Department of Electronics and Communication

Engineering
Malaviya National Institute of Technology Jaipur

DSIP Lab Assignment

Submitted by: Priya Godika

College ID: 2023UEC1352

Submitted to Prof. K. K. Sharma

7th May 2025
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Question 1
Create two sinusoidal signals with amplitude–frequency pairs as given below:

a) (2, 5) + (1.6, 10) + (0.3, 20)

b) (1.8, 2) + (0.8, 25)

1 clc ; % Clears the command window

2 clear ; % Removes all variables from the workspace
3 close all ; % Closes all open figure windows
4 t = 0:0.001:1; % Time vector for 1 second duration with 1 kHz
sampling rate
5

6 x1 = 2* sin (2* pi *5* t ) + 1.6* sin (2* pi *10* t ) + 0.3* sin (2* pi *20* t ) ;
7 x2 = 1.8* sin (2* pi *2* t ) + 0.8* sin (2* pi *25* t ) ;
8 figure ;
9 subplot (2 ,1 ,1) ;
10 plot (t , x1 ) ;
11 title ( ’ Signal 1 a ’) ;
12 xlabel ( ’ Time ( s ) ’) ;
13 ylabel ( ’ Amplitude ’) ;
14 subplot (2 ,1 ,2) ;
15 plot (t , x2 ) ;
16 title ( ’ Signal 1 b ’) ;
17 xlabel ( ’ Time ( s ) ’) ;
18 ylabel ( ’ Amplitude ’) ;
Listing 1: Generate sinusoids

Figure 1: Signal 1a Plot

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Figure 2: Signal 1b Plot

Question 2
Convolute the two sinusoidal signals created in Question 1.
1 clc ;
2 clear ;
3 close all ;
4 t = 0:0.001:1; % Time vector for 1 second duration with 1 kHz
sampling rate
5 % Constructing Signal x1 & x2 by summing sine waves of
different frequencies and amplitudes
6 x1 = 2* sin (2* pi *5* t ) + 1.6* sin (2* pi *10* t ) + 0.3* sin (2* pi *20* t ) ;
7 x2 = 1.8* sin (2* pi *2* t ) + 0.8* sin (2* pi *25* t ) ;
8 conv_x = conv ( x1 , x2 , ’ same ’) ;
9 figure ;
10 plot (t , conv_x ) ;
11 title ( ’ Convolution of x1 and x2 ’) ;
12 xlabel ( ’ Time ( s ) ’) ;
13 ylabel ( ’ Amplitude ’) ;
Listing 2: Convolution

Figure 3: Convolution Result

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Question 3
Find the correlation between the signals from Question 1. Show one figure with the
outputs of Questions 2 and 3.
1 clc ;
2 clear ;
3 close all ;
4 t = 0:0.001:1;
5 x1 = 2* sin (2* pi *5* t ) + 1.6* sin (2* pi *10* t ) + 0.3* sin (2* pi *20* t ) ;
6 x2 = 1.8* sin (2* pi *2* t ) + 0.8* sin (2* pi *25* t ) ;
7 conv_x = conv ( x1 , x2 , ’ same ’) ;
8 % Compute the normalized cross - correlation between x1 and x2
9 [ corr_x , lags ] = xcorr ( x1 , x2 , ’ normalized ’) ;
10 figure ;
11 subplot (2 ,1 ,1) ;
12 plot (t , conv_x ) ;
13 title ( ’ Convolution of x1 and x2 ’) ; xlabel ( ’ Time ( s ) ’) ;
ylabel ( ’ Amplitude ’) ;
14 subplot (2 ,1 ,2) ;
15 plot ( lags , corr_x ) ;
16 title ( ’ Correlation of x1 and x2 ’) ; xlabel ( ’ Lag ’) ;
ylabel ( ’ Normalized Correlation ’) ;
Listing 3: Correlation and Convolution

Figure 4: Convolution Output

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Figure 5: Correlation Output

Question 4
Find the Fourier transforms of the signals from Question 1 (use fftshift; show 4 plots
in one figure).
1 clc ;
2 clear ;
3 close all ;
4 t = 0:0.001:1; % Time vector for 1 second duration with 1 kHz
sampling rate
5

6 % Defining the frequency vector for plotting

7 f = linspace ( -500 , 500 , length ( t ) ) ;
8 x1 = 2* sin (2* pi *5* t ) + 1.6* sin (2* pi *10* t ) + 0.3* sin (2* pi *20* t ) ;
9 x2 = 1.8* sin (2* pi *2* t ) + 0.8* sin (2* pi *25* t ) ;
10 % Computing the Fourier Transform of x1 and x2
11 X1 = fftshift ( fft ( x1 ) ) ; X2 = fftshift ( fft ( x2 ) ) ;
12 figure ;
13 subplot (2 ,2 ,1) ;
14 plot (f , abs ( X1 ) ) ;
15 title ( ’ Mag Spectrum of x1 ’) ;
16 subplot (2 ,2 ,2) ;
17 plot (f , angle ( X1 ) ) ;
18 title ( ’ Phase Spectrum of x1 ’) ;
19 subplot (2 ,2 ,3) ;
20 plot (f , abs ( X2 ) ) ;
21 title ( ’ Mag Spectrum of x2 ’) ;
22 subplot (2 ,2 ,4) ;
23 plot (f , angle ( X2 ) ) ;
24 title ( ’ Phase Spectrum of x2 ’) ;
Listing 4: Fourier Transform of x1 and x2
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Figure 6: Figures of Q4

Question 5
Perform the following operations on the signals from Question 1a and 1b:

a) Add 1a and 1b.

b) Multiply 1a and 1b.

1 clc ;
2 clear ;
3 close all ;
4 t = 0:0.001:1;
5 x1 = 2* sin (2* pi *5* t ) + 1.6* sin (2* pi *10* t ) + 0.3* sin (2* pi *20* t ) ;
6 x2 = 1.8* sin (2* pi *2* t ) + 0.8* sin (2* pi *25* t ) ;
7 % Performing point - wise addition of x1 and x2
8 x_add = x1 + x2 ;
9 % Performing point - wise multiplication of x1 and x2
10 x_mult = x1 .* x2 ;
11 figure ;
12 subplot (2 ,1 ,1) ;
13 plot (t , x_add ) ; title ( ’ Addition of x1 and x2 ’) ;
14 subplot (2 ,1 ,2) ;
15 plot (t , x_mult ) ; title ( ’ Multiplication of x1 and x2 ’) ;
Listing 5: Addition and Multiplication
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Figure 7: Addition Result Multiplication Result

Question 6
Find the Fourier transform of the signals obtained in Question 5a and 5b.
1 clc ;
2 clear ;
3 close all ;
4 t = 0:0.001:1;
5 f = linspace ( -500 , 500 , length ( t ) ) ; % Frequency vector from -500
Hz to 500 Hz
6

7 x1 = 2* sin (2* pi *5* t ) + 1.6* sin (2* pi *10* t ) + 0.3* sin (2* pi *20* t ) ;
8 x2 = 1.8* sin (2* pi *2* t ) + 0.8* sin (2* pi *25* t ) ;
9 x_add = x1 + x2 ;
10 x_mult = x1 .* x2 ;
11 % Compute the Fourier Transform of the added and multiplied
signals
12 X_add = fftshift ( fft ( x_add ) ) ; X_mult = fftshift ( fft ( x_mult ) ) ;
13 figure ;
14 subplot (2 ,1 ,1) ;
15 plot (f , abs ( X_add ) ) ; title ( ’ Mag Spectrum of Addition ’) ;
16 subplot (2 ,1 ,2) ;
17 plot (f , abs ( X_mult ) ) ;
18 title ( ’ Mag Spectrum of Multiplication ’) ;
Listing 6: Fourier Transform of Combined Signals
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Figure 8: FT of Addition FT of Multiplication

Question 7
Create filters with these specs and show magnitude phase responses:

a) fp = 8 Hz, fq = 20 Hz

b) fp = 15 Hz, fq = 5 Hz

c) fp = [10, 20] Hz, fq = [5, 25] Hz

1 clc ;
2 clear ;
3 close all ;
4 fs = 1000; % Sampling frequency in Hz
5 [ b1 , a1 ] = butter (4 , 8/( fs /2) , ’ low ’) ; % Normalized cutoff
frequency = 8 / ( fs /2)
6 [ h1 , w1 ] = freqz ( b1 , a1 ,1024 , fs ) ;
7 [ b2 , a2 ] = butter (4 , 15/( fs /2) , ’ low ’) ; % Normalized cutoff
frequency = 15 / ( fs /2) [ h2 , w2 ] = freqz ( b2 , a2 ,1024 , fs ) ;
8 [ b3 , a3 ] = butter (4 , [10 20]/( fs /2) , ’ bandpass ’) ; % Normalized
passband = [10 20] / ( fs /2)
9 [ h3 , w3 ] = freqz ( b3 , a3 ,1024 , fs ) ;
10 % Plotting the magnitude and phase response of the first filter
11 figure ;
12 subplot (2 ,1 ,1) ;
13 plot ( w1 , abs ( h1 ) ) ; title ( ’ Filter1 Mag (8 Hz ) ’) ;
14 subplot (2 ,1 ,2) ;
15 plot ( w1 , angle ( h1 ) ) ; title ( ’ Filter1 Phase ’) ;
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16 figure ;
17 subplot (2 ,1 ,1) ;
18 plot ( w2 , abs ( h2 ) ) ; title ( ’ Filter2 Mag (15 Hz ) ’) ;
19 subplot (2 ,1 ,2) ;
20 plot ( w2 , angle ( h2 ) ) ; title ( ’ Filter2 Phase ’) ;
21 figure ;
22 subplot (2 ,1 ,1) ;
23 plot ( w3 , abs ( h3 ) ) ; title ( ’ Filter3 Mag (10 20Hz ) ’) ;
24 subplot (2 ,1 ,2) ;
25 plot ( w3 , angle ( h3 ) ) ; title ( ’ Filter3 Phase ’) ;
Listing 7: Filter Design and Responses

Figure 9: Filter Response 1

Question 8
Pass signals from Q1a, Q1b, Q2, Q5a, Q5b through the three filters; show time-domain
FFT.
1 clc ;
2 clear ;
3 close all ;
4 % Signal Generation
5 fs = 1000;
6 t = 0:1/ fs :1;
7 N = length ( t ) ;
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Figure 10: Filter Response 2

8 f = linspace ( - fs /2 , fs /2 , N ) ;
9 % Signal Definitions
10 x1 = 2* sin (2* pi *5* t ) +1.6* sin (2* pi *10* t ) +0.3* sin (2* pi *20* t ) ;
11 x2 = 1.8* sin (2* pi *2* t ) +0.8* sin (2* pi *25* t ) ;
12 % Signal Operations
13 conv_x = conv ( x1 , x2 , ’ same ’) ; x_add = x1 + x2 ; x_mult = x1 .* x2 ;
14 % Butterworth Filter Design
15 [ b1 , a1 ] = butter (4 ,8/( fs /2) , ’ low ’) ;
16 [ b2 , a2 ] = butter (4 ,15/( fs /2) , ’ low ’) ;
17 [ b3 , a3 ] = butter (4 ,[10 20]/( fs /2) , ’ bandpass ’) ;
18 % Signal Processing
19 signals = { x1 , x2 , conv_x , x_add , x_mult };
20 names = { ’ x1 ’ , ’ x2 ’ , ’ conv ’ , ’ add ’ , ’ mult ’ };
21 for i =1: length ( signals )
22 for j =1:3
23 b = eval ([ ’b ’ , num2str ( j ) ]) ; a = eval ([ ’a ’ , num2str ( j ) ]) ;
24 y = filter (b ,a , signals { i }) ; Y = fftshift ( fft ( y ) ) ;
25 figure ;
26 subplot (2 ,1 ,1) ; plot (t , y ) ; title ([ names { i } , ’ filt ’ ,
num2str ( j ) ]) ;
27 subplot (2 ,1 ,2) ; plot (f , abs ( Y ) ) ; title ([ ’ FFT of ’ , names { i } ,
’ filt ’ , num2str ( j ) ]) ;
28 end
29 end
Listing 8: Filtering and FFT of All Signals
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Figure 11: Filter Response 3

Figure 12: Filtered Signal Diagram

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Figure 13: Filtered Signal Diagram

Figure 14: Filtered Signal Diagram

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Figure 15: Filtered Signal Diagram

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Figure 16: Filtered Signal Diagram