IFFT on padded vector with zeros

hello,

I have a vector that padded with zeros and I want to perform IFFT on this vector, as follows: [ 1 2 3 4 0 0 0 . . . 0 0 4 3 2 1] In that case, do I need to multiply IFFT with scaling factor?

Thanks,

Answer 1

[Matt J]

You might have to scale by a length-dependent factor, depending on what it is you're trying to preserve. For example, if you want to satisfy Parseval's theorem, you have to scale by sqrt(length(x)),

    >> x1=[ 1 2 3 4  4 3 2 1];
    >> x2=[ 1 2 3 4 0 0 0 0  4 3 2 1];
    >> 
    >> y1=ifft(x1)*sqrt(length(x1));
    >> y2=ifft(x2)*sqrt(length(x2));

    >> [norm(x1), norm(y1)]   %Parseval satisfied

    ans =

        7.7460    7.7460

    >> [norm(x2), norm(y2)] %Parseval satisfied

    ans =

        7.7460    7.7460

Answer 2

[Michael Adelman]

I want to pad this vector with zeros before IFFT for OFDM transmission. In that case what scaling factor should be?