An ideal low pass filter has frequency response given by

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

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)

The value of the integral  is equal to          

Consider a signal defined by

Its Fourier Transform 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

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?