Question

Consider a signal x(t) = 20 sinc(10t) is to be represented by
samples using ideal (impulses) sampling.

a) Sketch the signal spectral density X(f).

b) Find the minimum sampling frequency that allows reconstruction
of x(t) from its samples.

c) Sketch the sampled spectrum Xs(f) in the range [-55, 55] with
sampling frequency fs = 25 Hz.

Answer #1

Given signal x(t) = sinc(t):
1. Find out the Fourier transform of x(t), find X(f), sketch
them.
2. Find out the Nyquist sampling frequency of x(t).
3. Given sampling rate fs, write down the expression of the
Fourier transform of xs(t), Xs(f) in terms of X(f).
4. Let sampling frequency fs = 1Hz.
Sketch the sampled signal xs(t) = x(kTs) and the Fourier
transform of xs(t), Xs(f).
5. Let sampling frequency fs = 2Hz. Repeat 4.
6. Let sampling frequency...

Consider the signal x(t) = 3 cos 2π(30)t + 4 .
(a) Plot the spectrum of the signal x(t). Show the spectrum as a
function of f in Hz. ?π? For the remainder of this problem, assume
that the signal x(t) is sampled to produce the discrete-time signal
x[n] at a rate of fs = 50 Hz.
b Sketch the spectrum for the sampled signal x[n]. The spectrum
should be a function of the normalized frequency variable ωˆ over
the...

The signal x(t)=sinc2(100t) is sampled with frequency
fs=150sample/sec 1. Determine the spectral representation of the
sampled signal (n=-3 to n=3). 2. Plot the spectral representation
of the sampled signal and determine if the signal has aliasing. 3.
Determine the minimum frequency of sampling (Nyquist sampling
frequency) so that the signal can be reconstructed using an ideal
low pass filter. Justify your answer.

Consider speech signal x(t), which has the magnitude spectrum
X(f)= rect(f/100).
Sketch the magnitude spectrum of the sampled x(t) resulted by
conducting natural sampling with the sampling freq 180Hz. Comment
on your result.
Discuss how to perform digital to analog conversion to recover
x(t). Is it possible to fully recover x(t) without distortion?
Justify your answer.

A signal x(t)=2 sin(62.8 t)*u(t) is sampled at a rate of 5 Hz,
and then filtered by a low-pass filter with a cutoff frequency of
12 Hz. Determine and sketch the output of the filter.

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,...

Question : Design the low and high pass filter for the signal,
x(t) = 10 sin (10 t) + 1 sin (1000 t) by MATLAB
Is below answer right?
at ?High pass , 5row
shouldn't this change from sin(100*t) ?
sin(1000*t)
x = 10*sin(10*t) + 1*sin(100*t); ? x = 10*sin(10*t) +
1*sin(1000*t); ???
.....................................................................................................................................................
?Low pass
clc;
rng default
Fs=2000;
t=linspace(0,1,Fs);
x=10*sin(10*t)+sin(1000*t)%given signal
n=0.5*randn(size(t));%noise
x1=x+n;
fc=150;
Wn=(2/Fs)*fc;
b=fir1(20,Wn,'low',kaiser(21,3));
%fvtool(b,1,’Fs’,Fs)
y=filter(b,1,x1);
plot(t,x1,t,y)
xlim([0 0.1])
xlabel('Time (s) ')
ylabel('Amplitude')
legend('Original Signal','Filtered Data')...

It is known that a real valued signal x(t) has been determined
only from its samples when the sampling frequency is ws=10,000
π t
For which values of w we can guarantee that F(w) it's equal to
zero?

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