Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 297

7.27. Design a lowpass FIR filter whose cutoff frequency is 1,000 Hz using the Hamming window
function for the following specified filter length. Assume that the sampling frequency is
8,000 Hz.
a. 21 filter coefficients
b. 31 filter coefficients
c. 41 filter coefficients
List the FIR filter coefficients for each design and compare the magnitude frequency
responses.
7.28. Design a 31-tap highpass FIR filter whose cutoff frequency is 2,500 Hz using the following
window functions. Assume that the sampling frequency is 8,000 Hz.
a. Hanning window function
b. Hamming window function
c. Blackman window function
List the FIR filter coefficients and plot the frequency responses for each design.
7.29. Design a 41-tap bandpass FIR filter with lower and upper cutoff frequencies of 2,500 Hz and
3,000 Hz, respectively, using the following window functions. Assume a sampling frequency
of 8,000 Hz.
a. Hanning window function
b. Blackman window function.
List the FIR filter coefficients and plot the frequency responses for each design.
7.30. Design a 41-tap band reject FIR filter with cutoff frequencies of 2,500 Hz and 3,000 Hz,
respectively, using the Hamming window function. Assume a sampling frequency of 8,000
Hz. List the FIR filter coefficients and plot the frequency responses.
7.31. Use the frequency sampling method to design a linear phase lowpass FIR filter with 17
coefficients. Let the cutoff frequency be 2,000 Hz and assume a sampling frequency of 8,000
Hz. List the FIR filter coefficients and plot the frequency responses.
7.32. Use the frequency sampling method to design a linear phase bandpass FIR filter with 21
coefficients. Let the lower and upper cutoff frequencies be 2,000 Hz and 2,500 Hz,
respectively, and assume a sampling frequency of 8,000 Hz. List the FIR filter coefficients
and plot the frequency responses.
7.33. Given an input data sequence
xðnÞ¼ 1 : 2 $ sin ð 2 pð 1 ; 000 Þn= 8 ; 000 Þ 1 : 5 $ cos ð 2 pð 2 ; 800 Þn= 8 ; 000 Þ
with a sampling frequency of 8,000 Hz, use the designed FIR filter with a Hamming window
in Problem 7.26 to filter 400 data points of xðnÞ , and plot the 400 samples of the input and
output data.