Take a Fourier transform of the time series, and determine the seven dominant fr

Question

Take a Fourier transform of the time series, and determine the seven dominant frequencies buried in the noisy time signal. All seven frequencies are either whole numbers or simple fractions of the form 1/n where n is an integer. A dominant frequency (for this problem, not necessarily generally) has an intensity exceeding six times the standard deviation of the intensity above the mean. Note that very low frequencies (less than 0.01Hz. ie- DC signals) can spoof your low-frequency output unless you subtract the mean of the data from the time series before you take the Fourier transform. The function fft and associated documentation will be necessary, and you may wish to use the mean and std functions to deduct the mean and find your peaks.

Explanation / Answer

Remember that the FFT is circular. Inputs which contain an integer number of cycles will come out clean as a single point, in the corresponding bin. Those which do not, act as if they are multiplied by a rectangular pulse in the time domain, which creates convolution by a sinc function in the frequency domain. Since sinc has unlimited support, your supposition that all bins except the closest two would be zero is incorrect. Finding a closed-form analytic solution may be impossible, in which case your best bet would be to start with the center frequency for the two strongest bins and use binary search to find the frequency in-between that most closely corresponds to your actual spectrum.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.