Question

A voltage signal is created by adding the output from a white noise generator and from a sinewave generator. The white noise is band limited in the range 30 to 80 Hz and has a root mean square value (rms) of 1.5 V. The sine wave has a frequency of 50 Hz and an amplitude of 1.0 V.

The signal is digitized at 200 samples per second and a spectral density is obtained by the Fast Fourier Transfer (FFT) algorithm, using the average of an enormous number of frames. Each frame contains 256 data points.

Assuming that the spectral density is incredibly accurate due to the huge number of averages, sketch the resulting spectral density. Your sketch should include scales and units on both the x and y-axis

Answer 1

use MATLAB to sketch spectral density

on x axis there will be frequency and with fft calculate y axis and this sketch is power spectral density

so there is signai A =sin(2*pi*50*t)

now there is white noise signal which adds with A hence a signal B= A+noise signal

so first we will plot( B(1:50))

title(noise signal)

now we will finf fast fourier transform fft

so K= fft(B,200)

now we will compute the power spectral density we will use CONJ ad we will form a frequency axis for 256 data points

Y axis, Syy=K.*conj(K)/256

X axis ,F=200/(0:256), lable frequency

plot(F,Syy)