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Use Fourier transforms to find the frequency components of a signal buried in noise.

Specify the parameters of a signal with a sampling frequency of 1 kHz and a signal duration of 1.5 seconds.

Form a signal containing a 50 Hz sinusoid of amplitude 0.7 and a 120 Hz sinusoid of amplitude 1.

Corrupt the signal with zero-mean white noise with a variance of 4.

Plot the noisy signal in the time domain. It is difficult to identify the frequency components by looking at the signal X(t).

Compute the Fourier transform of the signal.

Compute the two-sided spectrum P2. Then compute the single-sided spectrum P1 based on P2 and the even-valued signal length L.

Define the frequency domain f and plot the single-sided amplitude spectrum P1. The amplitudes are not exactly at 0.7 and 1, as expected, because of the added noise. On average, longer signals produce better frequency approximations.

Now, take the Fourier transform of the original, uncorrupted signal and retrieve the exact amplitudes, 0.7 and 1.0.

PFL stands for Preparation for Future Learning (various schools)

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The site was disturbed in 1858 when a road was cut through it In 1870, the Weehawken shoreline was reconfigured for the railroad tracks, and the dueling ground