FFT wrong value?

Question

Randomly building a very easy sound spectrum analyzer.

Given this python code:
http://rosettacode.org/wiki/Fast_Fourier_transform#Python
Implemented like this:

import math
from cmath import exp, pi

def fft(x):
    N = len(x)
    if N <= 1: return x
    even = fft(x[0::2])
    odd =  fft(x[1::2])
    return ([even[k] + exp(-2j * pi * k / N) * odd[k] for k in xrange(N / 2)] + 
            [even[k] - exp(-2j * pi * k / N) * odd[k] for k in xrange(N / 2)])

#res = fft([1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0])
res = [math.sin(k) / 2.0 + 0.5 for k in xrange(64)]  # positive sine wave
res = fft(res)

for k in xrange(64/2):
    # get the amplitude...
    sqr = math.sqrt(res[k].real * res[k].real + res[k].imag * res[k].imag)
    if sqr > 0:
        print 20 * math.log10(sqr)  # ...in decibels
    else:
        print "-INF"

I get these results:

30.1160980385
-22.9398603241
-18.5295301528
-15.0005952198
-11.9809319241
-9.15035811436
-6.26269080991
-3.05038111824
0.930742121289
6.85461898041
23.4890109499 <-- PEAK
11.1462405429
4.62796511517
1.22261338459
-1.03611868864
-2.69639200998
-3.98905968693
-5.03263380282
-5.89570135908
-6.62130526828
-7.23808293566
-7.76594168565
-8.21919399668
-8.60840088318
-8.94151058446
-9.22459042752
-9.46231245749
-9.6582838436
-9.81527579404
-9.93538377539
-10.0201395611
-10.070588143

Which are pretty OK. I have a 23 dB peak supposedly at the frequency of the input sine wave and everything seems fine.

Only thing, what is the first value: 30.1160980385? Is that some extremely loud bass going on? Or more likely a flaw in the algorithm. In this case how do I fix that.

Last question. Is it ok for the fft to have negative values as input? In the above example I used a sine wave which is always positive ranging in [0,1]. Do I screw up everything if I want to pass values ranging in [-1,1]?

EDIT:

I removed the edit because it was off-topic. You can read what it was about here:

FFT unexpected frequency shift after window function application

It looks like this is a learning project, which if true by all means keep learning how to implement the FFT yourself. If you want to use a robust library look at `scipy.fftpack` which will be faster than any pure-python solution. Take a look at http://stackoverflow.com/questions/19122157/fft-bandpass-filter-in-python/19124329#19124329 for example, and other uses of the library on SO for examples. — Hooked, Oct 04 '13 at 14:09

Paul R · Accepted Answer · 2013-10-04T10:30:37.497

2

You apparently have a large DC component due to the fact that your sine wave has an offset of +0.5. If you make your sine wave have a zero mean (i.e. a range of say +/- 0.5 or +/- 1.0) then your spectrum should look better at the DC (0 Hz) end.

Note also that you have not use a window function prior to the FFT so you will get spectral leakage (a "smearing" of the spectrum) and this can exacerbate the effect of any DC component.

edited Oct 04 '13 at 10:30

answered Oct 04 '13 at 10:25

Paul R

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Thank you, that makes sense. I now implemented a window function and edited my OP post. For some reason now the peak got shifted. I messed with the code perhaps? – user2464424 Oct 04 '13 at 14:04
Sorry, I'm not a Python programmer, so I can only give general advice on the DSP theory - the code looks OK to my untrained eye, but it sounds like you may still have some debugging to do... – Paul R Oct 04 '13 at 14:11
1

I put the shifting problem into another question: [link](http://stackoverflow.com/questions/19184597/fft-unexpected-frequency-shift-after-window-function-application/19189395). I eventually answered myself, lol. Just a stupid conceptual mistake about windowing :) – user2464424 Oct 04 '13 at 20:08

FFT wrong value?

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