Consider a continuous-time, real-valued signal  whose Fourier transform  exists.

Which one of the following statements is always TRUE?

Consider two continuous time signals x(t) and y(t) as shown below

If X(f) denotes the Fourier transform of x(t), then the Fourier transform of y(t) is__________.

The relationship between any N-length sequence x[n] and its corresponding N-point discrete Fourier transform X[k] is defined as         

Another sequence y[n] is formed as below

For the sequence x[n]={1,2,1,3}, the value of  Y[0] is __________

Let  be a strictly band-limited signal M bandwidth B and energy E. Assuming  the energy in the signal  is

The Fourier transform  of  is

Note:

In the table shown below, match the signal type with its spectral characteristics.         

Signal Type

(i) Continuous, aperiodic

(ii) Continuous, periodic

(iii) Discrete, aperiodic

(iv) Discrete, periodic

Spectral Characteristics

(a) Continuous, aperiodic

(b) Continuous, periodic

(c) Discrete, aperiodic

(d) Discrete, periodic

Let an input  having discrete time Fourier transform.

 be passed through an LTI system. The frequency response of the LTI system is . The output  of the system is

Let  be passed through an LTI system having impulse response . The output of the system is

Let  and  is shown in the figure below. For , the   is _________. (rounded off to the nearest integer).

Let  be a white Gaussian noise with power spectral density . If  is input to an LTI system with impulse response . The average power of the system output is __________ W. (Rounded off to two decimal place).

For a real signal, which of the following is/are valid power spectral density/densities?