KONGUNADU COLLEGE OF ENGINEERING & TECHNOLOGY

ELECTRONICS AND COMMUNICATION ENGINEERING TERMINAL EXAMINATION-I-ANSWER KEY

FIFTH SEMESTEREC2302 DIGITAL SIGNAL PROCESSING

1. What is Twiddle factor?

The complex number WN is called as Twiddle factor (or) Phase factor. It also represents an Nth root of unity. It is expressed by WN

kn = e –j2πkn / N

2. How many stages of decimations are required in the case of a 64 point radix 2DIT FFT algorithm?

The number of complex multiplications required using direct computation is N2 = 642 = 4096 .The number of complex multiplications required using FFT is (N/2) log2 N = (64/2) log264 = 192.

3. Find the 4 point DFT of the sequencex (n)={1,1 ,−1 ,−1 }.

N-1X(k) = Σ x(n) e –j2πkn / N k = 0,1,2,3…….N-1

n=0

X(K) ={0,2-j2,0,2+j2}

4. What is FFT?

The Fast Fourier Transform is an algorithm used to compute the DFT. It makes use of the symmetry and periodicity properties of twiddle factor to effectively reduce the DFT computation time. It is based on the fundamental principle of decomposing the computation of DFT of a sequence of length N into successively smaller DFTs.

5. Obtain the circular convolution of the following sequences

x (n)={1,2 ,1 },h (n)={1 ,−2,2 }.

The circular convolution of the above sequences can be obtained by using matrix method.

[h(0 ) h(2) h(1)h(1) h(0 ) h(2)h(2) h(1) h(0 ) ] [

x (0 )x (1)x (2 ) ]=[ y (0 )

y (1 )y (2 ) ]

[1 2 −2−2 1 22 2 1 ][121 ]=[32−1]y ( n)= {3,2 ,−1 }

6. Why the Butterworth response is called a maximally flat response?

This type of response is called as butterworth response because its main characteristics is

that the passband is maximally flat.That means there are no variations(ripples) in the

passband.

7. Compare Butterworth, Chebyshev filters.Sl.No Butterworth filter Chebyshev filter

1. All pole design All pole design

2. The poles lie on a circle in s-plane The poles lie on a ellipse in s-plane

3. The magnitude response is maximally flat at the origin and monotonically

decreasing function of Ω .

The magnitude response is equiripple in pass band and monotonically decreasing in the stop band.

4. The normalized magnitude response has

a value of

1√2 at the cut off frequency

Ωc .

The normalized magnitude response has a value

of

1√1+ε2

at the cut off frequencyΩc .

5. Only few parameters have to be calculated to determine the transfer function.

A large number of parameter has to be calculated to determine the transfer function.

8. Write frequency translation for BPF from LPF.

9. What is the relationship between analog and digital frequency in impulse invariant

transformation?

The relation between analog and digital frequency in impulse invariant transformation is given by Digital frequency, ω=ΩTWhere, Ω - Analog frequency and T - Sampling time period

10. Draw the basic butterfly of DIT - FFT structure.