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Math for DSP can be very difficult!!! It depends on applications, some of them do not require math but some of them do.
If you want to design, for example, system with adaptive filters or aplication in image processing with wavelets theory, you need to know funtional analysis, complex...
Of course,the output is zero.
What does mean,for example, x(t)=cost(t)?
It means that you consider a signal from t=-∞ to t=+∞.
Your signal are not cos(t) and sin(2t). Your signals are something else!
Like cost(t)[u(t1)-u(t2)]. Where , u(t) is unit step function.
Re: aliasing problem
You should consider the Fourier transform of a signal, not a signal in a time domain, and find out what is the highest frequency. So, what is the highest frequency?? It is the answer to your question.
The highest frequency of signal is f1
The sampling frequency is f2...
There is no such function!
Please , this is a math, not word games:?:
I have found this somewere
"Thus there is a link between continuity and differentiability: If a function is differentiable at a point, it is also continuous there. Consequently, there is no need to investigate for...
Purnapragma, V_C has explained about multiplication and convolution.
I think you do not understand your own question, and moreover you cannot undersand these things without knowledge of Fourier or Laplace transform.
Your "impulses" are impulses( delta functions) or step functions or...
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