An analog signal has the following form: x(t) = Asin(f0t) + Bsin(f1t) + Cn(t) wh

Question

An analog signal has the following form:

x(t) = Asin(f0t) + Bsin(f1t) + Cn(t)

where n(t) is a Gaussian noise process with zero mean and unit variance. A, B and C are real scalar constants, f0 and f1 are the frequencies of two sinusoids. You sample the signal at 100Hz. and take N=256 samples. Adjust the values A, B and C and f0 and f1 to find cases where:

(a) the rectangular window is able to clearly resolve the two sinusoidal components while the Blackman window is not.(use periodogram functions).

(b) the Blackman window is able to clearly show that there are two sinusoidal signals present while the rectangular window is not (use periodogram function).

(c) Averaging in the Welch method is able to show the presence of the two sinuisoidal signals while in the absence of averaging, these spectral peaks are obscured by noise (for this part use N=1024 rather than 256).(use pwelch function)

you can use matlab, but please leave explaination.

Explanation / Answer

Gaussian white noise signal of length L=100,000 using the randn function in Matlab and plot it. Here the underlying pdf is a Gaussian pdf with mean ?=0 and standard deviation ?=2. Thus the variance of the Gaussian pdf is ?2=4.
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