Question

Given a Cosine signal whose amplitude is 5 volt RMS, and frequency of 1 cycle per second, sample the signal at a rate of 8 samples per second. Using Matlab: Plot the sampled signal as a function of time, Plot the Fourier Coefficients as functions of frequency Plot the frequency spectrum of the signal, centered at 0.

Answer 1

To sample and analyze a cosine signal in Matlab, define the signal, sample it at the desired rate, compute Fourier Coefficients, and plot the time-domain signal and frequency spectrum with the frequency centered at zero.

Step-by-step explanation:

To sample a 5 volt RMS cosine signal at a frequency of 1 Hz at a rate of 8 samples per second using Matlab, we can follow a series of steps:

1. Define the signal with the given amplitude and frequency.
2. Choose a sampling period that corresponds to 8 samples per second, which is the reciprocal of the sampling rate (1/8 seconds).
3. Create a time vector based on the sampling period and duration of signal observation.
4. Sample the signal using the time vector and plot the signal as a function of time.
5. Calculate the Fourier Coefficients of the sampled signal.
6. Plot the coefficients as functions of frequency.
7. Create a frequency spectrum plot of the signal, with the frequency axis centered at 0.

Since the RMS value is given, we would need to calculate the peak amplitude of the cosine wave by multiplying the RMS value by the square root of 2, which would be approximately 7.07 volts (assuming a pure cosine wave without any DC offset).