Some Common FFT Misconceptions


Just for fun, I thought I'd try and list many of the
misconceptions that people seem to have regarding using
the FFT, as seen in various previous posts to comp.dsp.

The FFT is a widely used algorithm because the result has
something (not precisely understood) to do with frequencies.

Some Common FFT Misconceptions:

1.
The FFT will directly produce the frequency of some
phenomena, without regard to the relationship between FFT
length versus the period of any oscillations (e.g. what
rectangular window?), or any envelope on or modulation
of some periodic waveform.

2.
The FFT will find the correct frequency content without
regard to the relationship between the sample rate and the
highest frequency content present in the sampled phenomena,
or any other need for bandlimiting (for example, of closing
price data).
2b.
The sample rate only needs to be twice the highest
present, or twice the highest  frequency of interest for an
FFT to "find" that frequency.

3.
Since the FFT always produces "frequencies", there must
be some periodic phenomena within the sampled data.

4.
The perceive pitch of a musical or speech waveform is the
same as the frequency represented by the FFT magnitude peak.

5.
Windowing (non-rectangular) will always result in a more
accurate frequency estimation.

6.
One can perfectly filter out a signal band by just zeroing
out some bins between an FFT and IFFT.

7.
One can filter in the frequency domain without regard to the
length of the (significant) impulse response of the filter.

8.
One can reconstruct a signal from just the FFT magnitude
result.

9.
One can reconstruct a real signal by just feeding the
"positive frequency" bins to a generic IFFT.

10.
One can extrapolate a signal from an FFT without inferring
circular boundary conditions.

11.
The (complex) FFT contains no information about the time
domain envelope.

11.
The phase of a sinusoid (or how far that sinusoid is away
from Fs/4) does not affect the magnitude result of an FFT.

12.
Information from preceding, overlapping, or different length
FFT frames is of no interest in analyzing the spectrum of
some waveform.

13.
The "resolution" of a frequency estimation depends only
on the FFT length, and has nothing to do with anything
known about the signal-to-noise ratio in the sampled
data.
13b.
More "resolution" of frequency estimation is created by
zero-padding (...beyond that provided by other methods
of interpolation).

14.
An FFT is not just an efficient implementation of a DFT.
(Or: "What's a DFT?")

15.
Using an entire FFT is the best way to check for even a
very small number of frequencies (say a DTMF tone).

16.
The FFT can only operate on vector lengths that are an
integer power of 2.  (Or FFT's of vectors not a power of
2 are "really" slow.)

17.
The performance of an FFT implementation (on contemporary
PC's) depends mostly on the number of arithmetic operations
(or MACs or FMACs).

18.
An FFT is less accurate than using the defining DFT
formula for computation.

19.
???

The above are common FFT misconceptions, or sometimes just
poorly thought out or stated conceptions that can lead to
strange misinterpretations of the results of using an FFT.


IMHO. YMMV.
First posted: 2008-March-28 to comp.dsp
Last edited: 2008-March-31
Ron's DSP web page