Free Printable DTSP - REVISION 3

1.

The IIR filter design method that overcomes the limitation of applicability to only

Lowpass filter and a limited class of bandpass filters is

a)

Approximation of derivatives

b)

Impulse Invariance

c)

Bilinear Transformation

d)

Frequency sampling

2.

Neither the Impulse response nor the phase response of the analog filter is Preserved in the digital filter in the following method

a)

The method of mapping of differentials

b)

Impulse invariant method

c)

Matched Z - transformation technique

d)

bilinear transformation

3.

The poles of Butterworth filter lies on

a)

sphere

b)

ellipse

c)

parabola

d)

circle

4.

The transition band is more in

a)

butterworth filter

b)

Chebyshev type - 1

c)

Chebyshev type - 2

d)

FIR Filter

5.

What is the kind of relationship between Ω and ω?

a)

Many-to-one

b)

One-to-many

c)

One-to-one

d)

Many-to-many

6.

Canonical structure is a structure that is implemented using the minimum possible number of delay elements. __________________is a canonical structure.

a)

Direct form I

b)

Direct form II

c)

Both Direct form I & Direct form II

d)

None of these

7.

The nonlinear relationship $\Omega=\frac{2}{T_{d\ }}\tan\left(\frac{\omega}{2\ }\right)$ between digital frequency ω and the analog frequency In the bilinear transformation.

a)

Frequency (band) transformation

b)

Elliptic approximation

c)

Frequency warping

d)

Zero-phase filtering

8.

Computation of the analog frequency $\Omega$ from the digital frequency ω using the frequency warping formula so that
the frequency-distortion in bilinear transformation is compensated

a)

Spectral factorization

b)

Zero-phase filtering

c)

Prewarping

d)

all of the above

9.

The bilinear transformation is an invertible nonlinear mapping between the s-plane and the z-plane defined by

a)

$s=\frac{2}{T_{d\ }}\left(\frac{1-z^{-1}}{1+z^1}\right)$

b)

$s=\frac{2}{T_{d\ }}\left(\frac{1-z^{-1}}{1+z^{-1}}\right)$

c)

$s=\frac{2}{T_{d\ }}\left(\frac{1-z^1}{1+z^{-1}}\right)$

d)

$s=\frac{2}{T_{d\ }}\left(\frac{1+z^{-1}}{1-z^{-1}}\right)$

10.

The magnitude-squared response of an Nth-order low pass filter is given by

\left|H_{a\ }\left(j\Omega\right)\right|^2=\frac{1}{1+\left(\frac{\Omega}{\Omega_c}\right)^{2N}}

, Where N is the order of the filter and

\Omega_c

is the cut off frequency in rad/sec.Then

\left|H_a\left(j\Omega\right)\right|^{2\ }

is

a)

monotonically decreasing function of Ω

b)

monotonically increasing function of Ω

c)

Both (a) and (b)

d)

constant

11.

The magnitude-squared response of lowpass filter is given by $\left|H_a\left(j\Omega\right)\right|^2=\frac{1}{1+64\Omega^6}$ , then the order of filter is

a)

6

b)

4

c)

3

d)

12

12.

To obtain digital filter H(z) by impulse invariance transformation, transform analog poles $\left\{p_k\right\}$ into digital poles $\left\{e^{p_kT}\right\}$ , Where $H\left(z\right)$ is,

a)

$H\left(z\right)=\sum_{k=1}^N\frac{R_k}{1-e^{p_kT}Z^{-1}}$

b)

$H\left(z\right)=\sum_{k=1}^N\frac{R_k}{1-e^{p_kT}Z^{ }}$

c)

$H\left(z\right)=\sum_{k=1}^N\frac{R_k}{1+e^{p_kT}Z^{-1}}$

d)

$H\left(z\right)=\sum_{k=1}^N\frac{R_k}{e^{p_kT}Z^{-1}}$

13.

In the bilinear transformation, the relationship between $\omega$ and $\Omega$

a)

$\omega=2\tan^{-1\ }\left(\frac{\Omega T}{2}\right)$

b)

$\omega=2\tan^{\ }\left(\frac{\Omega T}{2}\right)$

c)

$\omega=\tan^{-1\ }\left(\frac{\Omega T}{2}\right)$

d)

$\omega=2\tan^{-1\ }\left(\frac{\Omega T}{2}\right)^2$

14.

If the bilinear transformation is used to convert a continuous-time to a discrete-time filter, the frequency transformation may be performed ______________ the bilinear transformation

a)

either before or after

b)

before

c)

after

d)

none of these

15.

If we use the impulse-invariance transformation, the frequency transformation should be performed____________ to obtain the discrete-time low pass filter.

a)

after

b)

before

c)

either before or after

d)

None of these

16.

The impulse invariance and bilinear mappings are two most popular transformations that convert analog into digital filters. The better and more versatile of the two is _______________

a)

bilinear mapping.

b)

impulse invariance mapping

c)

both

d)

Fourier transform

17.

A one-to-one analog to digital filter transformation that maps analog complex frequency s into digital complex frequency z

a)

Butterworth approximation

b)

Cauer filter

c)

Bilinear transformation

d)

Chebyshev approximation

18.

An analog to digital filter transformation that preserves the shape of the analog filter impulse response.

a)

Impulse-invariance transformation

b)

Frequency (band) transformation

c)

Frequency warping

d)

Prewarping

19.

Direct form I structure requires

a)

(M + N) delay elements

b)

(M -N) delay elements

c)

(M + N)/2 delay elements

d)

(M + N+2) delay elements

20.

3-dB Butterworth Lowpass Prototype Transfer Functions, when the order of filter N =1 is

a)

$\frac{1}{s+1}$

b)

$\frac{1}{s-1}$

c)

$\frac{1}{s^2+s+2}$

d)

$\frac{1}{s^2+1}$

21.

The Bilinear Transformation maps the left half of an s-plane to the__________ unit circle of the z-plane

a)

inside

b)

outside

c)

imaginary axis of

d)

centre of the

22.

The impulse-invariant design method maps the analog impulse response to the digital equivalent impulse response. It is not appropriate for the

a)

highpass and bandstop filter design.

b)

lowpass and bandpass filter design

c)

Low pass design

d)

Band pass design

23.

What is the duration of the unit sample response of a digital filter?

a)

Finite

b)

Infinite

c)

Impulse(very small)

d)

Zero

24.

Which of the following methods are used to convert analog filter into digital filter?

a)

Approximation of Derivatives

b)

Bilinear transformation

c)

Impulse invariance

d)

All of the mentioned

25.

For an analog LTI system to be stable, where should the poles of system function H(s) lie?

a)

Right half of s-plane

b)

Left half of s-plane

c)

On the imaginary axis

d)

At origin

26.

Which of the following filter transformation is not possible?

a)

High pass analog filter to low pass digital filter

b)

High pass analog filter to high pass digital filter

c)

Low pass analog filter to low pass digital filter

d)

None of the mentioned

27.

If a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is _____________

a)

Non periodic repetition

b)

Non periodic non-repetition

c)

Periodic repetition

d)

None of the mentioned

28.

What is the cutoff frequency of the Butterworth filter with a pass band gain KP=-1 dB at ΩP=4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS=8 rad/sec?

a)

3.5787 rad/sec

b)

1.069 rad/sec

c)

6 rad/sec

d)

4.5787 rad/sec

29.

What is the stop band frequency of the normalized low pass Butterworth filter used to design a analog band pass filter with -3.0103dB upper and lower cutoff frequency of 50Hz and 20KHz and a stop band attenuation 20dB at 20Hz and 45KHz?

a)

2 rad/sec

b)

2.25 Hz

c)

2.25 rad/sec

d)

2 Hz

30.

FIR filters stands for

a)

Finite Impulse Response

b)

Finite invariant Response

c)

Finite independent Response

d)

Filter invariant response

DTSP - REVISION 3

Total questions: 30

Worksheet time: 15mins

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