An ideal low pass filter has frequency response given by

Let  be its time domain representation. Then  __________ (round off to the nearest integer).

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?

The discrete-time Fourier transform of a signal  is  . Consider that  is a periodic signal of period  such that

Note that . The magnitude of the Fourier series coefficient  is __________ (Round off to 3 decimal places).

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

Consider a continuous-time signal x(t) defined by x(t) = 0 for |t| > 1, and x(t) = 1 – |t| for |t| ≤ 1. Let the Fourier transform of x(t) be defined as . The maximum magnitude of X(ω) is __________.

The causal realization of a system transfer function H(s) having poles at (2, –1), (–2,1) and zeroes at (2,1), (–2, –1) will be

The Fourier transform of a continuous-time signal x(t) is given by ;, where and denotes frequency. Then the value of at t=1 is ______ (up to 1 decimal place). (In denotes the logarithm to base e)

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 value of the integral  is equal to          

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

Consider a signal defined by

Its Fourier Transform is

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 function f(t) is shown in the figure.                

The Fourier transform  of f(t) is

A signal is represented by         

The Fourier transform of the convolved signal  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?

The Fourier transform of a signal h(t) is . The value of h(0) is

x(t) is a positive rectangular pulse from  to  with unit height as shown in the figure. The value of where  is the Fourier transform of x(t) is                 

A signal  where α is a real constant  is the input to a Linear Time invariant system whose impulse response  where β is a real constant.  If min(α,β) denotes the minimum of α and β, and similarly max(α,β) denotes  the maximum of α and β, and K is a constant, which one of the following statements is true about the output of the system?

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?