Explore topic-wise MCQs in Digital Signal Processing.

This section includes 13 Mcqs, each offering curated multiple-choice questions to sharpen your Digital Signal Processing knowledge and support exam preparation. Choose a topic below to get started.

1.

What is the energy density spectrum of the signal x(n)=anu(n), |a|<1?

A. ( frac{1}{1+2acos +a^2} )
B. ( frac{1}{1-2acos +a^2} )
C. ( frac{1}{1-2acos -a^2} )
D. ( frac{1}{1+2acos -a^2} )
Answer» C. ( frac{1}{1-2acos -a^2} )
Discussion
2.

What is the convolution of the sequences of x1(n)=x2(n)={1,1,1}?

A. {1,2,<strong>3</strong>,2,1}
B. {1,2,3,2,1}
C. {1,1,1,1,1}
D. {1,1,<strong>1</strong>,1,1}
Answer» B. {1,2,3,2,1}
Discussion
3.

If X( ) is the Fourier transform of the signal x(n), then what is the Fourier transform of the signal x(n-k)?

A. e<sup>j k</sup>. X(- )
B. e<sup>j k</sup>. X( )
C. e<sup>-j k</sup>. X(- )
D. e<sup>-j k</sup>. X( )
Answer» E.
Discussion
4.

What is the Fourier transform of the signal x(n)=a|n|, |a|&lt;1?

A. ( frac{1+a^2}{1-2acos +a^2} )
B. ( frac{1-a^2}{1-2acos +a^2} )
C. ( frac{2a}{1-2acos +a^2} )
D. None of the mentioned
Answer» C. ( frac{2a}{1-2acos +a^2} )
Discussion
5.

If x(n)=A, -M&lt;n&lt;M,; x(n)=0, elsewhere. Then what is the Fourier transform of the signal?

A. A ( frac{sin u2061(M- frac{1}{2}) }{sin u2061( frac{ }{2})} )
B. A<sup>2</sup> ( frac{sin u2061(M+ frac{1}{2}) }{sin u2061( frac{ }{2})} )
C. A ( frac{sin u2061(M+ frac{1}{2}) }{sin u2061( frac{ }{2})} )
D. ( frac{sin u2061(M- frac{1}{2}) }{sin u2061( frac{ }{2})} )
Answer» D. ( frac{sin u2061(M- frac{1}{2}) }{sin u2061( frac{ }{2})} )
Discussion
6.

What is the value of |X( )| given X( )=1/(1-ae-j ), |a|&lt;1?

A. ( frac{1}{ sqrt{1-2acos +a^2}} )
B. ( frac{1}{ sqrt{1+2acos +a^2}} )
C. ( frac{1}{1-2acos +a^2} )
D. ( frac{1}{1+2acos +a^2} )
Answer» B. ( frac{1}{ sqrt{1+2acos +a^2}} )
Discussion
7.

What is the value of XI( ) given ( frac{1}{1-ae^{-j }} ), |a|&lt;1?

A. ( frac{asin }{1-2acos +a^2} )
B. ( frac{1+acos }{1-2acos +a^2} )
C. ( frac{1-acos }{1-2acos +a^2} )
D. ( frac{-asin }{1-2acos +a^2} )
Answer» E.
Discussion
8.

What is the value of XR( ) given X( )= ( frac{1}{1-ae^{-j }} ),|a|&lt;1?

A. ( frac{asin }{1-2acos +a^2} )
B. ( frac{1+acos }{1-2acos +a^2} )
C. ( frac{1-acos }{1-2acos +a^2} )
D. ( frac{-asin }{1-2acos +a^2} )
Answer» D. ( frac{-asin }{1-2acos +a^2} )
Discussion
9.

If x(n) is a real and odd sequence, then what is the expression for x(n)?

A. ( frac{1}{ } int_0^ )[X<sub>I</sub>( ) sin n] d
B. ( frac{1}{ } int_0^ )[X<sub>I</sub>( ) sin n] d
C. ( frac{1}{ } int_0^ )[X<sub>I</sub>( ) cos n] d
D. ( frac{1}{ } int_0^ )[X<sub>I</sub>( ) cos n] d
Answer» C. ( frac{1}{ } int_0^ )[X<sub>I</sub>( ) cos n] d
Discussion
10.

If x(n) is a real signal, then x(n)= ( frac{1}{ } int_0^ )[XR( ) cos n- XI( ) sin n] d .

A. True
B. False
Answer» B. False
Discussion
11.

If x(n) is a real sequence, then what is the value of XI( )?

A. ( sum_{n=- }^ x(n)sin u2061( n) )
B. ( sum_{n=- }^ x(n)sin u2061( n) )
C. ( sum_{n=- }^ x(n)cos u2061( n) )
D. ( sum_{n=- }^ x(n)cos u2061( n) )
Answer» C. ( sum_{n=- }^ x(n)cos u2061( n) )
Discussion
12.

If x(n)=xR(n)+jxI(n) is a complex sequence whose Fourier transform is given as X( )=XR( )+jXI( ), then what is the value of xI(n)?

A. ( frac{1}{2 } int_0^{2 } )[X<sub>R</sub>( ) sin n+ X<sub>I</sub>( ) cos n] d
B. ( int_0^{2 } )[X<sub>R</sub>( ) sin n+ X<sub>I</sub>( ) cos n] d
C. ( frac{1}{2 } int_0^{2 } )[X<sub>R</sub>( ) sin n X<sub>I</sub>( ) cos n] d
D. None of the mentioned
Answer» B. ( int_0^{2 } )[X<sub>R</sub>( ) sin n+ X<sub>I</sub>( ) cos n] d
Discussion
13.

If x(n)=xR(n)+jxI(n) is a complex sequence whose Fourier transform is given as X( )=XR( )+jXI( ), then what is the value of XR( )?

A. ( sum_{n=0}^ )x<sub>R</sub> (n)cos n-x<sub>I</sub> (n)sin n
B. ( sum_{n=0}^ )x<sub>R</sub> (n)cos n+x<sub>I</sub> (n)sin n
C. ( sum_{n=- }^ )x<sub>R</sub> (n)cos n+x<sub>I</sub> (n)sin n
D. ( sum_{n=- }^ )x<sub>R</sub> (n)cos n-x<sub>I</sub> (n)sin n
Answer» D. ( sum_{n=- }^ )x<sub>R</sub> (n)cos n-x<sub>I</sub> (n)sin n
Discussion