 # (Q1) Perform a filter design using a method of your choice of a one...

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(Q1) Perform a filter design using a method of your choice of a one- Dimensional FIR or IIR filter at the following normalized Band of frequencies. In each case, plot the pole, zero locations on the z-plane as well as the frequency response. Transform the one-dimensional filter into 3-Dimensions and plot the frequency response of the filter. 1. a) Design a low-pass filter using a Blackman Window the following specs, while keeping the window order at a minimum  Sampling Frequency = 2Hz  Passband= 0-0.4Hz  Stopband = 0.5Hz—1 Hz  Pass ripple = 2%  Attenuation =93dB 2. b) Design a band-pass filter Using a Hamming Window with the following Specifications, while keeping the window order at a minimum  Sampling frequency = 2  Passband = 0.45Hz – 0.6Hz  Stopband =0 – 0.4Hz and 0.65Hz – 1 Hz  Passband ripple = 4%  Stopband ripple =4% 3. c) Design a band-stop filter Using a Von Hann Window with the following Specifications: while keeping the window order at a minimum.  Sampling frequency = 2  Stopband = 0.45Hz – 0.6Hz  Passband =0 – 0.4Hz and 0.65Hz – 1 Hz  Passband ripple = 4%  Stopband ripple =4% 4. d) Design a minimum order one-Dimensional FIR High Pass Filter using the Park-McClellan Method with the following Specification,  Sampling Frequency = 2Hz  Stopband= 0-0.4Hz  Passband = 0.5Hz—1 Hz  Pass ripple = 2%  Stopband Ripple =4% Digital Signal Processing e) Design an IIR Resonant filter that selects the frequency of 0.5Hz with a Sampling frequency of 2Hz. (Q2) Download a low-resolution image of your choice with no higher resolution than 480 X 480 pixels into MATLAB using the “imread” function. Use the “imshow” function in MATLAB to display the picture in Grayscale resolution. Pass image thru each 3-D filter you designed. In each case produce the frequency response of the filtered image. Display each filtered image and comment on the result. (Q3) The doppler shift effect can be applied to group of frequencies just as it can to a single frequency. On the piano, the F-Major chord is made up of the notes F, A, and C which correspond to the frequencies 349.228 Hz, 436.682 Hz, and 523.271 Hz respectively. Create three sine waves at these frequencies and add them together to synthesize the chord. Use a sample frequency of 44100 Hz and normalize the amplitude of the result to 1. Use the MATLAB® function to Doppler shift the F-major Chord by sliding them laterally over a course of 5 seconds to the frequencies 449.228 Hz, 536.682 Hz, and 623.271 Hz respectively (Essentially shifting them by 100Hz). Change the amplitude in a linear fashion so that the amplitudes are louder at higher frequencies. Use the Sound command to play the effect. After a 3 Second Pause, Reverse the effects with the same duration.

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clc;clear all;
Fp = 0.4;
Fst = 0.5;
Fs = 2;
R = (10^(0.02/20) - 1)/(10^(0.02/20) + 1); %Ripple
A = 10^(-93/20); %attenuation
Filt = firgr('minorder',[0 Fp/(Fs/2) Fst/(Fs/2) 1/(Fs/2)], [1 1 0 0],[R A]);
if (mod(length(Filt),2) == 0)
N = length(Filt);
else
N = length(Filt)+1;
end
Filt = firgr(N,[0 Fp/(Fs/2) Fst/(Fs/2) 1/(Fs/2)], [1 1 0 0],[R A]);
Filt = Filt.*blackman(length(Filt))';
figure;zplane(Filt);title('Pole-Zero Plot');
[h,w]=freqz(Filt);
H = abs(h);
H = 20*log10(H/max(H));
figure;
subplot(2,1,1);plot(w*(Fs/(2*pi)),H,'--k','Linewidth',2);
xlabel('Frequency(Hz)');ylabel('Magnitude');
title('1D Filter Magnitude Response');
subplot(2,1,2);plot(w*(Fs/(2*pi)),angle(h),'--k','Linewidth',2);
title('1D Filter Phase Response');
H3 = ftrans2(Filt);
figure;freqz2(H3);
title('2D Filter Response');

clc;clear all;
Fs1 = 0.4;
Fp1 = 0.45;
Fp2 = 0.6;
Fs2 = 0.65;
Fs = 2;
R1 = (10^(0.04/20) - 1)/(10^(0.04/20) + 1); %Ripple1
R2 = (10^(0.04/20) - 1)/(10^(0.04/20) + 1); %Ripple2
Filt = firgr('minorder',[0,Fs1/(Fs/2),Fp1/(Fs/2),Fp2/(Fs/2),Fs2/(Fs/2),1/(Fs/2)],[0 0 1 1 0 0],[R2 R1 R2]);
if (mod(length(Filt),2) == 0)
N = length(Filt);
else
N = length(Filt)+1;
end
Filt = firgr(N,[0,Fs1/(Fs/2),Fp1/(Fs/2),Fp2/(Fs/2),Fs2/(Fs/2),1/(Fs/2)],[0 0 1 1 0 0],[R2 R1 R2]);
Filt = Filt.*hamming(length(Filt))';
figure;zplane(Filt);title('Pole-Zero Plot');
[h,w]=freqz(Filt);
H = abs(h);
H = 20*log10(H/max(H));
figure...

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