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

Matlab code for A:

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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