Holooly Plus Logo
Holooly Plus Logo

Question 3.SGPYQ.41: The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (......

The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin 2ω)/w. The value of h(0) is

(a) \frac{1}{4}           (b) \frac{1}{2}            (c) 1            (d) 2

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.
Report Answer

Given that

F[h(t)]=H(j \omega)=\frac{(2 \cos \omega)(\sin 2 \omega)}{\omega}

Inverse Fourier transform of sinc function is a rectangular function

\begin{aligned} & F^{-1}[H(j \omega)]=h(t)=h_1(t)+h_2(t) \\ & h(0)=h_1(0)+h_2(0)=\frac{1}{2}+\frac{1}{2}=1 \end{aligned}

49

Related Answered Questions

Question: 3.PE.S2.3

The Nyquist sampling interval for the signal sinc (700t) + sinc (500t) is (a) 1/350 s (b) π/350 s (c) 1/700 s (d) 1/700 s  ...

Verified Answer:

(c) \begin{aligned}x & =\sin c(700 t)+\...
Question: 3.P.41

Determine the inverse Z-transform of x(z) = 1/2-4z^-1 +2z^-2 by long division method if (a) ROC |z| > 1 (b) ROC |z| < 1/2 ...

Verified Answer:

(a) For ROC |z| > 1, that is, ROC is exterior o...
Question: 3.SGPYQ.39

If x[n] = (1/3)^|n| – (1/2)^n u[n] , then the region of convergence (ROC) of its Z-transform in the z-plane will be (a) 1/3 < |z| < 3 (b) 1/3 <|z| <1/2 (c)1/2<|z| <3 (d) 1/3<|z| ...

Verified Answer:

Given that \begin{aligned} x(n) & =\l...
Question: 3.SGPYQ.40

Let y[n] denote the convolution of h[n] and g[n], where h[n] =(1/2)^n u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] =1/2, then g[1] equals (a) 0 (b) 1/2 (c) 1 (d) 3/2 ...

Verified Answer:

Given that h[n]=\left\lgroup \frac{1}{2} \...
Question: 3.SGPYQ.42

The input x(t) and output y(t) of a system are related as y(t) = ∫-∞^t x(τ) cos (3τ)dτ. The system is (a) time-invariant and stable (b) stable and not time-invariant (c) time-invariant and not stable (d) not time-invariant and not stable ...

Verified Answer:

Given the relation between input and output as [la...
Question: 3.SGPYQ.23

A cascade of three linear-time invariant systems is causal and unstable. From this, we conclude that (a) each system in the cascade is individually causal and unstable. (b) at least one system is unstable and at least one system is causal. (c) at least one system is causal and all systems are ...

Verified Answer:

For a cascaded system Input \rightarrow \b...
Question: 3.SGPYQ.43

The impulse response of a system is h(t) = t u(t). For an input u(t − 1), the output is (a) t²/2 u(t) (b) t(t-1) /2 u(t-1) (c) (t-1)²/2 u(t-1) (d) t²-1/2 u(t-1) ...

Verified Answer:

Given that impulse response is h(t) = tu(t). For i...
Question: 3.SGPYQ.44

Two systems with impulse responses h1 and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by (a) product of h1(t) and h2(t) (b) sum of h1(t) and h2 (t) (c) convolution of h1(t) and h2(t) (d) subtraction of h2(t) from h(t) ...

Verified Answer:

The overall impulse response of the cascaded syste...
Question: 3.SGPYQ.45

For a periodic signal v(t) = 30 sin 100t + 10 cos 300t + 6 sin(500t + π/4), the fundamental frequency in rad/s is (a) 100 (b) 300 (c) 500 (d) 1500 ...

Verified Answer:

Given that v(t) = 30 sin 100t +10 cos 300t + 6 sin...
Question: 3.SGPYQ.46

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is (a) 5 (b) 12 (c) 15 (d) 20 ...

Verified Answer:

Given that f_{\max }=5  kHz Accor...