaimer:
These are called "examples" to underline the fact that they are not
official. Some of them need review....
Openly speaking, they are exercise sets current at the
time of posting. I reserve the right to make some important
modifications before the actual lab, to give different sets to
different groups etc. (and I usually DO review the text before giving
it....).
Lab exercises:
Students do not need to print these
scripts  the official lab instructions will be available at the lab.
Old instructions below  this marker will be moved with updates
Past things archive (Attic)
dr inż. Jacek Misiurewicz
room 454 (GE)
Office hours: Mon 16:3017:00 (or by email appointment)
Institute of Electronic Systems
Instytut Systemów Elektronicznych
Institute of Electronic Systems
email:jmisiure@elka.pw.edu.pl
This page is "Continuously Expanding".///////////////////////