For the code below, Can you please help me to allow the decaying notes $($i$.$e$.$ with the windowing function$)$ to overlap slightly in time. Assuming the size of the overlap between two consecutive ADSR functions can be $100$ samples.

Is this goin to improve the sound quality?

Hint: Here is an example of how to concatenate two vectors with an overlap. Assume we have

vector $x$ and $y$ given by$,$

$x=\left[\begin{array}{cccccc}1& 2& 3& 4& 5& 6\end{array}\right]$

$y=\left[\begin{array}{cccccc}7& 8& 9& 1& 1& 11\end{array}\right]$

and we want to concatenate them with an overlap of two samples. The first step is to extend both

vectors, by pre and post padding them by zeros, to a length of the final concatenated vector. Note

that the length of the final vector is equal to length$(x)+$ length$($y$)-$ length$($overlap$).$ Therefore,

we should extend vector $x$ by post padding it with zeros of length equal to length$($y$)-$

length$($overlap$)$; similarly, we should extend vector y by pre padding it with zeros of length

equal to length$($ x $)-$length$($overlap$).$ Then, add the two extended vectors. Here is a MATLAB code

which performs the steps explained:

$y=[78891011]$;

overlap $=2$;

$x1=[x,$ zeros$(1,$ length$(y)-$overlap$)]$; $\frac{?}{?}\%$ post zero$-$padded $x$

$y=[$ zeros$(1,$length$(x)-$overlap$),y]$; $\frac{?}{?}\%$pre zero padded $y$

$z=x1+y$;

Also it could be done in one line as:

$z=[x(1$ :end$-$overlap$),x($ end$-$overlap $+1$ :end $)+y(1$ :overlap$),y($ overlap $+1$ :end $)]$

THE CODE:

$\%$ lab$1.$m

clear all

close all

clc

notes $=[\text{'}$A$\text{'}\text{'}$A$\text{'}\text{'}$E$\text{'}\text{'}$E$\text{'}\text{'}$E$\text{'}\text{'}$B$\text{'}\text{'}$C$\text{'}\text{'}$B$\text{'}\text{'}$A$\text{'}]$;

count $=[8000,4000,4000,4000,4000,4000,4000,4000,16000]$;

x$=[]$;

fs$=8000$;

for i $=1$:length$($notes$)$

m $=$ count$($i$)$;

n $=0$:m$-1$;

switch$($notes$($i$))$

case $\text{'}$A$\text{'}$

f$=220$;

case $\text{'}$B$\text{'}$

f$=220*2^(2/12)$;

case $\text{'}$C$\text{'}$

f$=220*2^(3/12)$;

case $\text{'}$D$\text{'}$

f$=220*2^(5/12)$;

case $\text{'}$E$\text{'}$

f$=220*2^(7/12)$;

case $\text{'}$F$\text{'}$

f$=220*2^(8/12)$;

case $\text{'}$G$\text{'}$

f$=220*2^(10/12)$;

end

y $=$ cos$(2*$pi$*$f$/$fs$*$n$)$;

ADSR $=[$linspace$(0,1,0\mathrm{.}05*$m$),$ linspace$(1,0\mathrm{.}8,0\mathrm{.}1*$m$),$ linspace$(0\mathrm{.}8,0\mathrm{.}8,0\mathrm{.}7*$m$),$ linspace$(0\mathrm{.}8,0,0\mathrm{.}15*$m$)]$;

$\%$ Ensure ADSR has the same length as $\text{'}$y$\text{'}$

ADSR $=$ ADSR$(1$:length$($y$))$;

x $=[$x$,$ y $.*$ ADSR$]$; $\%$ Apply ADSR envelope to the signal

end

soundsc$($x$,$ fs$)$;