The following charts illustrate a sampled signal and its magnitude spectrum base
ID: 2249294 • Letter: T
Question
The following charts illustrate a sampled signal and its magnitude spectrum based on FFT. Examine the frequency scale of spectrum chart and determine the sampling frequency.
The following charts illustrate a sampled signal and its magnitude spectrum based on FFT. Examine the frequency scale of spectrurm chart and determine the sampling frequency Combined Sine Waveform 15.0 10.0 5.0 0.0 5.0 10.0 15.0 0.0 0.1 0.2 0.3 0.4 0.5 ime (s) Single-sided FFT Spectrum 10.0 8.0 6.0 4.0 2.0 0.0 0.0 25.0 50.0 75.0 100.0 125.0 150.0 Frequency (Hz)Explanation / Answer
For a single sided spectrum of a signal in MATLAB the frequency is on x-axis is given by
f = Fs*(0:(L/2))/L where L is the length of the signl and and Fs is the sampling frequency.
T = 1/Fs; % Sampling period
t = (0:L-1)*T; % Time vector for plotting x(t)
The sampling frequency from the figure is given by 150*2 = 300 samples/sec.
Therefore Fs = 300;
T = 1/Fs = 1/300;
from combined waveform in figure 1, the time signal is from 0 sec to 0.42 sec.
therefore 0:1/300:0.42 is the time vector.
length of the signal is therefore given by L = length(0:1/300:0.42) = 127.
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