Tutorial # 5 DSP Batch-1

Questions 1. Windowing Method

a) Using a triangular window technique design a lowpass filter for the following

specification

Hd (ejω

) =

0 | | /2;0

2 / | | 2 / ; e -j5

b) Using a hanning window technique design a bandpass filter for the following specification

Hd (ejω

) =

| | /2;0

4/ | | 0;02 / | | 4 / ; e -j5

2. Windowing Method

a) Using a rectangular window technique design a lowpass filter with passband gain of unity,

cutoff frequency of 1000Hz and working at a sampling frequency of 5KHz.The length of

the impulse response should be 7.

b) Design a highpass filter using Hamming window, with a cutoff frequency of 1.2 rad/sec

and N=9.

3. Frequency Sampling Method

c) A HPF has the desired response as given below

Hd (ejω

) =

0 | | /2;0

2 / | | ; e

2

1j-

N

Determine the filter coefficients h(n) for N = 7 using frequency sampling Techniques.

d) Determine the coefficients of a linear phase FIR filter of the length N=15 has symmetric

unit sample response and a frequency response that satisfies the conditions

7,6,5,4;0

3,2,1,0;1

15

2

kfor

kforkH

4. Frequency Sampling Method

e) Using frequency sampling method, design a bandpass filter with the following

specifications

Sampling frequency F=8000 Hz

Cut off frequencies fc1 = 1000Hz

fc2 = 3000Hz

Determine the filter coefficients for N=7.

f) Use frequency sampling method to design a FIR LPF with c =4

, for N=15.