Eleda has a new song, Adiós , a highlight of which is a loud Soprano C note (104

Question

Eleda has a new song, Adiós, a highlight of which is a loud Soprano C note (1046.50 Hz). This was recorded live at her recent concert at Sheepish Stadium via a microphone connected to a preamp that approximates a consumer line level signal.

Upon inspection the signal recorded was found to be (in Volts):

Vmicrophone(t)=0.447cos(2093t)+0.314cos(100t)+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 secretive producer (Off-the-Record Records) only sampled this at 2,205 Hz (instead of the expected 44.1 KHz).

1) Please plot the Voltage signal from microphone ( Vmicrophone(t)Vmicrophone(t)) for t=0 to 1 second.

2) 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.

3) 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?  

4) Suppose that our singer catches a cold, and rather than producing a 1046.50 Hz sine wave, she produces a raspy 1046.50 Hz square wave. Does the sampled waveform change? If it changes, briefly detail how. If it stays the same, briefly explain why.

Explanation / Answer

Part 1:

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');

%Run the above code in matlab to plot the curve

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');

%Run this for the second part

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

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

plot(t,x);

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