DEPARTMENT OF BIOMEDICAL ENGINEERING
EC6502 PRINCIPLES OF DIGITAL SIGNAL PROCESSING
ASSIGNMENT- FINITE IMPULSE RESPONSE FILTERS
PART A
1. What is meant by FIR filter? And why it is stable?
2. Compare FIR filter over IIR filter.
3. What is a linear phase filter?
4. What is the condition for linear phase?
5. What is Gibb’s phenomenon?
6. Write procedure for designing FIR filter using windows.
7. List the characteristics of FIR filters designed using window functions.
8. Which type of (FIR/IIR) is decided for an application?
9. Why rectangular windows are not used in FIR filter design using window
method?
10. What are the desirable features of FIR filters?
11. Draw the direct form realization of FIR system.
PART B
1. Prove that the FIR filter has linear phase if unit impulse response satisfies the
condition h(n)=h(N-n-1), n=0,1,-------M-1. Also discuss symmetric and
antisymmetric cases of FIR filter.
2. Design an ideal differentiator with frequency response
H(ejω) = jω - π ≤ ω ≤ π
Using (a) rectangular window (b) Hamming window with N=7. Plot the
frequency response in both cases.
3. Design an ideal Hilbert transformer having frequency response
H(ejω) = j for - π ≤ ω ≤ 0
-j for 0≤ω≤π
Using a (a) rectangular window (b) Hanning window with N=11. Plot the
frequency response in both cases.
4. Design a low pass filter with 11 coefficients for the following specifications:
Passband frequency edge=0.25 KHz and sampling frequency=1KHz. Use
rectangular window, Hamming window and Hanning window in the design.
5. Design a bandpass filter for the following specifications fc1= 100 Hz, fc2= 200 Hz,
Fs=1000 Hz filter length=9. Use Hamming window.
6. Design an FIR filter to meet the following specifications: Passband edge= 2 KHz
Stopband edge= 5 KHz, stopband attenuation= 42 dB, sampling frequency Fs= 20
KHz. Use appropriate window function.
7. Design a 15-tap linear phase filter to the following discrete frequency response
(N=15) using frequency sampling method.
H(k)= 1 0k4
0.5 k=5
0.25 k=6
0.1 k=7
0 elsewhere
8. Explain in detail the frequency sampling technique to design FIR filter.
9. Determine the coefficients of a linear phase FIR filter of length N=15 which has a
symmetric unit sample response & a frequency which satisfies the condition
H(2k/15) =1 k=0,1,2,3
0 k=4,5,6,7
7. Realize the following FIR systems in (a) direct form (b) cascade form
(i) H(z)= 1+ 2/z + 1/2z2 - 1/2z3 - 1/2z4
(ii) H(z)= 1+ 2/z - 3/z2 – 4/z3 + 5/z4
8. Realize the following system functions using a minimum number of multipliers
(i) H(z)= 1+ 2/z + 3/z2 + 4/z3 + 3/z4+2/z5+1/z6
(ii) H(z)= (1 – 1/ 2z + 1/z2) (1- 1/ 4z + 1/z2)
9.Obtain FIR linear-phase and cascade realizations of the system
H(z)= (1 +1/ 2z-1 + z-2) (1+ 1/ 4 z-1 + z-2)
Prepared by
M.Dhanalakshmi AP/BME.
