Question

1. (9 points) In this Question, we are going to perform DSBSC modulation using MAT- LAB. The signal we want to use is a speech signal. Here is the block diagram of ths system we want to simulate: Modulation Demodulation ult gt) m(t) x Butterworth LPF mr(t) c(t) Gr(t) Figure 1: DSBSC modulation and demodulation. (a) Since we are working with speech signals, we will choose a sampling frequency that is much larger than the bandwidth of the signals. As we have seen in the lab, speech signals often range from 300Hz - 3kHz. Therefore, set fs = 96 kHz. Then compute ts. Also define the time variable t to be between 0 and 5-t, seconds with a step of ts. (b) Record a 5-second a speech signal (it must be 5 seconds) by talking into the mic of your laptop. You may use the following code to record the message: Use the following lines of code to record a message: speech = audiorecorder (fs, 16, 1); recordblocking (speech , RECORDING_TIME); m = getaudiodata (speech); Make sure you set the recording time to 5 seconds. Note: I expect you to use the help command to read more about audiorecorder, recordblocking, getaudiodata. Make sure you know exactly how they work. (C) Now our speech signal has been saved in the variable m. However, if you notice, m was created as a column vector. Use the transpose operator to turn it into a row vector using: m=m (d) Let us now listen to the signal using the following code: sound (m,fs) (e) Plot the spectrum of the message. Make sure you define the frequency variable properly f. Use xlim to show the important part of the spectrum. Do not forget the title, xlabel, ylabel, and units. (f) Create a carrier signal c(t) = cos(210000t). Then, modulate the message m(t) using the generated carrier c(t). Name the resultant signal y(t). Plot the spectrum of y(t). Use xlim to show the important part of the spectrum. Do not forget the title, xlabel, ylabel, and units.

Answer 1

Code for part a-part e

fs=96000;
ts=1/fs;
t=0:ts:5-ts;
speech=audiorecorder(fs,16,1);
recordblocking(speech,5);
m=getaudiodata(speech);
m=m';
sound(m,fs);
plot(t,m); %frequency wave response of recorded signal (1st Figure)

xlim([1 4]); %shows 1 wave of sound recorded in 5 seconds
title('Frequency Response');
xlabel('Time (seconds)');
ylabel('Message signal m(t)');

spectrum(t,m); %provides power spectrum of the signal message (2nd figure)

freqz(t,m) %provide frequency response and phase response (3rd figure)

q=fft(m);
tt=fftshift(abs(q));
plot(t,tt); %Another way of finding frequency response (4th figure)
xlim([1.5 3.5]);
ylim([0 1000]);

title('Frequency Response');
xlabel('Time (seconds)');
ylabel('Message signal m(t)');

. o X Figure 1 File Edit View O k Insert Tools Desktop Window A Help OE - O Frequency Response Message signal m(t) 1.5 3.5 2.5 Time (seconds) 01:59 Type here to search ^ • 4x la ENG 11-03-2020

- 0 x Figure 1 File Edit View O k Insert Tools Desktop Window A Help OE - O Pxx - X Power Spectral Density 10-28 10-29 10-30 TTTTTTTT 10-32 10-33 0 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 0.5 Frequency Type here to search 01:49 O AO ) C ENG 1 11-03-2020

. o X Figure 1 File Edit View O k Insert Tools Desktop Window A Help OE - O Magnitude (dB) Muhamhamhnuidhemophhhhhhhhhhmmmm O 0.1 0.2 0.3 0.4 0.7 0.8 9 0. 1 0.5 0.6 Normalized Frequency (xa rad/sample) 5 104 Phase (degrees) 0.1 0.2 0.3 0.4 0.7 0.8 0.9 0.5 0.6 Normalized Frequency (xa rad/sample) Type here to search o @ OG 01:51 O AO ) C ENG 1 11-03-2020 hd

. o X Figure 1 File Edit View O k Insert Tools Desktop Window A Help OE - O 1000 1.5 NE 2.5 3.5 Type here to search 02:55 OBA @ OA 40 4x M ENG 1 11-03-2020

part f

Code Continued

c=cos(2*pi*10000*t);
y=m.*c;
r=fft(y);
u=fftshift(abs(r));
plot(t,u);
xlim([1.5 3.5]);
ylim([0 800]);
title('Frequency Response');
xlabel('Time (seconds)');
ylabel('Message signal y(t)');

. o X Figure 1 File Edit View O k Insert Tools Desktop Window A Help OE - O 1.5 2.5 Type here to search O @ OA 03:00 40 4x M ENG 1 11-03-2020 h