dsp 2

                                                 DSP part -2

31. Write the steps in designing chebyshev filter?

1.   Find the order of the filter.

2. Find the value of major and minor axis.  λ

3. Calculate the poles.

4. Find the denominator function using the above poles.

5. The numerator polynomial value depends on the value of n. If n is odd: put s=0 in the denominator polynomial.

If n is even put s=0 and divide it by (1+e2)1/2

32. Write down the steps for designing a Butterworth filter?

1. From the given specifications find the order of the filter

2  find the transfer function from the value of N

3. Find Ωc

4  find the transfer function ha(s) for the above value of Ωc by su s by that value.

33. State the equation for finding the poles in chebyshev filter

sk=acos¢k+jbsin¢k,where ¢k=∏/2+(2k-1)/2n)∏

34. State the steps to design digital IIR filter using bilinear method

Substitute s by 2/T (z-1/z+1), where T=2/Ώ (tan (w/2) in h(s) to get h (z)

35. What is warping effect?

For smaller values of w there exist linear relationship between w and .but for larger values of w the relationship is nonlinear. This introduces distortion in the frequency axis. This effect compresses the magnitude and phase response. This effect is called warping effect

36. Write a note on pre warping.

The effect of the non linear compression at high frequencies can be compensated. When the desired magnitude response is piecewise constant over frequency, this compression can be compensated by introducing a suitable rescaling or prewar ping the critical frequencies.

37. Give the bilinear transform equation between s plane and z plane

s=2/T (z-1/z+1)

38. Why impulse invariant method is not preferred in the design of IIR filters other than low pass filter?

In this method the mapping from s plane to z plane is many to one. Thus there ire

an infinite number of poles that map to the same location in the z plane, producing an aliasing effect. It is inappropriate in designing high pass filters. Therefore this method is not much preferred.

39. By impulse invariant method obtain the digital filter transfer function and the differential equation of the analog filter h(s) =1/s+1

H (z) =1/1-e-Tz-1

Y/x(s) =1/s+1

Cross multiplying and taking inverse lap lace we get, D/dt(y(t)+y(t)=x(t)

40. What is meant by impulse invariant method?

In this method of digitizing an analog filter, the impulse response of the resulting

digital filter is a sampled version of the impulse response of the analog filter. For e.g. if the transfer function is of the form, 1/s-p, then

H (z) =1/1-e-pTz-1

41. What do you understand by backward difference?

One of the simplest methods of converting analog to digital filter is to

approximate the differential equation by an equivalent difference equation. d/dt(y(t)/t=nT=(y(nT)-y(nT-T))/T

42. What are the properties of chebyshev filter?

1. The magnitude response of the chebyshev filter exhibits ripple either in the stop

band or the pass band.

2. The poles of this filter lies on the ellipse

43. Give the Butterworth filter transfer function and its magnitude characteristics for different orders of filter.

The transfer function of the Butterworth filter is given by

H (jΏ) =1/1+j (Ώ/Ώc) N

44. Give the magnitude function of Butterworth filter.

The magnitude function of Butterworth filter is

|h(jΏ)=1/[1+(Ώ/Ώc)2N]1/2 ,N=1,2,3,4,….

45. Give the equation for the order N, major, minor axis of an ellipse in case of chebyshev filter?

The order is given by N=cosh-1(((10.1αp)-1/10.1αs-1)1/2))/cosh-1Ώs/Ώp

A= (µ1/N-µ-1/N)/2Ωp

B=Ωp (µ1/N+ µ-1/N)/2

46. Give the expression for poles and zeroes of a chebyshev type 2 filters

The zeroes of chebyshev type 2 filter SK=jΏs/sinkФk, k=1….N The poles of this filter xk+jyk

xk= Ώsσk/ Ώs2+σk2

yk=ΏsΏk/ Ώs2+σk2   σk=acosФk

47. How can you design a digital filter from analog filter?

Digital filter can de designed from analog filter using the following methods

1. Approximation of derivatives

2. Impulse invariant method

3. Bilinear transformation

48.  write down bilinear transformation.

s=2/T (z-1/z+1)

49. List the Butterworth polynomial for various orders.

N	Denominator polynomial
1	S+1
2	S2+.707s+1
3	(s+1)(s2+s+1)
4	(s2+.7653s+1)(s2+1.84s+1)
5	(s+1)(s2+.6183s+1)(s2+1.618s+1)
6	(s2+1.93s+1)(s2+.707s+1)(s2+.5s+1)
7	(s+1)(s2+1.809s+1)(s2+1.24s+1)(s2+.48s+1)

50. Differentiate Butterworth and Chebyshev filter.

Butterworth dampimg factor 1.44 chebyshev 1.06

Butterworth flat response       damped response.

51. What is filter?

Filter is a frequency selective device ,which amplify particular range of

frequencies and attenuate particular range of frequencies.

52. What are the types of digital filter according to their impulse response?

IIR(Infinite impulse response )filter

FIR(Finite Impulse Response)filter.

53. How phase distortion and delay distortion are introduced?

The phase distortion is introduced when the phase characteristics of a filter is

nonlinear with in the desired frequency band.

The delay distortion is introduced when the delay is not constant with in the desired frequency band.

54.  what is mean by FIR filter?

The filter designed by selecting finite number of samples of impulse response

(h(n) obtained from inverse fourier transform of desired frequency response

H(w))  are called FIR filters

55. Write the steps involved in FIR filter design

Choose the desired frequency response Hd(w)

Take the inverse fourier transform and obtain Hd(n)

Convert the infinite duration sequence Hd(n) to h(n)

Take Z transform of h(n) to get H(Z)

56. What are advantages of FIR filter?

Linear phase FIR filter can be easily designed .

Efficient realization of FIR filter exists as both recursive and non-recursive structures.

FIR filter realized non-recursively stable.

The round off noise can be made small in non recursive realization of FIR filter.