[SciPy-User] frequency components of a signal buried in a noisy time domain signal

[Ivo Maljevic]

Nils,
Yes, FFT can be used to visualize the frequency content of a signal buried
in the noise, especially if it is is narrowband,
even though more advanced spectral analysis is required for advanced
applications.

I cannot help you with non-uniformly spaced samples (some sort of
interpolation comes to mind), but next power of 2 should be trivial. Without
checking for the argument type, you can implement the function like this:

def nextpow2(n):
    m_f = np.log2(n)
    m_i = np.ceil(m_f)
    return 2**m_i


Hope it helps,
Ivo

On 26 February 2010 14:05, Nils Wagner <nwagner at iam.uni-stuttgart.de> wrote:

> Hi all,
>
> A common use of Fourier transforms is to find the
> frequency components of a signal buried in a noisy time
> domain signal.
>
> I found a Matlab template at
>
> http://www.mathworks.com/access/helpdesk/help/techdoc/ref/fft.shtml
>
> Matlab has a function
>
> nextpow2(L)
>
> Is there a similar build-in function in numpy/scipy ?
>
> I tried to convert the m-file into a pythonic form.
> What is needed to obtain a similar figure of the
> single-sided amplitude spectrum using
> numpy/scipy/matplotlib ?
>
>
> from numpy import sin, linspace, pi
> from numpy.random import randn
> from pylab import plot, show, title, xlabel, ylabel
> from scipy.fft import fft
>
> Fs = 1000. #                          Sampling frequency
> T  = 1./Fs #                          Sample time
> L  = 1000  #                          length of signal
> t  = arange(0,L)*T
> x  = 0.7*sin(2*pi*50*t)+sin(2*pi*120*t)
> y  = x + 2*randn(len(t))
> plot(Fs*t[:50],y[:50])
> title('Signal corrupted with zero-mean random noise')
> xlabel('Time (milliseconds)')
> #
> #
> #
> #NFFT = 2^nextpow2(L); # Next power of 2 from length of y
>
> Y = fft(y,NFFT)/L
> f = Fs/2*linspace(0,1,NFFT/2+1)
> plot(f,2*abs(Y[:NFFT/2+1]))
> title('Single-sided amplitude spectrum of y(t)')
> xlabel('Frequency (Hz)')
> ylabel('|Y(f)|')
> show()
>
>
> What can be done in case of nonequispaced data ?
>
> http://dx.doi.org/10.1137/0914081
>
> Thanks in advance
>
>                     Nils
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