EEE4510 : Introduction to Digital Signal Processing : Design a second-

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The implementation of the filter is shown below.

2.

Part b
Filter’s difference equation,  can be calculated from part  of the question.

Part d
The MATLAB program attached verifies that the output
w = 0:2*pi:10*pi;
H =0*exp(j*w)-0*exp(j*w);
subplot(211)
plot(w,abs(H))
grid
hold
plot([0*pi 0*pi],[0 3],’r’)
plot([0*pi 0*pi],[0 3],’r’)
ylabel(‘Magnitude’)
subplot(212)
plot(w,angle(H))
grid
hold
plot([0 0.005*pi],[-2 3],’r’)
ylabel(‘Phase (rad)’)
xlabel(‘Digital Frequency omega’)

The blue lines on figure 1 show that the frequency response of the system is zero since,

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Figure 1: MATLAB Results
3
Part a

The implementation of the filter is done through the MATLAB code shown below and the output plot is shown in figure 2.
w = 0:pi/200:pi;
H = 1 – exp(-j*w) + exp(-j*2*w);
subplot(211)
plot(w,abs(H))
grid
hold
plot([0.4*pi 0.4*pi],[0 3],’r’)
plot([0.6*pi 0.6*pi],[0 3],’r’)
ylabel(‘Magnitude’)
subplot(212)
plot(w,angle(H))
grid
hold
plot([0.4*pi 0.4*pi],[-2 3],’r’)
ylabel(‘Phase (rad)’)
xlabel(‘Digital Frequency omega’)

Figure 2: Filter Implementation

Part b

Solving for N yields,
Part c
It is not possible to design an M-point moving averaging filter because of the frequency restrictions.
4.
Part a

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Part b
The phase and magnitude plot using “dltidemo” command is shown in figure 3
%MATLAB code using dltidemo command
w = -pi:pi/100:pi;
H = freqz([0.5 -0.5],1,w); %use a custom w axis
subplot(211)
plot(w,abs(H))
axis([-pi pi 0 1.1]); grid; ylabel(‘Magnitude Response’)
subplot(212)
plot(w,angle(H))
axis([-pi pi -1.8 1.8]); grid;
ylabel(‘Phase Response (rad)’)
xlabel(‘hat  ………

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