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Dijamin Bisa, atau bisa mengulang kembali. Kami juga dapat membantumembuatkan aplikasi atau program matlab/lainnya. Anda akan dilatih oleh Tim Profesional - HUBUNGI MASTER ENGINEERING EXPERT (MEE) 081219449060. Email: kursusmatlab@gmail.com

i=sqrt(-1);

abs(i)

factorial(6)

log2(512)

x=-5:0.1:5;

subplot (2,1,1)

y=sinc(x);

plot(x,y)

xlabel(‘x’)

ylabel(‘sinc(x)’)

title(‘The sinc function’)

subplot(2,1,2)

plot(x,abs(y))

xlabel(‘x’)

ylabel(‘abs(sinc(x))’)

title(‘Magnitude of sinc function’)

Y=fft(y,128);

subplot(2,1,1)

plot(Y)

subplot(2,1,2)

plot(abs(Y))

invY=ifft(Y,128);

subplot(2,1,1)

plot(invY)

subplot(2,1,2)

plot(abs(invY))

subplot(2,1,1)

plot(abs(y))

clear

8.1.1 Part B

Below is the script file used in the lecture. It is available electronically (called eg7.m) – ask a demonstrator or Dr Phillips when you need a copy of it.

%simple example of FFT use

%setting up the signal

t=0:0.001:0.6;

x=sin(2*pi*40*t)+sin(2*pi*100*t) %40 Hz and 100 Hz sine waves added

y=x+2*randn(size(t)); %noise added

%randn(size(t)) gives an array of normally distributed random entries

% that is the same size as t

plot(t(1:50),y(1:50)) %plots first 50 points i.e. to 0.05 s

title('40 Hz plus 100 Hz corrupted by noise')

xlabel('time (seconds)')

pause(2) %waits 2 seconds before continuing

%the fft and output

Y=fft(y,512); %performs the fft. Note 512 elements - power of 2 (2^9)

Pyy=Y.*conj(Y)/512;

%Y will have complex elements. The power spectrum is real

%so do an element by element multiplication by complex conjugate

f=1000*(0:256)/512;

plot(f,Pyy(1:257)) %we are only interested in half the data points

%as the same information is provided in the second half of Pyy

title('Frequency content of corrupted signal')

xlabel('Frequency (Hz)')

Run this file. You may wish to change pause(2) above to pause (so that you can see the first plot, before hitting a key). Now apply a Hamming window to the data by appropriately inserting the lines

win=0.54+0.46*cos((2*pi*t/0.512)-pi)

ywin=y.*win

[Notice that win as given here is defined as non-zero for values of t>0.512. This does not matter here as we only FFT the first 512 points]

Plot y, win and ywin over the full range of t so that you can see the impact of applying the window. You could use plot(t,y,t,ywin,t,win) which would plot them on the same set of axes or you could use subplots. You may wish to include further pauses. To look at the impact on the power spectrum include the lines:

Ywin=fft(ywin,512);

Pywyw=Ywin.*conj(Ywin)/512;

f=1000*(0:256)/512;

plot(f,Pywyw(1:257))

The plot, suitably labelled, should be included as part of a subplot, along with the plot for the power spectrum Pyy without windowing.

8.1.2 Part C

The following is a Matlab script file that is intended to perform the task mentioned below. HOWEVER the code provided below is NOT in the right order. Your task is to rearrange the order of the code so that it performs the actions described below. The scrambled code is available electronically (called eg8.m) – ask a demonstrator or Dr Phillips when you need a copy of it.

win=0.5+0.5*cos((2*pi*(n/N-T/2))/T);

H=fft(h,N);

plot(abs(H))

T=0.6;

clear

Hwin=fft(hwin,N);

title('FFT of Truncated Impulse Response')

hwin=h.*win;

h=20*sinc(20*(n/N-T/2));

title('FFT of Magnitude of Windowed Impulse Response')

pause(2)

N=128;

n=0:1:76;

plot([0:N-1],abs(H),[0:N-1],abs(Hwin))

title('FFT of Truncated and Windowed Impulse Responses')

pause(2)

plot(abs(Hwin))

When rearranged properly the working script file should calculate the magnitude of the Fast Fourier Transform (FFT) of the following truncated sampled filter impulse response (arising from an ideal low pass filter with 5 Hz cut off):

where n is an integer and where N has been chosen to be 128. The script file should also generate a windowed impulse response using h(n) and the (delayed) Hann window

and calculate the magnitude of the FFT of that windowed impulse response. The script should plot the results of the two FFTs separately, with a short pause between them, and then, after pausing again, plot them together on the same set of axes. Note that the Hann window is here only applied to a range of n which is less than the range operated on by the FFT (the rest of the range up to 128 being padded with zeros).

2012

Digital Signal Processing ETI265 2012

Introduction

In the course we have 2 laboratory works for 2012. Each laboratory work is a 3 hours lesson. We will use MATLAB for illustrate some features in digital signal processing.

Equipment: PC with Matlab and input/output of sound.

Matlab:

Matlab toolboxes: Signal Processing toolbox

Data acquisition toolbox

Lab 1: Real time spectral analysis using Fourier transform and

estimation of impulse responses using correlation function

Task 1. Real time spectral analysis using Fourier transform

Task 2. Real time spectrogram

Task 3. Estimation of impulses responses using correlation

Task 4. Modulation

Task 5: SSB-modulator

Lab 2: Design of IIR-filters

Task 1: Relation between poles and filter spectrum

Task 2: Design of IIR-filter from filter specification

Task 3 Notch filters

Task 4: Filter music signals

Laboratory work 1:

Real time spectral analysis using the Fourier transform

In this laboratory work we will use MATLAB for illustrate some features in digital signal processing. Start Matlab and update the Matlab path.

Connect the microphone to PC ’ mic in’ connector. You can use the speakers in the PC or connect external headphones.

Task 1. Real time spectral analysis using Fourier transform

Start Matlab.

At the Matlab prompt, type

sigfftio_lin (or sigfftio_log or demoai_fft’)

Now a spectrum analyzing window will be opened, see below

Item 1: Say the word ‘smile’ slowly and look at the spectra of the vowels ‘i’ and ‘e’.

Fill in the diagram below and estimate the pitch.

My pitch is…………...(some mean value).

Item 2: Try to generate a sound with as flat spectrum as possible.

(‘oral white noise’)

Task 2. Real time spectrogram

A spectrogram is a time-frequency plot of the signal. A sliding window is applied to the signal and the short time Fourier transform are determined for each time-window. The plot has time on the x-axis and frequency on the y-axis.

See help spectrogram for more information

Type

N=20000; Fmax=4000; record_spectra_china

% N=no of samples (Fs=10 kHz),

%Fmax = max freq in the plot (<5000 Hz)

Now 2 seconds of ‘mic in’ will be recorded and then the spectrogram will be shown.

Item 1: Pronounce the Chinese words below and see if you have the correct

pitch (tone). Let the Chinese students show the correct pitch.

Use also some Swedish words with Chinese tone.

Task 3. Estimation of impulses responses using correlation

Correlation functions are often used in estimation of unknown systems.

Input – Output Relations using correlation functions (from the slides)

Autocorrelation function for the output

Cross correlation function for input-output signal

If the autocorrelation for the input is a delta function, , we

direct have the impulse response .

If the autocorrelation for the input is not a delta function, we have to estimate the impulse response from the expression for the cross correlation. This is not included in this course.

But still, we can find a lot of information even in this case.

We will here use pre-generated signals. In files on the computer there are pairs of input and output signals from various unknown filters. Try to estimate these impulse responses.

Matlab script for computing the correlation function used below. This script exist in the Matlab path.

% lab_sigcorr.m Compute and plot correlation -N0<0<N0

% [rxy,n]=lab_sigcorr(x,y,N0);

function [rxy,n]=lab_sigcorr(x,y,N0)

Nx=length(x); Ny=length(y);

if Nx==Ny N=Nx; else N=min(Nx,Ny); end

rxy=xcorr(x(1:N),y(1:N));

rxy=rxy(N-N0:N+N0);

n=-N0:N0;

Item 1: Music through an echo filter.

First we listen to music through an echo filter (reverberation). We can hear the effect of the echoes but it will be difficult to estimate the time delays.

The input and output signals are stored in files with input in the left channel and output in the right channel. Listen to the signals and then try to estimate the delay using correlation functions.

Type the command below

Load the signals and plot and listen to them.

load sig_music; x=sig_music(:,1); y=sig_music(:,2); % load input and output signals

soundsc(x,10000); pause(10), soundsc(y,10000);

Use also the plot command to plot parts of the signals.

subplot(211), plot(x), subplot(212), plot(y) % Plot input and output

Now, use correlation functions to estimate the delays (the impulse response).

Write type sigcorr to show the Matlab code.

subplot(211), N0=2000;[rxx,n]=sigcorr(x,x,N0);plot(n,rxx);grid on % input auto correlation

subplot(212), N0=2000;[ryx,n]=sigcorr(y,x,N0);plot(n,ryx);grid on % cross correlation

Estimate the delay in the impulse response. The delays are ……...ms (my guess).

Item 2: Use white noise as the input to the echo filter.

We use white noise as the input and repeat the instructions from item 1. White noise has the correlation equal to a delta spike, i.e. the autocorrelation function for white noise is rxx(l)=δ(l).

Type the command below

load sig_noise; x=sig_noise(:,1);y=sig_noise(:,2); % Load input and output data

Note: Decrease the pause to 4 s.

Use also the plot command to plot parts of the signals.

subplot(211), plot(x), subplot(212), plot(y) % Plot input and output

Now, use correlation functions to estimate the delas (impulse response).

subplot(211), N0=2000;[rxx,n]=sigcorr(x,x,N0);plot(n,rxx);grid on % input auto correlation

subplot(212), N0=2000;[ryx,n]=sigcorr(y,x,N0);plot(n,ryx);grid on % in-out cross correlation

With white noise as input it will be easier to estimate the impulse response. The estimate the delays in the impulse response are ….............................…...ms.

Item 3: White noise through a band pass filter.

We have now estimated the impulse response of an echo filter. Next step is to estimate a band pass filter impulse response. Load the input-output signals and listen to them.

Type the command below

load sig_bandpass_noise; x=sig_bandpass_noise(:,1);y=sig_bandpass_noise(:,2);

soundsc(x,10000);pause(4),soundsc(y,10000);

subplot(211), N0=2000;[rxx,n]=sigcorr(x,x,N0);plot(n,rxx);grid on % input auto correlation

subplot(21), N0=2000;[ryx,n]=sigcorr(y,x,N0);plot(n,ryx);grid on % cross correlation

You can hear that the output signal is a narrow band signal. Check the spectrum by taking the Fourier transform of ryx(n) by typing

sigfftp(ryx,10000,10000,1000); % plot spectra up to 1 kHz, Fs=10 kHz

Task 4: Modulation

In most communication systems the signals are transladed from a lower frequency band up to a higher frequencies. This is called modulation. We know the formula

This means that when we multiply two signals we will have the sum and difference of the angles. When we have signals, this formula is

The multiplication gives then one signal at the frequency and one at the frequency and this frequencies is called the lower and the upper side band.

An example of the frequency contents is shown below with .

Item 1: Check this in Matlab by typing:

N=20000;n=1:N;x=sin(2*pi*0.05*n); speech_modulation_lab_a

Item 2:

Now, change the input frequency to f=0.1, i.e.

and fill in the diagram below.

Item 3: Speech scrambler

A special case of the above example occurs then we have the figure below. This is often called speech scrambling in the literature. You shall test this system in Matlab .

Item 1: Test the system with sound as input. Follow the instructions below.

load sig_music; x=sig_music(:,1); %load sound signal

x=sig_music(:,1); N=length(x); n=[1:N]'; speech_scrambler_lab_a % speech scrambler

Try to explain the results from Matlab.

Matlab scrip for speech scrambler

%speech_scrambler_lab_a.m demo of speech scrambler bm 2011

% Use: N=20000;n=1:N;x=sin(2*pi*0.1*n); speech_scrambler_lab_a

y=(-1).^n.*x;

sound(0.5*x,10000);pause(10);sound(0.5*y,10000)

subplot(211),sigfftp(x,1,N,1);

subplot(212),sigfftp(y,1,N,1);

Item 2:

To further analyze the system we use sinusoids as the input, .

Test the speech scrambler with this signal. First, fill in the spectra in the figure below.

Spectrum |X(f)| and |Y(f)|.

Check your solution by typing

N=4000; n=[1:N]'; x=sin(2*pi*0.1*n); speech_scrambler_lab_a

Task 5: SSB-modulator

I all communication systems, frequency translation are used. We move information signals from low frequencies up to higher frequencies before transmission and at the receiver side we received the signal and then translate the signals back to low frequencies. This procedure is called modulation-demodulation and the equipment is called modem.

We illustrate this with an SSB-modulation-demodulation system often used in communication systems. A time-discrete system is given below (SSB modulator).

Test this using the Matlab script below.

%ssb_lab_2011.m demo of SSB-mod/demoulation bm 2011

% Use: N=20000;x=sin(2*pi*0.1*n);deltaf=0.025;,ssb

% Use: N=20000;n=[1:N]'; x=sin(2*pi*0.1*n); deltaf=0;, ssb_lab_2011

% x=sig_music(:,1);N=length(x);deltaf=0.025;,ssb_lab_2011, soundsc(xe,10000);

fc=.25;

n=[1:N]';

hlp=fir1(500,2*.25);

xa=x;

xb=xa.*sin(2*pi*fc*n);

xc=filter(hlp,1,xb);

xd=xc.*cos(2*pi*(fc+deltaf)*n);

xe=filter(hlp,1,xd);

subplot(511),sigfftp(xa,1,N);

subplot(512),sigfftp(xb,1,N);

subplot(513),sigfftp(xc,1,N);

subplot(514),sigfftp(xd,1,N);

subplot(515),sigfftp(xe,1,N);

Item 5.1: Music through the SSB system

First, test the SSB modulator/demodulator with music (deltaf=0). Type

load sig_music; x=sig_music(:,1); soundsc(x,10000);

x=sig_music(:,1);N=length(x);deltaf=0.0; ssb_lab_2012, soundsc(xe,10000);

The figure below shows the spectra in the points A, B, C, D and E.

Note that the x-axis is 0<f<0.5.

Item 5.2. A sinousoids through the the SSB modulator/demodulator.

To analyze the SSB system, we now use a sinusoids as input signal (deltaf=0).

N=20000;n=[1:N]'; x=sin(2*pi*0.1*n); deltaf=0;, ssb_lab_2012

Fill in the spectra in the points A, B, C, D and E in the figure below.

Then check the result in Matlab using

N=20000;n=[1:N]'; x=sin(2*pi*0.1*n); deltaf=0; ssb_lab_2012

Item 5.3: Demodulation with wrong frequency

Finally, we check the case when deltaf=0.02, i.e. we use the wrong frequency in the last step in the demodulator. Type

N=20000;n=[1:N]'; x=sin(2*pi*0.1*n); deltaf=0.02; ssb_lab_2012

Explain what's happen in the SSB system for various values of deltaf. The spectra is shown below.

Laboratory work 2: Design of IIR filters

Introduction

In this laboratory work we will design FIR and IIR filters. First, we will show

the relation between pole-zero plots and the magnitude spectra and impulse responses for digital filters. The we will design notch filters which will be tested in both Matlab

Preparation exercise 1

Combine the pole-zero plot and the magnitude spectra |H(f)| below. Show the pair of pole-zero plot and magnitude spectra corresponding to the same system.

Pole-zero plot Magnitude spectra |H(f)|

Preparation exercise 2

Sketch the magnitude spectra |H(f)| for the given the pole-zero plots.

Kursus Matlab di Jakarta Selatan KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060

Selasa, 13 Januari 2015

Kami juga dapat membantu membuatkan aplikasi atau program matlab/lainnya. Anda akan dilatih oleh Tim Profesional - HUBUNGI KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060. Email: kursusmatlab@gmail.com

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