A strong spectral line lies midway between two frequency bins

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Computational Physics · Scientific programming for physicists

Scientific Computing for Physicists, Ch Spectra with error bars: the fast transform, convolution and spectral estimation

Problem

A strong spectral line lies midway between two frequency bins. Its leakage ten bins away, relative to its own peak, is about

-26\,\mathrm{dB}

with no window (rectangular),

-67\,\mathrm{dB}

with a Hann window and

-96\,\mathrm{dB}

with a four-term Blackman-Harris window. The three windows' equivalent noise bandwidths are

1.00

1.50

and

2.00

bins. A second, genuine line lies ten bins from the strong one and is

60\,\mathrm{dB}

weaker. ((a)) Decide for each of the three windows whether the weak line stands above the strong line's leakage at the weak line's position. ((b)) The weak line must also be seen against broadband noise, whose power in each bin grows in proportion to the window's equivalent noise bandwidth. Of the windows that pass part (a), state which should be used. ((c)) The strong line is retuned to sit exactly on a bin. Which windows now show the weak line?

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