I am confused about this Q&amp;A :  Interpolation by factor of 2

If my input signal 
$$
x[n]= x0,x1,x2,x3
$$
then according to the threads explaination my $v[n]$ will be 

$$
v[n]=x0,0,x1,0,x2,0,x3,0
$$

$x[n] \rightarrow$ zeropad $\rightarrow v[n]$

$v[n]\rightarrow$ LPF $\rightarrow y[m]$

My $y[m]$ is the output of LPF which removes aliases. So basically LPF transfer function is given as 

$$
y[m] = v[n]*h[n]
$$

i,e. $y[m]=\displaystyle\sum_{n=0}^{\infty}h(m-n)v(n)$

So here $h[m]$ is my filter coefficients and  $v[n]$ is my zero padded input signal...
so, if I multiply zero with my filter coefficients, then my output will also be zero...

If I send 10 input samples, after zero padding I will get 20 samples, out of which 10 will be zero....

So what is the use of getting zero as my output? Correct me if am wrong (I know I am wrong, but please give me some idea how zero padding &amp; LPF is helping in this regard).

For FIR filter: $y(n)=h(0)x(n)+h(1)x(n−1)+....+h(N−1)x(n−N+1)$,
 where $x(n)$ is the input signal,
 $y(n)$ is the output signal, 
$h(n)$ is the impulse response, 
and $N$ is the filter length. 

For simplicity, I am taking order $N=4$,and some random numbers

    (time) n --&gt; [ 0  1  2  3] 
         x[n]--&gt; [ 2  4  6  8] 
         h[n]--&gt; [.1 .2 .3 .4] 


what is $y[2.5]$??? 

                  n--&gt;[0 0.5 1 1.5 2 2.5 3 3.5]  
               v[n]--&gt;[2  0  4  0  6  0  8  0 ] (after zero padding)


Lets calculate for $y[2.5]=h(0)x(2.5)+h(1)x(1.5)+h(2)x(0.5)+h(3)x(-0.5)$ 

so here $x(2.5)=x(1.5)=x(0.5)=0$

Please answer this to clear my confusion???


Question: PHP getting cover image from Google Books API
Answer: You mean by scraping it? Theres probably legal issues if you do that...

But looking at their site (and only one result), the image is in this part of the html:

&lt;div class="bookcover"&gt;&lt;a href="http://books.google.com/books?id=btIQAAAAYAAJ&amp;amp;printsec=frontcover&amp;amp;source=gbs_ge_summary_r&amp;amp;cad=0" &gt;&lt;img src="http://bks0.books.google.com/books?id=btIQAAAAYAAJ&amp;printsec=frontcover&amp;img=1&amp;zoom=1&amp;edge=curl&amp;imgtk=AFLRE70zzwoUCkgdipXt2aghe0i9TUKTDTH4s71IXTEPNlUNi9dN-aiJDCtxor4tL3yqq8KrHzEiHTyysqSFu2vH2QNm3JNCjyjm3f-B_N2VKYZqrcaqHfUXDdOea2f3FBR3nFIUxtk7" alt="Front Cover" title="Front Cover" width=128 border=1 id=summary-frontcover &gt;&lt;/a&gt;&lt;/div&gt;


Use something like http://php.net/manual/en/class.domxpath.php to extract it. Should be quite straight forward. You will probably not want to just use file_get_contents() for the image though, use curl or something.