When working on a laboratory, your coworkers ask you to perform Fourier analysis

Question

When working on a laboratory, your coworkers ask you to perform Fourier analysis to find frequency

information about some signals they are measuring on an oscilloscope. They give you this

information in a MATLAB workspace file named voltage.mat .

(a) You are first given oscilloscope data that was recorded at a sampling rate of 150 Hz. The

voltage V(t) and the time t of the measurements are the V150 and t150 variables in your

workspace file.

Using MATLAB, perform the following tasks:

i. Plot voltage as a function of time for 0< t < 1/8s

ii. How long did we sample the signal?

iii. Take the Fourier Transform F (V (x)) of the voltage, (you may use fft() to do so), and

plot the magnitude of the frequency response |F (V (x))|  as a function of frequency f [Hz].

iv. What are the primary frequency components in this signal?

(b) Another of your coworkers was sampling the same voltage signal with a slightly more modern

oscilloscope, and she was able to obtain a sampling rate of 200 Hz. The measurements she

obtained are saved as the V200 and t200 variables in your workspace file.

Repeat part a) using the 200 Hz data. Are there any discrepancies in the frequency data when

the sampling frequency fs = 200 Hz? If there are, discuss your observations, and explain the

source of the discrepancies.

(c) You also have data for the signal that was captured with fs = 300 Hz; this data is stored as

the V300 and t300 variables in your workspace file. Repeat part b) using this data.

(d) Finally, your research group re-ran the calculations with an oscilloscope capable of sampling

the voltage signal at 600 Hz. This data is available to you in the V600 and t600 variables in

your workspace file. Repeat part b) using this data.

Please access the voltage.mat file at https://drive.google.com/file/d/0B1gNpRvpWsloS05sd0hvR2dVX0E/edit?usp=sharing or

https://docs.google.com/file/d/0B1gNpRvpWsloS05sd0hvR2dVX0E/edit?pli=1

it is 105 kb file with all the data. I need this question solved urgently. Please send me a correct working code completely finished in matlab. Please save me. Thank You.

Explanation / Answer

a) i. plot( t150(1 : 150/8), V150(1:150/8));

ii. no of samples in t150 = 1201

sampling has been taken for 1200/150 =8 s

iii. fs = 150;

V = fft(V150);

f = fs/2*linspace(-1,1,length(V150));

plot(f, abs(V));

iv. From the graph max frequency component are 0 Hz and 50 hz

b) i. plot( t200(1 : 200/8), V200(1:200/8));

ii. no of samples in t200 = 1601

sampling has been taken for 1600/200 =8 s

iii. fs = 200;

V = fft(V200);

f = fs/2*linspace(-1,1,length(V200));

plot(f, abs(V));

iv. From the graph max frequency component are 25 Hz and 75 hz

there is change in maximum frequency component which is 25 Hz and 75 Hz in 2nd acse while 0 Hz and 50 Hz in 1 st case. This due to under sampling and aliasing.

c )   i. plot( t300(1 : 300/8), V300(1:300/8));

ii. no of samples in t300 = 2401

sampling has been taken for 2400/300 =8 s

iii. fs = 300;

V = fft(V300);

f = fs/2*linspace(-1,1,length(V300));

plot(f, abs(V));

iv. From the graph max frequency component are 25 Hz and 75 hz

d ) i. plot( t600(1 : 600/8), V600(1:600/8));

ii. no of samples in t600 = 4801

sampling has been taken for 4800/600 =8 s

iii. fs = 600;

V = fft(V600);

f = fs/2*linspace(-1,1,length(V600));

plot(f, abs(V));

iv. From the graph max frequency component are 25 Hz and 75 hz

in b) c) and d) teh max frequency components are same because signhal is sampled above nyquist rate while it is different in a) due to sampling below nyquist rate and thereore aliasing

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.