3. For all parts of this problem the input signal is given by x[n]= 1 +2 cos(0.4

Question

3. For all parts of this problem the input signal is given by x[n]= 1 +2 cos(0.4m+0.2) +1.5 cos(0.6n_04) frequency 0.4 and passes the DC and 0.6 input components. Demonstrate your results using MATLAB. Hint: Examine how two of the t H problem 2 a) Design a second-order FIR filter that notches out the normalized notched out the normalized frequency /3. b) Design an N -point moving averaging filter that notches out the normalized frequency 0.4 and passes the DC and 0.6 input components. What should N be? Use MATLAB to verify your design. c) Is it possible to design an M -point moving averaging filter that notches out the normalized frequency 0.6 and passes the DC and 0.4 input components? Explain.

Explanation / Answer

lowpassFilt = dsp.LowpassFilter('DesignForMinimumOrder',false, ...
'FilterOrder',N,'PassbandFrequency',Fp,'SampleRate',Fs,...
'PassbandRipple',0.01, 'StopbandAttenuation',80);
tic
while toc < 10
x = randn(256,1);
y = lowpassFilt(x);
scope(y);
end
vbwFilter = dsp.VariableBandwidthFIRFilter('CutoffFrequency',1e3);
tic
told = 0;
while toc < 10
t = toc;
if floor(t) > told
% Add 1 kHz every second
vbwFilter.CutoffFrequency = vbwFilter.CutoffFrequency + 1e3;
end
x = randn(256,1);
y = vbwFilter(x);
scope(y);
told = floor(t);
end

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