All answers are in the form of True/False with a explantion as to why:
1) An ideal band-pass filter centered (at ± 0) can be created by just multiplying the sinc function
by cos(0t) in the the time domain.
2) Nyquist theorem deals with windowing of a signal in the time domain, which is translated into
leakage in the frequency domain.
3) The global frequency response of an LTI system composed of two LTI systems in parallel
with each other is simply the addition of the individual frequency responses of the systems.
4) We can find the H(j) of an unknown LTI system by stimulating it with a impulse and taking
the Fourier Transform of its response. Another more realistic way is to stimulate the LTI system
with a unit step function (signal), take the Fourier Transform of its response, multiply it by (j) for
every 0 and divide it by pi at =0.
^I believe that one is true, but I am needing help forming an explanation.
5) A first step towards sampling an unknown analog signal without aliasing is to low-pass filter
the signal.
Solution
1) False
Because fourier transform of sinc function is rectanctangular function in frequency domain, and
fourier transform of cos function is impuse function. So when when multiply in time domain that
means convoution in frequency domain. And if ve convolude rectangular function with impulse
function then it would be rectangular pulse train. Which is not ideal band paas filter at w=0.
2) False
It would be either window or leakage in time domain or frequency domain.
3) TRUE
It is simply understand by block reduction method in control system. When there is another
forward block we add both maid forward block with secondry forward block. OR LTI is linear in
nature so add in parallel and multiply in series.
4) TRUE
Its because the response or tansfer function of any system is called impulse response. It means
when the input is Impuse function what is the output of that system. Same as the relation
between unit imulse response and impuse respone in just fouries tranfer of unit step function.
Because the fourier transform of impulse is unity. so if input is unit step function multiply it by
(j) for every 0 and divide it by pi at =0.(1/(i)+(),)
5)FALSE
Low paas filter use after sampling to recover the original signal..
All answers are in the form of TrueFalse with a explantion as to wh.pdf
1. All answers are in the form of True/False with a explantion as to why:
1) An ideal band-pass filter centered (at ± 0) can be created by just multiplying the sinc function
by cos(0t) in the the time domain.
2) Nyquist theorem deals with windowing of a signal in the time domain, which is translated into
leakage in the frequency domain.
3) The global frequency response of an LTI system composed of two LTI systems in parallel
with each other is simply the addition of the individual frequency responses of the systems.
4) We can find the H(j) of an unknown LTI system by stimulating it with a impulse and taking
the Fourier Transform of its response. Another more realistic way is to stimulate the LTI system
with a unit step function (signal), take the Fourier Transform of its response, multiply it by (j) for
every 0 and divide it by pi at =0.
^I believe that one is true, but I am needing help forming an explanation.
5) A first step towards sampling an unknown analog signal without aliasing is to low-pass filter
the signal.
Solution
1) False
Because fourier transform of sinc function is rectanctangular function in frequency domain, and
fourier transform of cos function is impuse function. So when when multiply in time domain that
means convoution in frequency domain. And if ve convolude rectangular function with impulse
function then it would be rectangular pulse train. Which is not ideal band paas filter at w=0.
2) False
It would be either window or leakage in time domain or frequency domain.
3) TRUE
It is simply understand by block reduction method in control system. When there is another
forward block we add both maid forward block with secondry forward block. OR LTI is linear in
nature so add in parallel and multiply in series.
4) TRUE
Its because the response or tansfer function of any system is called impulse response. It means
when the input is Impuse function what is the output of that system. Same as the relation
between unit imulse response and impuse respone in just fouries tranfer of unit step function.
Because the fourier transform of impulse is unity. so if input is unit step function multiply it by
(j) for every 0 and divide it by pi at =0.(1/(i)+(),)
5)FALSE
2. Low paas filter use after sampling to recover the original signal.
