Approximation for mean(abs(fft(vector)))?

Question

Some MatLab code I'm trying to simplify goes through the effort of finding FFT, only to take the absolute value, and then the mean:

> vector = [0 -1 -2 -1 0 +1 +2 +1];
> mean(abs(fft(vector)))
ans = 2

All these coefficients are built up, then chopped back down to a single value. The platform I'm working on is really limited, and if I can get by without using FFT, all the better. Is there a way to approximate these operations without FFT?

Can assume vector will be at most 64 values in length.

Answer 1

I think this is a just a very inefficient way of calculating the RMS value of the signal. See Parseval's Theorem. You can probably just simplify the expression to:

sqrt(mean(vector.*vector))

Answer 2

If your vector is real and has zero average as in your example, you can take advantage of the fact that the two halves of the DFT are complex-conjugate (from basic signal processing) and save half the abs computations. Also, use sum, which is faster than mean:

fft_vector = fft(vector);
len = length(fft_vector)/2; 
sum(abs(fft_vector(1:len)))/len