Please correct 'discreet' to 'discrete' (where ever it appears in the above

response). Thanks for your patience.

On 5/30/09, Arunkumar K.P. wrote:

>

> Since the description of your problem confines to the discreet domain, the

> resolution of an N point DFT is given by 1/N on discreet frequency scale.

> Therefore to "resolve" a monochromatic wave of frequency 1/90 (i.e period > 90
samples) from another of discreet frequency 1/75 (i.e. period = 75

> samples) you need to take a DFT whose resolution is better than
(1/75-1/90).

> To make use of a power of two points FFT, this would mean to use atleast
512

> sample points for the signal records [512 is the nearest power of two

> greater than 90*75/(90-75)E0]. Probably you would have used a 512 point or

> 1024 point FFT to find the spectral components over a simulated signal with

> a record length more than 450 samples. This is enough to resolve period 75

> and period 90 waves. But to resolve period 84 and period 90 waves you must

> use atleast 2048 point FFT [2048 is the nearest power of two geater than

> 90*84/(90-84)60] over a signal simulated for more than 1260 points.

>

> The second part of your problem is not very clear to me. May be you are

> referring to the problem of resolving a strong sinusoid and a weak sinusoid

> (strong and weak refer to the amplitudes) which lies close by. If two
waves

> one with period P1 samples and another with period P2 samples are such that

> N is some integer multiple of both P1 and P2 (eg. P1d samples, P22

> samples and N24 samples of signal record) then it is always possible to

> resolve the two waves using an N point FFT regardless of their relative

> amplitude. But this is seldom the case in practice and one has to resolve

> waves of arbitrary periods. One way to solve the problem of "spectral

> leakage" (i.e. a strong frequency affecting a weak frequency) is to use

> an "appropriate" window that results in a lower side-lobe level than a

> rectangular window whose side-lobe level is -13dB. The choice of window

> depends on the kind of resolution (ie main lobe width of the FFT filter)
and

> the level of intereference suppression (typically through side-lobes) your

> application demands. Interestingly there are other spectrum estimators than

> FFT which yield superior resolution and intereference rejections.

>

> Best Regards,

> Arunkumar KP

>

> On 5/26/09, acepsut wrote:

>

>> Hello all,

>>

>> I have a problem about period amplitude and phase distortion when

>> performing a fourier trasform. The problem arise when I have two periods

>> with different amplitude but very close.

>>

>> An example; I create one cosine function with period amp` and phase

>> 2.2 rad, another one with period= 75 amp0 phase=1.1 and then sum togheter.

>>

>> If I perform an FT on this sum of cosines I get correctly periods,

>> amplitudes and phases for each function. But if I change the period of

>> second cosine from 75 to 84, I do not have correct values of this one.

>>

>> Higher amplitude of cosine with period= 90 create a distortion on second

>> one, and I get uncorrect period amplitude and phase only in the cosine
with

>> period, I get period.x, higher amplitude and of course an incorrect

>> phase on angle plot.

>>

>> Why does this strange occurs? And what to do to have correct values of

>> lower magnitude cosine?

>>

>> Thanks in advance

>>

>> Alberto

>>

>>

>>