KELOMPOK PROYEK AKHIR SINYAL DAN SISTEM 1. Muh Ilham Akbar Iffagano
PROJECT 1
2. Reyfista Pangestu - Ahmad Salaam Mirfananda
PROJECT 3
3. Ubay M Noor - Amirsyah Rayhan M
PROJECT 6
4. Dita Tessa Parastika - Ismi Rosyiana Fitri
PROJECT 30
5. M. Audy F. - Muhammad Raditya Gumelar
PROJECT 25
6. Widi Destrianda - Benni Mustafa
PROJECT 27
7. Ginas Alvianingsih - Dwinanri Egyna
PROJECT 7
8. Muhammad Erfinza - Angga Hilman Hizrian
PROJECT 24
9. Andreas P. Aji - Ferdy Kurniawan
PROJECT 20
10. M.Hilmy Iskandar - Martino Adisuwono
PROJECT 19
11. Aiman Setiawan- Suharsono Halim
PROJECT 22
12. Muhammad Haekal - Daniel Moses
PROJECT 17
13. Ilham Dwi P - Harianto Adriprasetyo
PROJECT 29
14. Claudia Khansa - Faya Safirra
PROJECT 11
15. Dawud Shibghotulloh - Diamod Ravi
PROJECT 36
16. Jendra Riyan Dwiputra - Andik Suprayogi
PROJECT 9
17. Qashtalani Haramaini - Ilyasa Rafif
PROJECT 23
18. Fajar Tri Wardana - Rahmat Sigalingging
PROJECT 8
19. Agnes Grace S N - Susan Wiguna
PROJECT 5
20. Luthfan Fauzan - Restu Nugroho
PROJECT 33
21. Ahmad Dzul Faiq - M. Al Fatih
PROJECT 34
22. Samuel Zakaria - Ester Nugraheny N.P
PROJECT 18
23. Rachmat Romario Akbara - Yohan Binsar H.G
PROJECT 26
24. Rialdo Stefan Josua - Hirzi Hasan
PROJECT 12
25. Adhelia Irawan - Maulidya Falah
PROJECT 14
26. Chaizar Ali Fachrudien - Achyar Maulana Pratama
PROJECT 2
27. Erdi Nindito Rumono – Samsudiat
PROJECT 28
28. Zaky Ramadhan - Antonius Listyo
PROJECT 10
29. Findal Darmaja - Josan Putra
PROJECT 16
30. Jodi Malikan - Bagus Setiawan
PROJECT 21
31. Ganang Rizky - Pradana Damara
PROJECT 37
32. Kenny Prasetyo – Rizky Muhammad Reza
PROJECT 13
33. Andhika Kumara D - Ahmad Fauzi Arief
PROJECT 4
34. Budianto - Andre Jatmiko
PROJECT 32
35. Dara Azka – Abi Iqbal Prasetyo
PROJECT 35
36. Erasmus NK – Dhani Teja K.
PROJECT 15
37. Muhammad Iqbal – Barry Muhammad
PROJECT 31
Pembagian Proyek dilaksanakan secara undi, bila perlu penjelasan hubungi @ilhamiff 08976692668
SIGNALS AND SYSTEMS PROJECT 2014 General instructions: 1. Make a user-friendly GUI application program by using MATLAB 2. Generalize the input parameters in each application you make, if you are given a specific value, you must be able to input some other values as well.
PROJECT 1 Generate analog and discrete signals and do some basic operations on those signals, such as adding, subtracting, multiplying, flipping, delaying, etc.
PROJECT 2 Make an application that can be used to determine if a given system is LTI or not. In particular, if the system is linear or not, if the system is time invariant or not.
PROJECT 3 Make an application that is bale to calculate the average power of continuous and discrete time periodic signals. The input signals can be generated by using the wellknown functions or the arbitrary functions.
PROJECT 4 Write a MATLAB program to decompose a continuous or a discrete time signal into its odd and even parts.
PROJECT 5 A Sample and Hold circuit is used to help the conversion of an analog signal to be digital one. The circuit conducts the sample operation and followed by uniform quantizer. You are required to simulate the digitalization process using MATLAB. Also, demonstrate the effect of sampling frequency.
PROJECT 6 You are supposed to write a MATLAB program to plot the magnitude spectrum of
x t
3e
0.2t
cos10t for t 10 .
Because this is an infinite length signal, you should
truncate the signal by choosing the proper length. Try to simulate and analyze the effect of signal length and also the number of frequency sampling points. Also, demonstrate the effect of windowing. In particular, you are asked to compare for different window functions.
PROJECT 7 You are asked to simulate the impact of DFT length on resolution. For example, consider a test signal
sin 2 1000 t sin 2 1100 t sin 2 3000 t .
x t
You
generate an 0.0024 second sample of that signal using a sample rate if 10000 kHz. You use rectangular or Hamming window to compute the windowed DFT’s with three lengths: 25, 128, and 1024. Your program is expected to answer these questions: 1. How do the rectangular window results compare to the hamming window results? 2. Are you able to see from the frequency response magnitude that the signal contains three separate sinusoids? If so, for which DFT length can you distinguish the sinusoids? 3. What does increasing the DFT length accomplish?
PROJECT 8 The same as PROJECT 7, but in this project you must evaluate the impact of window length of resolution. In specific, your program is expected to answer these questions: 1. How do the rectangular window results compare to the Hamming window results? 2. Are you able to see form the frequency response magnitude that the signal contains three separate sinusoids? If so, for which DFT length can you distinguish the sinusoids? 3. What does increasing the length of the data window accomplish?
PROJECT 9 In this project, you asked to analyse the sidelobe levels and leakage of a window. Consider two sinusoidal signals:
x1 t
and x t
sin 2 50 t
2
.
0.031sin 2 77.5 t
You sample the signals at a rate of 1000 Hz over an interval of 0.127 seconds. Let
x n
signal
x1 n x
and n
. Use a 1024-DFT to compute the windowed transforms of the total
x2 n
x
1
. n
Compare the results for 128-point rectangular and 128-point
Hamming windows. Your program is expected to answer these questions: 1. Describe what you observe in these plots. 2. How do the sidelobe levels of the windows affect the results? 3. Which window(s) allow you to detect the presence of both sinusoids? Why?
PROJECT 10 An application of signals and systems course is an echo cancellation. In this project youa re asked to demonstrate an echo cancellation system. Echos can result from reflections of walls in a room or mismatched switching equipment in telephone lines. The effect of a single echo can be modelled as y n x n x n N , where the voice signal,
N is
the delay, and
x
,
y n
x n
y n
yn
n
is a constant. An echo removal system must
be described by difference equation of the echo equation above with input replaced by
is
and output y n replaced by N . In this simulation, try
N
x
, n
1000 and
x
n
which is equivalent to
0.5 .
PROJECT 11 In this project you will filter an audio signal. First, you should have an audio signal. You design a 40th-order lowpass filter with cutoff frequency 0.125 f s (you can use fir1 command). Then, you pass both the left and right channel signals of your audio snippet through the filter.
PROJECT 12 Using an audio signal, demonstrate the Nyquist sampling theorem.
PROJECT 13 In this project, you are asked to do a digital music synthesis: Beethoven’s Fifth Symphony using MATLAB. Please consult http://www.cse.yorku.ca/~mohammad/3451F13/docs/Lab3.pdf Note that you can also compose other music!!!
PROJECT 14 Write a MATLAB program to show the correlation between two signals. In particular, your program should be used to determine the periodicity of a signal by using the autocorrelation property. Autocorrelation also has an application to quantify the effect of noise on a periodic signal. Show this in your program.
PROJECT 15 You are asked to develop an understanding of how AM radio signals are modulated and
demodulated.
Please
http://www.ece.tamu.edu/~hpfister/courses/ecen314/project2.pdf
consult for
further
information.
PROJECT 16 Provide a program to analyse the frequency response of a causal discrete-time LTI system implemented using the difference equation. For example, we have
0.1x n 0.1176x n 1 0.1x n 2 1.7119 y n 1 0.81y n 2
y n
You are asked to plot H f . Also, provide an output signal if given an input signal, for example
x n
cos 0.1 n
. u
n
PROJECT 17 Demonstrate the time shifting and frequency shifting properties of the DTFT.
PROJECT 18 You are asked to design a noise reduction system. Suppose you record a noisy sound (signal) and then you sample it to be
x
. n
You are asked to identify the spectrum
corresponds to the noise and speech signals by using DTFT. You can remove the noise afterwards.
PROJECT 19 This project is similar to PROJECT 10, however, in this project you must estimate the echo parameters. In a real problem you do not know the parameters: delay and constant. Suppose you are given the data
(which is corrupted by an echo) but
y n
suppose you do not know the value of the delay of r
xx
,
y n
n
x
r yy n
n *x
y n
*
y
n
and let
r xx n
N .
Let
be the autocorrelation
r yy n
be the autocorrelation of
. You must first find a formula for the signal r n in terms of n
yy
x
r
,
xx
n
n
. PROJECT 20 Make a program to find the Fourier series coefficients for a periodic signal. For
example,
x t
. Also, you should show the convergence of the Fourier series
cos t
of the periodic pulse signal. Sometimes the integration formula for the Fourier series coefficient is difficult to carry out. In these cases, the coefficients can be obtained numerically.
Remember
a
formula
f t dt T f mT .
For
example,
m
c k
1
T
T
x t e
jk 0t
dt can be approximated as c k
T M 1
T
x mT e
jk 0m T
. You
m0
compare the results.
PROJECT 21 In this project, you will examine the effects of a low pass filter on speech. Write a MATLAB script to read an audio file into Matlab. (wavread), filter the sound file with a 40th order low pass FIR filter with a cutoff of 1000 Hz. (f ir1, filter), a note on using fir1 to generate the coefficients for the low-pass filter: you specify a cutoff frequency that’s been normalized to the Nyquist frequency = fs/2. Generate and plot the amplitude of the transfer function of the filter in dB vs. frequency in Hz. (freqz) Play the audio file after it has been sent through the filter. In addition to plotting the frequency response of the filter, do the following plots: use fft to plot the frequency response of the original signal, use fft to plot the frequency response of the filtered signal (should be very enlightening), do amplitude vs. index plots of the signal, before and after filtering
PROJECT 22 You use high pass filter in PROJECT 21. Note that filter the sound file with a 40th order high pass FIR filter with a cutoff of 3000 Hz. (fir1, filter)
PROJECT 23 Use a band pass filter to reduce noise in a set of simulated audio tones. Write a MATLAB script to generate a sequence in MATLAB which samples the signal f t
f 3
1
sin 2
10
f1t sin 2 f 2t sin 2 f 3t , where
659.255 where
f 1
440 ,
f 2
554.365 ,
and
it simulates the A-major chord. Generate a noisy musical chord
consisting of the sampled signal plus a noisy time-domain signal, you can use randn in MATLAB. Filter the sound file with a 60 th order band pass FIR filter with a cutoff of f LO
and 0.9 f 1
f HI
1.1 f 3 .
Use fir1. Listen to the music before and after being filtered.
PROJECT 24 In this project you are asked to learn signal sampling, manipulation, and playback. Please see http://www.cse.yorku.ca/~mohammad/3451F13/docs/Lab2.pdf
PROJECT 25 In this project you should do Fourier sound synthesis. Please see http://www.cse.yorku.ca/~mohammad/3451F13/docs/Lab4.pdf
PROJECT 26 You will create a signal with added high frequency noise 1. Typeload mtlb 2. You can hear a voice say "MATLAB." This is the signal to which you will add noisesoundsc(mtlb,Fs) 3. Create a noise signal noise = cos(2*pi*3*Fs/8*(0:length(mtlb)-1)/Fs)';(You can hear the noise signal by typing soundsc(noise,Fs))(You can also use random function to introduce noise) 4. Add the noise to the original signalu = mtlb + noise; 5. Scale the signal with noiseu = u/max(abs(u));(You scale the signal to try to avoid overflows later on. You can hear the scaled signal with noise by typing soundsc(u,Fs)) 6. Display the frequency spectrum using FFT 7. View the scaled signal with noisespecgram(u,256,Fs);colorbar(In the spectrogram, you can see the noise signal as a horizontal line at about 2800 Hz,which is equal to 3*Fs/8). 8. Use low-pass filters to eliminate high frequencyb = ones(1,10)/10; % 10 point averaging filterfy = filtfilt(b,1,x); % Noncausal filteringfyy = filter(b,1,x); % Normal filtering 9. Use FFT to plot the power spectrum of the filter signal and compare it to both, the originaland the corrupted signals. You will be provided an ECG ( Electrocardiogram) signal with noise.Your task is to create a matlab program to determine the frequency of the noise and elimi nate thenoise signal.
PROJECT 27 1. The periodic signal x(t) is shown below. Determine the fundamental period T0. Write a MATLAB code to plot x(t), using enough points to get "smooth" curve. This is just reproducing the curve provided below. 2. Compute the Fourier series coefficients for x(t) (if you can find it in the book, that is ok). Plot the single-sided and double-sided spectra up to the 10th harmonic. 3. Plot partial sums of the Fourier series for x(t) (terms 1 through N in the infinite series). In your opinion, what is the value of N that results in a "good" reproduction of x(t). Document your work, include plots to illustrate your work and your conclusions. Include your MATLAB code.
PROJECT 28 Consider the following two signals: x1 (t )
1, | t | 3 0, elsewhere
x 2 (t )
1, | t | 1 0, elsewhere
a) Plot these two signals on the same figure. Use a time axis of [ -5,5]. Add labels, etc b) Derive (mathematically) the Fourier Transforms X1(f) and X2(f) of these two signals c) Write a program to compute the Fourier Transforms numerically, and compare with b) Note: you can use the Matlab command trapz for numerical integration c) Plot the magnitude spectrum for the signals on the same figure. d) Discuss your results and explain the relationship between the spectra X1(f) and X2(f).
PROJECT 29 The impulse response h(t) for a particular LTI system is shown below. All parts of this lab make use of this h (t). h(t) = [3e-3t + 5 e-2t + e-t (4 cos(3t)+ 6 sin(3t)) + e-4t ] . u(t) 1. Plot the impulse response for h(t) directly from the above equation by creating a time vector. 2. Use the r e s i d u e function to determine the transfer function H(s) . Determine the locations of the poles and zeros of H(s) with the roots function, and plot them in the s-plane (x for poles, o for zeros). 3. Use the freqs function to plot the magnitude and phase of the transfer function. Document your work, include plots to illustrate your work and your conclusions. Include your MATLAB code.
PROJECT 30 Consider the system block diagram shown below:
(a) Use the series function to find the numerator and denominator polynomial coefficient vectors for the cascade connection of G1(s) and G2(s). Use the printsys function to find the overall transfer function
=
. Hint: in the Matlab help, terms like SYS, SYS1, etc., refer to the specification of a system by a pair of vectors that give the coefficients for the numerator and denominator polynomials of the transfer function. For example, >> numG1= [1 1]; >> denG1=[1 2]; >> numG2=[1]; >> denG2=[500 0 0]; >> [num,den]=series(numG2,denG2,numG1,denG1); >> printsys(num,den); (b) Use impulse to plot the system impulse response g(t). Note: impulse assumes that the system is causal (ROC of the transfer function is a right half -plane). (c) Use step to plot the system step response. (d) Plot the signal
= − cos5 for t ϵ [0, 5] using a time resolution of 0.002 sec. Use lsim with a left-hand argument to plot the system response for t ϵ [0, 5] when r(t) is the system input. Use a time resolution of 0.002 sec for your plot. (e) Use pzmapwith left-hand arguments to observe the poles and zeros of G(s). Is the system stable? (Justify your answer). (f) Usepzmapwithout left-hand arguments to generate a pole-zero plot for G(s).
PROJECT 31 Consider the feedback system depicted in the block diagram below:
Note that the gain of the feedback path is unity (1). (a) Use feedback to find the numerator and denominator polynomial coefficient vectors of the closed-loop transfer function
= For feedback, you will need the numerator and denominator polynomial coefficient vectors for the series connection of G1(s) and G2(s) that you obtained in the above (problem (1)). The transfer function of the feedback path in the system block diagram above is equal to one, so you can describe it with the numerator polynomial coefficient vector [1] and the denominator polynomial coefficient vector [1]. (b) Use printsysto find G(s). (c) Use impulseto plot the system impulse response g(t). Give a brief qualitativedescription of the main effect of adding feedback to this system as compared tothe system in problem (1). (d) Use pzmapwith left-hand arguments to observe the poles and zeros of G(s). Isthe system stable? (Justify your answer). (e) Use pzmapwithout left-hand arguments to generate a pole-zero plot for G(s). (f) Plot the signal −
=
cos500
for t ϵ [0, 20000] using a time resolution of 10 sec. Use lsim to plot the system response when r(t) is the system input for t ϵ [0, 20000] using a time resolution of 10 sec.
PROJECT 32 Consider the feedback system depicted in the block diagram below:
(a) Use feedback to find the numerator and denominator polynomial coefficient vectors of the closed-loop transfer function
= (b) Use printsys to find G(s). (c) Use impulse to plot the system impulse response g(t). (d) Use pzmap with left-hand arguments to observe the poles and zeros of G(s). Is itcausal? Is the system stable? (Justify your answers). (e) Use pzmap without left-hand arguments to generate a pole-zero plot for G(s).
PROJECT 33 H is a causal discrete-time LTI system with input x[n] and output y[n] related by the linear constant coefficients difference equation y[n] = 0.6y[n − 1] + x[n] (a) Find the transfer function H(z) analytically (using paper and pencil). Use zplane to generate a pole-zero plot for H(z). Is the system stable? (Justify your answer). Note:You should get the vector [1] for the numerator polynomial coefficientvector of H(z). On some versions of Matlab, this will create an incorrect polezeroplot; the plot may show an incorrect zero at z = 1. If this happens, you canfix it by using [1 0] for the n umerator coefficient vector. The vectors [1] and [1 0]actually specify the same numerator for H(z), since 1 = 1 + 0z−1. (b) Use freqzto plot the magnitude |H(ej!)| and phase ]H(ej!) of the system using N = 1024 points. frequency response
( )
(c) Use impzto plot the system impulse response h[n].
PROJECT 34 Second Order Response Consider a transfer function of the following form corresponding to a right-sided response.
= 2[] || The pole p is complex. Let = For this question, r=0.9 and = /2.
(a) Use the Matlab function zplane to plot the poles and zeros of H (z ) . (b) Use freqz to calculate the complex frequency response. Plot the magnitude and phase of thefrequency response corresponding to H (z ) . Categorize this response in terms of is it lowpass,highpass, bandpass, or bandstop. (c) The group delay of a response is given by
=
A “good” group delay is one which is constant with frequency. What does this constancy imply for thephase? Why would filter designers prefer to deal with group delay rather than phase response? Use the Matlab f unction grpdelay to get the group delay associated with the filter given above. Plot the group delay. What are the units of group delay? Label the axis appropriately. (d) Plot the impulse response of the filter (first 20 or so samples).
PROJECT 35 DTFT for FIR signals We have been using the routine freqz to compute frequency responses. In this problem you will write your own DTFT routine for finite length sequences. The DTFT will be of the form function H = DTFTFIR (h, n, w) nw = length(w); nh = length(h); for (k = 1:nw) H(k) = … end return The input to this routine is a set of response values (h) with corresponding values of time indices (n), and a vector of frequencies for which the response is to be evaluated. Test your routine against freqz using the following two sets of responses (use frequencies from 0 to π in, say, 100 steps). Plot the magnitude response and the phase response for each case. (a) h = [4 3 2 1 1 2 3 4]; n = -2:5; Explain the shape of the phase response curve – specifically, why are there jumps in the function? Hint: where do the jumps occur with respect to the magnitude curve? (b) n = 0:20; h = n .* (0.9).^n;
PROJECT 36 DTFT for IIR signals We have been using the routine freqz to compute frequency responses. In this problem you will write your own DTFT routine for infinite length sequences specified by a numerator polynomial and a denominator polynomial (polynomials in 1 z ). The DTFT will be of the form function H = DTFTIIR (b, a, w) nw = length(w); nb = length(b); na = length(a); for (k = 1:nw) H(k) = … end return To do this first consider the rational polynomial
−1 ⋯ − 1 = = −1 ⋯ − 1 It is then clear that the frequency response corresponding to H (z ) for a series of frequencies is the point-bypoint division of the frequency response of B(z ) divided by the frequency response of A(z ) . Write your DTFT routine and test it on the following responses. Plot the magnitude and phase for each, comparing the results with those from freqz. (a) 1 + + +3 (b) 1−.18 + .81
ℎ[] = 0.5 =
PROJECT 37 The following program can be used to verify the time shifting property of discrete-time Fourier transform(DTFT): clf; w = -pi:2*pi/255:pi; wo = 0.4*pi; D = 10; num = [1 2 3 4 5 6 7 8 9]; h1 = freqz(num, 1, w); h2 = freqz([zeros(1,D) num], 1, w); subplot(2,2,1) plot(w/pi,abs(h1));grid title('Magnitude Spectrum of Original Sequence') subplot(2,2,2) plot(w/pi,abs(h2));grid title('Magnitude Spectrum of Time-Shifted Sequence') subplot(2,2,3) plot(w/pi,angle(h1));grid title('Phase Spectrum of Original Sequence') subplot(2,2,4) plot(w/pi,angle(h2));grid title('Phase Spectrum of Time-Shifted Sequence') Q.1 which parameter controls the amount of time-shift? Q.2 Repeat the above program for signal in 5.21 and for -5<=n<=5, and time shift value +5. Q.3 describe the function of freqz. Q.4 Write a program to show the frequency-shifting of DFT for following signal and frequency-shift value of 0.4*pi (i.e., wo= 0.4*pi).
