Signal System Task 2 Assignment Solution and Analysis Report

This document presents a detailed solution to a Signal System Task 2 assignment. The solution addresses four problems related to signal processing. Problem 1 focuses on estimating the largest sampling interval for perfect signal reconstruction, considering different signal equations. Problem 2 involves determining the continuous-time (CT) filter approximated by a discrete-time (DT) system and finding an appropriate cutoff frequency for the Anti-Aliasing Filter (AAF). Problem 3 requires determining the sampling frequency when a signal cos(1000t) is sampled, resulting in cos(100t). Problem 4 analyzes the feasibility of sampling a vibration signal with a limited sampling rate, defines the cutoff frequency of an ideal AAF, and determines the order of the required filter. The solution utilizes formulas and calculations to arrive at the final answers, referencing key concepts in signal processing.

SIGNAL SYSTEM 0
Signal System

SIGNAL SYSTEM 1
Task 2
Question 1
a. Sin33t/t+ sin2t
By changing the above equation we can find sapling interval which is given below:
[3*(sin3t+ sin3t)/4t]+ sin2t
In which, Wmax= 9
Or, 2π *Fmax= 9
Fmax= 9/2 ……………………………………. (1)π
We now that, Fs= fmin
Or, Fs= 2Fmax (Schneider 5-10).
So, Fs= 2(9/2 )= 9/ …………………… (2)π π
Therefore, Ts= 1/Fs
Ts= /9π
b. Sin33t/t4 + sin2t
As per the above calculation we can find sampling interval in which Wnr is ∞ which will be
helpful for solving the question.
Wnr = max(∞, 4)
Or, Wnr= ∞
Therefore, Ts = 0
c. (Sin33t/t2)* sin2t

SIGNAL SYSTEM 2
It is determined that two input signals convolve with least frequency signal so, the
minimum frequency will be considered in this situation.
So, Wmax= 2
Wmax= 2π *Fmax= 2
Fmax= 1/π
Fmin= 2Fmax= 2/π
Or, Ts= /2π
d. (Sin3t/t)* Sin22t
(Sin3t/t)* (1-cos2t/2)
Here, Wmax= 3
Fmax= 3/2π
Fin= 2(3/2 )= 3/π π
Therefore, Ts= /3π
Question 2
It is determined that the applied frequency is 10 KHz and discrete time transfer function is
given below:
HDT (Z)= 0.05/z(z-0.95)
Here sampling time= 1/10= 0.1 ms
We now that, Z= est
Z= est/2/e-st/2 (Leube, Katharina and Siegfried 5-9)
Or, Z= (1+ st/2)/(1-st/2)
Z= (1+0.05ms)/ (1-0.05ms)

SIGNAL SYSTEM 3
Therefore, HDT (Z)= HCT(s)= 0.05/[(1+0.05ms)/ (1-0.05ms)*( (1+0.05ms)/ (1-0.05ms)-
0.95)]
Here, HCT(s) is defined as the continuous time filter.
It is reported that the cutoff frequency may be managed using cutoff frequency of the above
signal. So, we need to determine the value of cutoff frequency.
Now, poles of HCT(s)= -2*104 rad/seconds and -513 rad/seconds
It is found that the dominant pole lies at (-513). Therefore, the value of cutoff frequency is
513 rad/seconds which is related to the 81.6 Hz. Therefore, it is recommended that the
antialiasing filter should include around 100 Hz cutoff frequencies.
Question 3
As per the given information x(t)= cost(1000t)
So, Wm= 1000
Y(t)= cos(100t)
Now, we now that Wm± n*Ws= W
Therefore, 100= 1000± n*Ws
If, n= -1
1000- Ws= 100
Or, Ws= 900
Therefore, Fs= 900/ 2π

SIGNAL SYSTEM 4
Question 4
Part 1
It is determined that sampling at 5 kHz frequency implies that consumer can reconstruct
frequencies up to 1 kHz which contains the desired frequency ranger. Therefore, it is
reported that this proposed task is feasible.
Part 2
There are major two ideal components involve in the sampling process including analyzing
tool and anti-aliasing filter. In the given question sampling frequency is 5 kHz. Now, the
anti-aliasing filter must have a larger order for effectively transfer the signal. Therefore, it
is reported that an ideal anti-aliasing filter must have 1 kHz or 2 kHz cutoff frequency.
Part 3
A filter must consent the input signal up to 1kHz unchanged and roll-off debauched for
decreasing the peak magnitude by -60dB. From the given figure it is determined that the
peak below 1kHz frequency is around 6 and the top of the largest frequency is 13.
Therefore, AAF has an angle frequency of 1 kHz and magnitude of - 47dB at 3kHz.
Since log10(3) = 0.48 and the frequency intermission 1-3kHz is about ½, that means the
filter must roll-off. It is reported that each pole resembles to a roll-off -20dB/dec, due to
which the developed filter should be at least 5th order.
It is found that the required filter should be 5th order filter with 1 KHz cutoff frequency.

SIGNAL SYSTEM 5
Work Cited
Schneider, Tizian "Influence of sensor network sampling rate on multivariate statistical
condition monitoring of industrial machines and processes ". Multidisciplinary digital
publishing institute proceedings. 2.13. 2018: 5-10.
Leube, Alexander , Rifai Katharina, and Wahl Siegfried, "Sampling rate influences saccade
detection in mobile eye tracking of a reading task". J. eye mov. res. 10.3. 2017: 5-9.