We can recreate the illusion of sound sources in $3-$dimensional space using vectorize operations. We will study both delay and basic attenuation to create the illusion of sound positioned directly to the left of the listener. Consider the following sample of a stereo audio recording $($transposed as a row$)$:

L $[4,-4,2,-2,2,-2,4,-4,0,4,-4,0,0,0]$

R $[4,-4,2,-2,2,-2,4,-4,0,4,-4,0,0,0]$

We can insert $3$ zeros at the beginning of the right column, and remove $3$ entries a the end of the right column to delay the right channel by $3$ samples. This correspond to a delay of $0\mathrm{.}0625ms$ at a sample rate of $48kHz.$

L $[4,-4,2,-2,2,-2,4,-4,0,4,-4,0,0,0]$

R $[0,0,0,4,-4,2,-2,2,-2,4,-4,0,4,-4]$

Question $1)$ Using one of your previously recorded speech signals $($saying the phrase "the quick brown fox jumps over the lazy dog"$),$ copy the column to the right to create two identical columns, and save this signal to a WAV file. Label this file with the convention $$team$[[$yourteam#$]]-$stereosoundfile$-[[$delay$]].$wav$.$ Then, delay

the second column by the average number of samples calculated

previously, and save this signal. Finally, delay the second column

by $1$ms$,10$ms$,$ and $100$ms$,$ and save these. Have each team

member listen to the files and compare the acoustic experience of

each of these files $(0$ms$,$ avghead, $1$ms$,10$ms$,100$ms$).$

The second "trick" we can use is an attenuation of the right channel to model the human head. We can apply an attenuation of about $-3dB$ by multiplying by $0\mathrm{.}5.$

L $[4,-4,2,-2,2,-2,4,-4,0,4,-4,0,0,0]$

R $[2,-2,1,-1,1,-1,2,-2,0,2,-2,0,0,0]$

L $[4,-4,2,-2,2,-2,4,-4,0,4,-4,0,0,0]$

R $[0,0,0,2,-2,1,-1,1,-1,2,-2,0,2,-2]$

Question $2)$ Attenuate the right channel of the $0$ms delay audio by $-1\mathrm{.}5$dB$,-3$dB$,$and $-6$dB$,$ and save these signals to WAV files. Label these files with the convention $$team$[[$yourteam#$]]-$stereosoundfile$-[[$delay$]]-[[$attenuation$]].$wav$.$ Perform the same operation to the average

head delay file. Have each team member listen to the files and

compare the acoustic experience of each of these files $(0$ms$,0$ms$1\_5$dB$,0$ms$-3$dB$,0$ms$-6$dB$,$ avghead, avghead$-1\_5$dB$,...).$

Question $3)$ Which delay and attenuation values produced the most convincing illusion that the sound source is to the left of the listener? How might you improve the basic model to improve the illusion or support sounds from other locations in $3$D space?