Question

Pink has a new song, Noise, a highlight of which is a loud Mezzo-soprano As note (880 Hz) This was recorded live at the recent concert at 1E6 Dreams Stadium via a microphone connected to a preamp that approximates a consumer line level signal [t: 1 million dreams is 2,740 person years at 1 dream/day] Upon inspection the signal recorded was found to be (in Volts) microphone(t)-0.42cos(1 760π) +0.3 1 4cos(1 000 + 1 It appears that joint between the 3.5 mm connector and the unbalanced wire was not properly shielded and thus introducing a 50 Hz whine. To add insult to injury, the recording was rushed to get ahead of a demolition for refurbishment, so by accident it was sampled at 1,044 Hz (instead of the expected 44.1 KHz) (a) Please plot the Voltage signal from microphone(Vmicrophone (t)) for t-0 to 1 second (b) Please plot the sampled, digitized signal captured on a basic audio card with simple line level (i.e., no negative voltage rail). Again, for t-0 to 1 second [hint: a line level signal is basically an alternating current signal with a DC offset] (c) It is proposed that all this can be solved "easily" by changing the anti-aliasing (or band-limiting) filter to add a high-pass filter with a cut-off of 100 Hz between the pre-amp and the line-level input on the audio card. Briefly discuss if this will work? hint: it might help to generate a plot of the signal with this filter]

Answer 1

Given that

we have to plot the voltage signal from microphone

a) enter the following program in matlab to plot the voltage signal obtained from the microphone

fs=2205;

T=1/fs;

t=0:T:1;

Vt=0.447*cos(2093*pi*t)+0.314*cos(100*pi*t)+1;

plot(t,Vt);title('voltage signal from the microphone');

xlabel('time (s)');ylabel('Voltage');

the signal is as follows

voltage signal from the microphone 1.8 1.6 1.4 1.2 0.8 0.6 0.4 0.2 0 0. 02 03 04 0.5 06 0.7 0.8 0.9 time (s)

b) without dc offset the signal is plotted using the following equation

fs=2205;

T=1/fs;

t=0:T:1;

Vt=0.447*cos(2093*pi*t)+0.314*cos(100*pi*t);

plot(t,Vt);title('voltage signal from the microphone');

xlabel('time (s)');ylabel('Voltage');

the waveform is

voltage signal from the microphone 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 0 0. 02 03 04 0.5 06 0.7 0.8 0.9 time (s)

c) enter the following to design the high pass filter in matlab

d=fdesign.highpass('N,Fc',10,100,2205);
designmethods(d);
Hd = design(d);
y = filter(Hd,Vt);
plot(t,y);

this is not goining to work since the sampling frequency is still at 2205Hz and not at 44100Hz

d) enter the following to get the square wave plot

x = square(t);
plot(t,x);

the waveform changes its shape since it is a square wave now