why doubling is done from 2 to end-1 only in plotting single sided spectrum: P1(2:end-1) = 2*P1(2:end-1); ?

The full code is:

Y = fft(X); 
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
plot(f,P1); 
title('Single-Sided Amplitude Spectrum of X(t)');

[Adam]

Really?! What aspect do you not understand? It just multiplies that part of the array by two and puts the result back in the same place.

[Abhishek Maurya]

Thanks i understand that aspect. I wanted to know what 'end' does? And what this line is suppose to do to in plotting single sided spectrum.The full code is: Y = fft(X); P2 = abs(Y/L); P1 = P2(1:L/2+1); P1(2:end-1) = 2*P1(2:end-1); f = Fs*(0:(L/2))/L; plot(f,P1); title('Single-Sided Amplitude Spectrum of X(t)');

[David Fletcher]

The 'end' just references the last (end) position of the vector, so it effectively replaces everything from the second position to the last but one (end-1) position.

[Adam]

The reason you double the values in a single-sided spectrum is that your full spectrum is based on negative frequency components also and is symmetric (in this example at least) so in order to keep the same total magnitude in the spectrum you double the magnitudes of the positive spectrum when you throw away the negative spectrum.

[Abhishek Maurya]

I understand this . why it is done only from 2 to end-1?

[Adam]

The 1st indexed point is the 0-frequency, the end point is the nyquist frequency. These remain unchanged as they are not part of the repeated spectrum

[Abhishek Maurya]

Thankyou to Adam,John D'Errico and everybody else who showed their interest in answering questions.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[John D'Errico]

end (when used as a subscript) is a shorthand to indicate the last position for the corresponding index.

So V(end) refers to the last element of a vector V. V(2:end) takes all elements but the first in a vector. And V(2:end-1) is the 2nd through penultimate element. This also applies to array indexing.

Therefore

P1(2:end-1) = 2*P1(2:end-1);

merely doubles the indicated elements in the vector P1.

I suppose use of the end keyword might have been confusing to some. They might have created some new keyword name for use in subscripting. They might, for example, have given us a lastIndex keyword, which might be clearer to some. But that in turn is longer to write, and establishes an entirely new keyword, possibly disabling some older code. Since end already existed as a keyword, but one that had no valid context in a subscript, it was deemed safe to use for indexing.

[P Sun]

Hi John, thank you for your answer.

Do you have any idea about why don't use the first and last values?

Many thanks.

Answer 2

[KL]

You probably need to read about matrix indexing.

https://www.mathworks.com/company/newsletters/articles/matrix-indexing-in-matlab.html

https://www.mathworks.com/help/matlab/ref/end.html#bvih9bm

simple example,

>> A = 1:5
A =
     1     2     3     4     5
>> A(end)
ans =

       5
>> A(end-1)
ans =
     4