Problem 5 (20 points). A microphone was used to record the acoustic emissions ge

Question

Problem 5 (20 points). A microphone was used to record the acoustic emissions generated by a steel part when impacted with a hammer. This data was saved in a data file called Microphone_data.csv. The first column represents the time in seconds, and the second column is the microphone voltage amplitude, [V]. 0.05 0.1 Time [s) 0.15 0.2 Figure 2. Impact acoustic signal recorded with a microphone. a) Using Fourier Transform find the harmonics composing the microphone data signal. b) Design a filter that would keep the first harmonic and remove all the higher harmonics.

Explanation / Answer

% In the said question no data is given

% Solution-(a) Harmonics of Microphone Data Sgnal

filename = 'Microphone_data.csv';
X = csvread(filename,0,2,[0,2,1039,2]);
Fs = 0.00378; % Sampling frequency
T = 1/Fs; % Sampling period
L = 1040; % Length of signal
t = (0:L-1)*T; % Time vector
Fn = Fs/2; % Nyquist Frequency
FX = fft(X)/L; % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn; % Frequency Vector
Iv = 1:length(Fv); % Index Vector
figure(1)
plot(Fv, abs(FX(Iv))*2)
grid
title('Fourier Transform Of Original Signal ‘X’')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
FXdcoc = fft(X-mean(X))/L; % Fourier Transform (D-C Offset Corrected)
figure(2)
plot(Fv, abs(FXdcoc(Iv))*2)
grid
title('Fourier Transform Of D-C Offset Corrected Signal ‘X’')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
[FXn_max,Iv_max] = max(abs(FXdcoc(Iv))*2); % Get Maximum Amplitude, & Frequency

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% question-(b): Filter Design to reject higher harmoncs

Wp = 2*Fv(Iv_max)/Fn; % Passband Frequency (Normalised)
Ws = Wp*2; % Stopband Frequency (Normalised)
Rp = 10; % Passband Ripple (dB)
Rs = 30; % Stopband Ripple (dB)
[n,Wn] = buttord(Wp,Ws,Rp,Rs); % Butterworth Filter Order
[b,a] = butter(n,Wn); % Butterworth Transfer Function Coefficients
[SOS,G] = tf2sos(b,a); % Convert to Second-Order-Section For Stability
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(3)
freqz(SOS, 4096, Fs); % Filter Bode Plot
title('Lowpass Filter Bode Plot')
S = filtfilt(SOS,G,X); % Filter ‘X’ To Recover ‘S’
figure(4)
plot(t, X) % Plot ‘X’
hold on
plot(t, S, '-r', 'LineWidth',1.5) % Plot ‘S’
hold off
grid
legend('‘X’', '‘S’', 'Location','N')
title('Original Signal ‘X’ & Uncorrupted Signal ‘S’')
xlabel('Time (sec)')
ylabel('Amplitude')

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