Let  be the Fourier transform of the signal

The value of the derivative of  at  is ________ (rounded off to 1 decimal place).

The Fourier transform  of the signal  is given by

Which one of the following statements is true?

Let an input x(t) = 2 sin(10πt) + 5cos(15πt) + 7sin(42πt) + 4cos(45πt) is passed through an LTI system having an impulse response,                

The output of the system is

Let f(t) be an even function i.e., f(–t) = f(t) for all t. Let the Fourier transform of f(t) be defined as . Suppose  for all ω and F(0) = 1. Then

Let, where  denotes convolution, Let c be a positive real-valued constant. Choose the correct expression for z (ct).         

Let the signal be passed through an LTI system with frequency response , as given in the figure below

The Fourier series representation of the output is given as

Suppose  and  have the Fourier transforms as shown below.                 

Which one of the following statements is TRUE?

The output of a continuous-time, linear time-invariant system is denoted by  where x(t) is the input signal. A signal z(t) is called Eigen-signal of the system T, when , where  is a complex number, in general and is called an Eigen value of T. Suppose the impulse response of the system T is real and even. Which of the following statements is TRUE?

Suppose the maximum frequency in a band-limited signal x(t) is 5kHz. Then, the maximum frequency in x(t)cos, in kHz, is ____________.

The filters F1 and F2 having characteristics as shown in figures (a) and (b) are connected as shown in figure (c)

The cut – off frequencies of F1 and F2 are  and  respectively. If , the resultant circuit exhibit the characteristics of a

Let f(t) be a continuous time signal and let  be its Fourier transform defined by

Define g(t) by

What is the relationship between f(t) and g(t)?

Consider an LTI system with transfer function

If the input to the system is and the steady state output is , then the value of A is

A continuous-time LTI system with system function  has the following pole-zero plot. For this system, which of the alternatives is TRUE?        

A differentiable non constant even function x(t) has a derivative y(t), and their respective Fourier Transformers are . Which of the following statements is TRUE?

Let  (where rect (x) =1 for  and zero otherwise).  Then if , the Fourier Transform of  will be given by

Let a signal be applied to a stable linear lime-invariant system. Let the corresponding steady state output be represented as. Then which of the following statements is true?