A spectrum analyser digitises a signal for a record length

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Coupled oscillators, normal modes and Fourier analysis · Coupled oscillators, normal modes and Fourier analysis

Modes, Packets and Media, Ch The continuum limit, Fourier series and the spectrum of a measured signal

Problem

T=0.40\,\mathrm{s}

, sampled at a rate far above the Nyquist requirement. The signal contains two pure tones at

2000.0\,\mathrm{Hz}

and

2002.0\,\mathrm{Hz}

. ((a)) State the frequency resolution of this record and decide whether the two tones are resolved in its spectrum. ((b)) Find the minimum record length, at the same sampling rate, that would resolve them.

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