1
GATE ECE 2001
Subjective
+5
-0
The Fourier transform $$G(\omega )$$ of the signal g(t) in Fig.(1) is given as
$$G(\omega ) = {1 \over {{\omega ^2}}}({e^{j\omega }} - j\omega {e^{j\omega }} - 1)$$.

Using this information, and the time-shifting and time-scaling properties, determine and Fourier transform of signals in Fig (2), (3) and (4).

GATE ECE 2001 Signals and Systems - Fourier Transform Question 1 English 1 GATE ECE 2001 Signals and Systems - Fourier Transform Question 1 English 2 GATE ECE 2001 Signals and Systems - Fourier Transform Question 1 English 3 GATE ECE 2001 Signals and Systems - Fourier Transform Question 1 English 4
2
GATE ECE 1998
Subjective
+5
-0
Consider a rectangular pulse g(t) existing between $$t = \, - {T \over 2}\,and\,{T \over 2}$$. Find and sketch the pulse obtained by convolving g(t) with itself. The Fourier transform of g(t) is a sinc function. Write down the Fourier transform of the pulse obtained by the above convolution.
3
GATE ECE 1995
Subjective
+5
-0
A signal v(t)= [1+ m(t) ] cos $$({\omega _c}t)$$ is detected using a square law detector, having the characteristic $${v_0}(t) = {v^2}(t)$$. If the Fourier transform of m(t) is constant, $${M_0}$$, extending from - $${f_{m\,}}\,to\, + {f_{m\,}}$$, sketch the Fourier transform of $${v_0}(t)$$ in the frequency range-$${f_{m\,}}\, < f < {f_{m\,}}$$.
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