diff --git a/BW_IIR filter.m b/BW_IIR filter.m
new file mode 100644
index 0000000..fe0f17d
--- /dev/null
+++ b/BW_IIR filter.m	
@@ -0,0 +1,64 @@
+%IIR BUTTERWORTH FILTER
+syms s
+kp=-2;
+ks=-10;
+wp=20;
+ws=30;
+j=sqrt(-1);
+N=log((10^(-kp/10)-1)/(10^(-ks/10)-1))/(2*log(wp/ws))
+N=round(N)+1
+wc=wp/(10^(-kp/10)-1)^(1/(2*N))
+H1=1/(s+1);
+H2=1/(s^2+1.414*s+1);
+H3=1/((s^2+s+1)*(s+1));
+H4=1/((s^2+0.765368*s+1)*(s^2+1.84776*s+1));
+H5=1/((s+1)*(s^2+0.6180*s+1)*(s^2+1.6180*s+1));
+
+if N==1
+H(s)=H1;
+elseif N==2
+H(s)=H2;
+elseif N==3
+H(s)=H3;
+elseif N==4
+H(s)=H4;
+elseif N==5
+H(s)=H5;
+end
+H(s)=H(s/wc)
+H(s)=H(j*wp)
+n=abs(H(s))
+
+m=20*log(H(s))
+%IIR BUTTERWORTH FILTER
+syms s
+kp=-2;
+ks=-10;
+wp=20;
+ws=30;
+j=sqrt(-1);
+N=log((10^(-kp/10)-1)/(10^(-ks/10)-1))/(2*log(wp/ws))
+N=round(N)+1
+wc=wp/(10^(-kp/10)-1)^(1/(2*N))
+H1=1/(s+1);
+H2=1/(s^2+1.414*s+1);
+H3=1/((s^2+s+1)*(s+1));
+H4=1/((s^2+0.765368*s+1)*(s^2+1.84776*s+1));
+H5=1/((s+1)*(s^2+0.6180*s+1)*(s^2+1.6180*s+1));
+
+if N==1
+H(s)=H1;
+elseif N==2
+H(s)=H2;
+elseif N==3
+H(s)=H3;
+elseif N==4
+H(s)=H4;
+elseif N==5
+H(s)=H5;
+end
+H(s)=H(s/wc)
+H(s)=H(j*wp)
+n=abs(H(s))
+
+m=20*log(H(s))
diff --git a/BW_IIR_filter.m b/BW_IIR_filter.m
new file mode 100644
index 0000000..fe0f17d
--- /dev/null
+++ b/BW_IIR_filter.m
@@ -0,0 +1,64 @@
+%IIR BUTTERWORTH FILTER
+syms s
+kp=-2;
+ks=-10;
+wp=20;
+ws=30;
+j=sqrt(-1);
+N=log((10^(-kp/10)-1)/(10^(-ks/10)-1))/(2*log(wp/ws))
+N=round(N)+1
+wc=wp/(10^(-kp/10)-1)^(1/(2*N))
+H1=1/(s+1);
+H2=1/(s^2+1.414*s+1);
+H3=1/((s^2+s+1)*(s+1));
+H4=1/((s^2+0.765368*s+1)*(s^2+1.84776*s+1));
+H5=1/((s+1)*(s^2+0.6180*s+1)*(s^2+1.6180*s+1));
+
+if N==1
+H(s)=H1;
+elseif N==2
+H(s)=H2;
+elseif N==3
+H(s)=H3;
+elseif N==4
+H(s)=H4;
+elseif N==5
+H(s)=H5;
+end
+H(s)=H(s/wc)
+H(s)=H(j*wp)
+n=abs(H(s))
+
+m=20*log(H(s))
+%IIR BUTTERWORTH FILTER
+syms s
+kp=-2;
+ks=-10;
+wp=20;
+ws=30;
+j=sqrt(-1);
+N=log((10^(-kp/10)-1)/(10^(-ks/10)-1))/(2*log(wp/ws))
+N=round(N)+1
+wc=wp/(10^(-kp/10)-1)^(1/(2*N))
+H1=1/(s+1);
+H2=1/(s^2+1.414*s+1);
+H3=1/((s^2+s+1)*(s+1));
+H4=1/((s^2+0.765368*s+1)*(s^2+1.84776*s+1));
+H5=1/((s+1)*(s^2+0.6180*s+1)*(s^2+1.6180*s+1));
+
+if N==1
+H(s)=H1;
+elseif N==2
+H(s)=H2;
+elseif N==3
+H(s)=H3;
+elseif N==4
+H(s)=H4;
+elseif N==5
+H(s)=H5;
+end
+H(s)=H(s/wc)
+H(s)=H(j*wp)
+n=abs(H(s))
+
+m=20*log(H(s))
diff --git a/Chebyshev_IIR.m b/Chebyshev_IIR.m
new file mode 100644
index 0000000..4ddbb18
--- /dev/null
+++ b/Chebyshev_IIR.m
@@ -0,0 +1,33 @@
+%Chebyshev Filter
+syms s
+kp=-2;
+ks=-20;
+wp=1;
+ws=1.3;
+j=sqrt(-1);
+e=sqrt(((1/(10^(kp/20)))^2)-1);
+dp=1-(1/sqrt(1+(e^2)));
+ds=10^(ks/20);
+%discrimination factor
+d=sqrt(((1-dp)^(-2)-1)/((ds^(-2))-1));
+%selectivity factor
+k=wp/ws;
+N=(acosh(1/d))/(acosh(1/k));
+N=round(N)+1;
+%to find a and b
+
+a1=(1/2)*(((1+sqrt(1+e^2))/e)^(1/N));
+a2=(1/2)*(((1+sqrt(1+e^2))/e)^(-1/N));
+a=a1-a2;
+b=a1+a2;
+
+for k=1:1:N
+S(k+1)=(-a)*sin(((2*k)-1)*(pi/(2*N)));
+end
+
+for k=1:1:N
+w(k+1)=b*cos(((2*k)-1)*(pi/(2*N)));
+end
+for m=1:1:N
+l(m+1)=(s-(S(m)+(j*w(m))));
+end
\ No newline at end of file
diff --git a/DFT.m b/DFT.m
new file mode 100644
index 0000000..daab82d
--- /dev/null
+++ b/DFT.m
@@ -0,0 +1,26 @@
+x = [1,2,3,4];
+N = length(x);
+% k = (1:N)
+X = zeros(1, N);
+j = sqrt(-1);
+disp("DFT of x(n) ")
+%DFT of x(n) 
+for k = 0:N-1
+ for n= 0:N-1
+ X(k+1) = X(k+1) + x(n+1)*(exp(-j * n * k *2 *pi / N))
+ end
+end
+ny = (1:N);
+X_mag = abs(X);
+X_phase = angle(X);
+figure("Name","DFT")
+subplot(2,1,1)
+stem(ny,X_mag,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Mag")
+title("Magnitude plot")
+subplot(2,1,2)
+stem(ny, X_phase,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Phase")
+title("Phase plot")
diff --git a/DFT2.m b/DFT2.m
new file mode 100644
index 0000000..17d64fc
--- /dev/null
+++ b/DFT2.m
@@ -0,0 +1,26 @@
+x = [1,2,3,4,5];
+N = length(x);
+% k = (1:N)
+X = zeros(1, N);
+j = sqrt(-1);
+disp("DFT of x(n) ")
+%DFT of x(n) 
+for k = 0:N-1
+ for n= 0:N-1
+ X(k+1) = X(k+1) + x(n+1)*(exp(-j * n * k *(2 *pi / N)))
+ end
+end
+ny = (1:N);
+X_mag = abs(X);
+X_phase = angle(X);
+figure("Name","DFT")
+subplot(2,1,1)
+stem(ny,X_mag,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Mag")
+title("Magnitude plot")
+subplot(2,1,2)
+stem(ny, X_phase,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Phase")
+title("Phase plot")
\ No newline at end of file
diff --git a/FFT.m b/FFT.m
new file mode 100644
index 0000000..c04f9d5
--- /dev/null
+++ b/FFT.m
@@ -0,0 +1,67 @@
+syms Wnkm(k,m) Wnk(k)
+x = [1 2 3 4 5 6 7 8];
+N = length(x);
+f1 = (zeros(1,round(N/2)));
+f2 = (zeros(1,round(N/2)));
+y=1;
+%Decimating into EVEN and ODD
+for i=1:N
+ if rem(i,2)==0
+ f2(y) = x(i);
+ y=y+1;
+ else
+ f1(y) = x(i);
+end
+end
+j=sqrt(-1);
+Wnkm(k,m) = exp((-j*4*pi*k*m)/N);
+Wnk(k) = exp((-j*2*pi*k)/N);
+F1 = (zeros(1,round(N/2)));
+F2 = (zeros(1,round(N/2)));
+%F1(k)
+for k=1:(round(N/2))
+ for m=1:(round(N/2))
+ F1(k) = F1(k) + f1(m)*Wnkm(k-1,m-1);
+ end
+end
+%F2(k)
+for k=1:(round(N/2))
+ for m=1:(round(N/2))
+ F2(k) = F2(k) + f2(m)*Wnkm(k-1,m-1);
+ end
+end
+F1;
+F2;
+X1 = (zeros(1,round(N/2)));
+X2 = (zeros(1,round(N/2)));
+%X1(k) = X(k) and X2(k) = X(k+N/2)
+for k=1:(round(N/2))
+ X1(k) = F1(k) + Wnk(k-1)*F2(k);
+ X2(k) = F1(k) - Wnk(k-1)*F2(k);
+end
+X_without_fft = [X1,X2]
+%X_without_fft = 1×8 complex
+% 36.0000 + 0.0000i -4.0000 + 9.6569i -4.0000 + 4.0000i -4.0000 + 1.6569i 
+%⋯
+X_mag = abs(X_without_fft);
+X_phase = angle(X_without_fft);
+f = 1:N;
+figure("Name","FFT")
+subplot(3,1,1)
+stem(f,x,"filled","LineWidth",3)
+title("Input sequence")
+ylabel("x(n)")
+xlabel("N")
+grid
+subplot(3,1,2)
+stem(f,X_mag,"filled","LineWidth",3)
+title("Magnitude spectrum")
+ylabel("Magnitude")
+xlabel("Frequency")
+grid
+subplot(3,1,3)
+stem(f,X_phase,"filled","LineWidth",3)
+title("Phase spectrum")
+ylabel("Phase")
+xlabel("Frequency")
+grid
diff --git a/FIR.m b/FIR.m
new file mode 100644
index 0000000..30aaf37
--- /dev/null
+++ b/FIR.m
@@ -0,0 +1,58 @@
+N=7;
+wc=1;
+alpha=(N-1)/2;
+n=0:1:N-1;
+%Desired impulse response
+for i=0:1:(N-1)
+ if(i~=alpha)
+ hd(i+1)=(sin(wc*(i-3))/(pi*(i-3)));
+ else
+ hd(i+1)=wc/pi;
+ end
+end
+subplot(5,1,1);
+stem(n,hd);
+xlabel('n');
+ylabel('hd(n)');
+title('Desired impulse response');
+wHm = zeros(1,7);
+%Hamming window
+for j=0: 6
+ wHm(j+1)=0.54-(0.46*cos(2*pi*j/(N-1)));
+end
+subplot(5,1,2);
+stem(n,wHm);
+xlabel('n');
+ylabel('whm(n)');
+title('Hamming window');
+%Impulse response
+hn=hd.*wHm;
+subplot(5,1,3);
+stem(n,hn);
+xlabel('n');
+ylabel('h(n)');
+title('Impulse response');
+hw=[];
+for w=0:(1/pi):pi
+ t=0;
+ temp=0;
+ const=hn(alpha+1);
+ for m=0:1:((N-3)/2)
+ temp=temp+(2.*hn(m+1).*cos(w.*(alpha-m)));
+ end
+ temp=temp+const;
+ hw=[hw, temp];
+end
+w=0:1/pi:pi;
+%Magnitude response
+subplot(5,1,4);
+stem(w,hw);
+xlabel('w');
+ylabel('|H(w)|');
+title('Magnitude response');
+phase=-w*alpha;
+subplot(5,1,5);
+stem(w,phase);
+xlabel('w');
+ylabel('Phase');
+title('Phase response');
\ No newline at end of file
diff --git a/FIR1.m b/FIR1.m
new file mode 100644
index 0000000..40c9124
--- /dev/null
+++ b/FIR1.m
@@ -0,0 +1,49 @@
+wc=1;
+N=51;
+alpha=(N-1)/2;
+n=0:1:N-1;
+%Rectangular window
+for j=0:1:(N-1)
+ wR(j+1)=1;
+end
+subplot(5,1,1);
+stem(n,wR);
+xlabel('n');
+ylabel('wR(n)');
+title('Rectangular window');
+%Bartlett window
+for j=0:1:(N-1)
+ wBr(j+1)=1-(2.*abs(j-((N-1)/2)))/(N-1);
+end;
+subplot(5,1,2);
+stem(n,wBr);
+xlabel('n');
+ylabel('wBr(n)');
+title('Bartlett window');
+%Hamming window
+for j=0:1:(N-1)
+ wHm(j+1)=0.54-(0.46*cos(2*pi*j/(N-1)));
+end;
+subplot(5,1,3);
+stem(n,wHm);
+xlabel('n');
+ylabel('whm(n)');
+title('Hamming window');
+%Hanning window
+for j=0:1:(N-1)
+ wHn(j+1)=0.5-(0.5*cos(2*pi*j/(N-1)));
+end;
+subplot(5,1,4);
+stem(n,wHn);
+xlabel('n');
+ylabel('whn(n)');
+title('Hanning window');
+%Blackmann window
+for j=0:1:(N-1)
+ wBl(j+1)=0.42-(0.5*(cos(2*pi*j/(N-1))))+(0.08*(cos(4*pi*j/(N-1))));
+end;
+subplot(5,1,5);
+stem(n,wBl);
+xlabel('n');
+ylabel('wbl(n)');
+title('Blackmann window');
\ No newline at end of file
diff --git a/IDFT.m b/IDFT.m
new file mode 100644
index 0000000..d7c4b5b
--- /dev/null
+++ b/IDFT.m
@@ -0,0 +1,25 @@
+X = [1,2,3,4];
+N = length(X);
+x = zeros(1,N);
+j = sqrt(-1);
+disp("IDFT of X(K)")
+%IDFT of X(K)
+for n=1:N
+ for k=1:N
+ x(n) = (x(n) + X(k)*(exp(j * n * k *(2 *pi / N)))) / N
+ end
+end
+ny = (1:N);
+x_mag = abs(x);
+x_phase = angle(x);
+figure("Name","IDFT")
+subplot(2,1,1)
+stem(ny,x_mag,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Mag")
+title("Magnitude plot")
+subplot(2,1,2)
+stem(ny, x_phase,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Phase")
+title("Phase plot")
\ No newline at end of file
diff --git a/IFFT.m b/IFFT.m
new file mode 100644
index 0000000..bd58914
--- /dev/null
+++ b/IFFT.m
@@ -0,0 +1,73 @@
+disp("Inverse Fast Fourier Transform - DITIFFT")
+%Inverse Fast Fourier Transform - DITIFFT
+syms Wnkm(k,m) Wnk(k)
+X = [11 1+j 0 1-2j 0 1+2j 0 1-j];
+X = conj(X);
+N = length(X);
+f1 = (zeros(1,round(N/2)));
+f2 = (zeros(1,round(N/2)));
+y=1;
+%Decimating into EVEN and ODD
+for i=1:N
+ if rem(i,2)==0
+ f2(y) = X(i);
+ y=y+1;
+ else
+ f1(y) = X(i);
+ 
+ end
+end
+j=sqrt(-1);
+Wnkm(k,m) = exp((-j*4*pi*k*m)/N);
+Wnk(k) = exp((-j*2*pi*k)/N);
+F1 = (zeros(1,round(N/2)));
+F2 = (zeros(1,round(N/2)));
+%F1(k)
+for k=1:(round(N/2))
+ for m=1:(round(N/2))
+ F1(k) = F1(k) + f1(m)*Wnkm(k-1,m-1);
+ end
+end
+%F2(k)
+for k=1:(round(N/2))
+ for m=1:(round(N/2))
+ F2(k) = F2(k) + f2(m)*Wnkm(k-1,m-1);
+ end
+end
+x1 = (zeros(1,round(N/2)));
+x2 = (zeros(1,round(N/2)));
+%X1(k) = X(k) and X2(k) = X(k+N/2)
+for k=1:(round(N/2))
+ x1(k) = (F1(k) + Wnk(k-1)*F2(k))/N;
+ x2(k) = (F1(k) - Wnk(k-1)*F2(k))/N;
+end
+x_without_ifft = [x1,x2]
+%x_without_ifft = 1×8
+% 1.8750 1.5518 0.6250 1.5518 0.8750 1.1982 2.1250 ⋯
+X_mag = abs(X);
+X_phase = angle(X);
+f = 1:N;
+%FFT with using inbuilt function
+X = [11 1+j 0 1-2j 0 1+2j 0 1-j];
+x_with_ifft = ifft(X)
+%x_with_ifft = 1×8
+ %1.8750 1.5518 0.6250 1.5518 0.8750 1.1982 2.1250 ⋯
+figure("Name","IFFT")
+subplot(3,1,1)
+stem(f,X_mag,"filled","LineWidth",3)
+title("X(k) Magnitude spectrum")
+ylabel("Magnitude")
+xlabel("Frequency")
+grid
+subplot(3,1,2)
+stem(f,X_phase,"filled","LineWidth",3)
+title("X(k) Phase spectrum")
+ylabel("Phase")
+xlabel("Frequency")
+grid
+subplot(3,1,3)
+stem(f,x_without_ifft,"filled","LineWidth",3)
+title("Output sequence")
+ylabel("x(n)")
+xlabel("N")
+grid
diff --git a/IIIR.m b/IIIR.m
new file mode 100644
index 0000000..f400f26
--- /dev/null
+++ b/IIIR.m
@@ -0,0 +1,14 @@
+t=linspace(0,1,1000);
+x=sin(2*pi*t);
+z=awgn(x,1);
+N=40;
+f=10;
+fs=200;
+w=2*pi*f/fs;
+[b,a]=butter(N,w);
+fvtool(b,a);
+iir=filter(b,a,z);
+subplot(2,1,1)
+plot(t,z);
+subplot(2,1,2)
+plot(t,iir);
\ No newline at end of file
diff --git a/IIR.m b/IIR.m
new file mode 100644
index 0000000..9a5cd75
--- /dev/null
+++ b/IIR.m
@@ -0,0 +1,15 @@
+t=linspace(0,1,1000);
+x=sin(2*pi*t);
+z=awgn(x,1);
+N=40;
+f=10;
+fs=200;
+w=2*pi*f/fs;
+[b,a]=butter(N,w);
+fvtool(b,a);
+iir=filter(b,a,z);
+subplot(2,1,1)
+plot(t,z);
+subplot(2,1,2)
+plot(t,iir);
+
diff --git a/IIR_basic.m b/IIR_basic.m
new file mode 100644
index 0000000..63aa851
--- /dev/null
+++ b/IIR_basic.m
@@ -0,0 +1,15 @@
+kp=-1;
+ks=-20;
+wp=4;
+ws=8;
+n=(log((10^(-kp/10)-1)/(10^(-ks/10)-1)))/(2*(log(wp/ws)))
+wc=(wp)/((10^(-kp/10)-1)^(1/10))
+
+for k=(2*N)-1
+    theta_k=((pi*k)/N)+(pi/(2*N))+(pi/2)
+end
+s0=((pi/(2*N))+(pi/2))
+s1=((pi*1)/N)+(pi/(2*N))+(pi/2)
+s2=((pi*2)/N)+(pi/(2*N))+(pi/2)
+s3=((pi*3)/N)+(pi/(2*N))+(pi/2)
+s4=((pi*4)/N)+(pi/(2*N))+(pi/2)
\ No newline at end of file
diff --git a/SP_OPEN_ENDED.m b/SP_OPEN_ENDED.m
new file mode 100644
index 0000000..07b2f9d
--- /dev/null
+++ b/SP_OPEN_ENDED.m
@@ -0,0 +1,73 @@
+BW = "1 octave";  % Bandwidth
+N  = 8;           % Filter order
+F0 = 1000;        % Center frequency (Hz)
+Fs = 48000;       % Sampling frequency (Hz)
+of = octaveFilter(FilterOrder=N,CenterFrequency=F0,  ...
+                  Bandwidth=BW,SampleRate=Fs);
+Nx = 100000;
+scope1 = spectrumAnalyzer(SampleRate=Fs,Method="filter-bank", ...
+    AveragingMethod="exponential",PlotAsTwoSidedSpectrum=false, ...
+    FrequencyScale="log",FrequencySpan="start-and-stop-frequencies", ...
+    StartFrequency=1,StopFrequency=Fs/2,YLimits=[-60 10], ...
+    RBWSource="property",RBW=1);
+tic
+while toc < 20
+    % Run for 20 seconds
+    x1 = randn(Nx,1);
+    y1 = of(x1);
+    scope1(y1)
+end
+ofb = octaveFilterBank("1/3 octave",Fs,FilterOrder=N);
+freqz(ofb,NFFT=2^16)   % Increase FFT length for better low-frequency resolution
+set(gca,XScale="log")
+axis([20 Fs/2 -50 5])
+title("1/3-Octave Filter Bank Magnitude Response")
+
+pinkNoise = dsp.ColoredNoise(Color="pink", ...
+                             SamplesPerFrame=Nx, ...
+                             NumChannels=1);
+
+scope2 = spectrumAnalyzer(SampleRate=Fs,Method="filter-bank", ...
+    AveragingMethod="exponential",PlotAsTwoSidedSpectrum=false, ...
+    FrequencyScale="log",FrequencySpan="start-and-stop-frequencies", ...
+    StartFrequency=20,StopFrequency=Fs/2,YLimits=[-40 30], ...
+    RBWSource="property",RBW=10);
+
+centerOct = getCenterFrequencies(ofb);
+nbOct = numel(centerOct);
+bandPower = zeros(1,nbOct);
+nbSamples = 0;
+
+tic
+while toc < 10
+    xp = pinkNoise();
+    yp = ofb(xp);
+    bandPower = bandPower + sum(yp.^2,1);
+    nbSamples = nbSamples + Nx;
+    scope2(yp)    
+end
+b = 10^(3/10); % base-10 octave ratio
+% Compute power (including pressure reference)
+octPower = 10*log10(bandPower/nbSamples/4e-10);
+
+bar(log(centerOct)/log(b),octPower);
+set(gca,Xticklabel=round(b.^get(gca,"Xtick"),2,"significant"));
+title("1/3-Octave Power Spectrum")
+xlabel("Octave Frequency Band (Hz)")
+ylabel("Power (dB)")
+
+spl = splMeter(Bandwidth="1/3 octave", ...
+               OctaveFilterOrder=N, ...
+               SampleRate=Fs, ...
+               FrequencyWeighting="z-weighting");
+
+scope3 = dsp.ArrayPlot(Title="Pink Noise SPL", ...
+                       XLabel="Octave Frequency Band Number", ...
+                       YLabel="Power (dB)",YLimits=[0 100]);
+tic
+while toc < 10
+    xp = pinkNoise();
+    yp = spl(xp);
+    ypm = mean(yp,1).';
+    scope3(ypm)
+end
\ No newline at end of file
diff --git a/SSPP.m b/SSPP.m
new file mode 100644
index 0000000..3c1cc95
--- /dev/null
+++ b/SSPP.m
@@ -0,0 +1,72 @@
+N = 99;
+[LPAnalysis, HPAnalysis, LPSynthsis, HPSynthesis] = firpr2chfb(N, 0.45);
+fvt = fvtool(LPAnalysis,1, HPAnalysis,1, LPSynthsis,1, HPSynthesis,1);
+fvt.Color = [1,1,1];
+legend(fvt,'Hlp Lowpass Decimator','Hhp Highpass Decimator',...
+    'Glp Lowpass Interpolator','Ghp Highpass Interpolator');
+% Analysis section
+analysisFilter = dsp.SubbandAnalysisFilter(LPAnalysis, HPAnalysis);
+% Synthesis section
+synthFilter = dsp.SubbandSynthesisFilter(LPSynthsis, HPSynthesis);
+x = zeros(50,1);
+x(1:3)   = 1;
+x(8:10)  = 2;
+x(16:18) = 3;
+x(24:26) = 4;
+x(32:34) = 3;
+x(40:42) = 2;
+x(48:50) = 1;
+sigsource = dsp.SignalSource('SignalEndAction', 'Cyclic repetition',...
+    'SamplesPerFrame', 50);
+sigsource.Signal = x;
+
+% Scope to compare input signal with reconstructed output
+sigcompare = dsp.ArrayPlot('NumInputPorts', 2, 'ShowLegend', true,...
+    'Title', 'Input and reconstructed signals',...
+    'ChannelNames',{'Input signal','Reconstructed signal'});
+
+% Scope to plot the RMS error between the input and reconstructed signals
+errorPlot = timescope('Title', 'RMS Error', 'SampleRate', 1, ...
+    'TimeUnits', 'seconds', 'YLimits', [-0.5 2],...
+    'TimeSpanSource', 'property','TimeSpan',100,...
+    'TimeSpanOverrunAction','scroll');
+
+% To calculate the transfer function of the cascade of Analysis and
+% Synthesis subband filters
+tfestimate = dsp.TransferFunctionEstimator('FrequencyRange','centered',...
+    'SpectralAverages', 50);
+% Scope to plot the magnitude response of the estimated transfer function
+magplot = dsp.ArrayPlot('PlotType','Line', ...
+    'YLabel', 'Magnitude Response (dB)',...
+    'Title','Magnitude response of the estimated transfer function',...
+    'XOffset',-25, 'XLabel','Frequency (Hz)',...
+    'YLimits',[-5 5]);
+% Scope to plot the phase response of the estimated transfer function
+phaseplot = dsp.ArrayPlot('PlotType','Line', ...
+    'YLabel', 'Phase Response (degrees)',...
+    'Title','Phase response of the estimated transfer function',...
+    'XOffset',-25, 'XLabel','Frequency (Hz)',...
+    'YLimits',[-180 180]);
+
+for i = 1:100
+    % Use the same signal as input in each iteration.
+    input = sigsource();
+    % Analysis
+    [hi, lo] = analysisFilter(input);
+    % Synthesis
+    reconstructed = synthFilter(hi, lo);
+
+    % Compensate for the delay caused by the filters and compare the
+    % signals. Since input signal is periodic, compare the current
+    % frames of input and output signals.
+    sigcompare(input(2:end), reconstructed(1:end-1));
+
+    % Plot error between signals
+    err = rms(input(2:end) - reconstructed(1:end-1));
+    errorPlot(err);
+
+    % Estimate transfer function of cascade
+    Txy = tfestimate(input(2:end), reconstructed(1:end-1));
+    magplot(20*log10(abs(Txy)));
+    phaseplot(angle(Txy)*180/pi);
+end
diff --git a/circular_convolution.m b/circular_convolution.m
new file mode 100644
index 0000000..d1682a0
--- /dev/null
+++ b/circular_convolution.m
@@ -0,0 +1,23 @@
+x = [1,2,3];
+h = [3,4,5,6];
+n1=length(x);
+n2 = length(h);
+n = max(n1,n2);
+a = 1:n;
+x = [x,zeros(1,n-n1)];
+h = [h,zeros(1,n-n2)];
+y = zeros(1,n);
+for i =0:n-1
+ for j = 0:n-1
+ k = mod((i-j),n);
+ y(i+1) = y(i+1) + x(j+1)*h(k+1);
+ end
+end
+figure("Name","Circular conv");
+subplot(2,1,1);
+stem(a,y,"LineWidth",3)
+title("Circular Convolution: Without Inbuilt Function")
+y = cconv(x,h,6);
+subplot(2,1,2);
+stem(y,"LineWidth",3)
+title("Circular Convolution: With Inbuilt Function");
diff --git a/comb_func.m b/comb_func.m
new file mode 100644
index 0000000..0d9224f
--- /dev/null
+++ b/comb_func.m
@@ -0,0 +1,57 @@
+%dt comb
+stem(ones(1,10), 'LineWidth', 2)
+xlabel("Time");
+ylabel("Amplitude");
+
+t = (-1: .1 : 1)';
+impulse = t == 0;
+unitStep = t >= 0;
+ramp = t .* unitStep;
+exponential_inc = exp(1 * t);
+exponential_dec = exp(-1 * t);
+xlabel("Time");
+ylabel("Amplitude");
+
+% Impulse unitStep Ramp
+stem(t,[impulse unitStep ramp],"LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
+hold off
+
+% Exponential 
+stem(t,exponential_inc,"LineWidth",3)
+hold on
+stem(t,exponential_dec,"LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
+hold off
+
+% Rectangular pulse
+fs = 1000;
+T = 10*(1/50);
+t = -0.1:.01:T-1/fs;
+w = 20e-3;
+x = rectpuls(t,w);
+stem(t,x,"LineWidth",3)
+xlabel("Time")
+ylabel("Amplitude")
+title("Rectangular")
+grid on
+
+%Triangle 
+t = (0:0.01:0.4);
+f = 10;
+stem(t,sawtooth(2 * pi * f * t,1/2),"k-","LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
+
+% Sinc And sa
+x = linspace(-5,5,50); 
+sc = sinc(x);
+sa = sin(x) ./ x;
+stem(x,sc,"k-","LineWidth",3)
+hold on
+stem(x,sa,"r-","LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
+hold off
diff --git a/linear_circular.m b/linear_circular.m
new file mode 100644
index 0000000..d9f954a
--- /dev/null
+++ b/linear_circular.m
@@ -0,0 +1,14 @@
+x = [2 1 2 1];
+y = [1 2 3];
+clin = conv(x,y);
+xpad = [x zeros(1,6-length(x))];
+ypad = [y zeros(1,6-length(y))];
+ccirc = ifft(fft(xpad).*fft(ypad));
+subplot(2,1,1)
+stem(clin,'filled',"LineWidth",3)
+ylim([0 11])
+title('Linear Convolution of x and y')
+subplot(2,1,2)
+stem(ccirc,'filled',"LineWidth",3)
+ylim([0 11])
+title('Circular Convolution of xpad and ypad')
\ No newline at end of file
diff --git a/linear_conv_fft.m b/linear_conv_fft.m
new file mode 100644
index 0000000..bd7f95c
--- /dev/null
+++ b/linear_conv_fft.m
@@ -0,0 +1,53 @@
+x = [1 1 1 1];
+h = [1 0 1 0];
+n1 = length(x);
+n2 = length(h);
+N = n1+n2-1;
+x = [x,zeros(1,N-n1)];
+h = [h,zeros(1,N-n2)];
+%To find X(k) and H(k)
+X = fft(x);
+H = fft(h);
+%Y(k)
+Y = X.*H;
+%IFFT to get y(n)
+syms Wnkm(k,m) Wnk(k)
+Y = conj(Y);
+f1 = (zeros(1,round(N/2)));
+f2 = (zeros(1,round(N/2)));
+y=1;
+%Decimating into EVEN and ODD
+for i=1:N
+ if rem(i,2)==0
+ f2(y) = Y(i);
+ y=y+1;
+ else
+ f1(y) = Y(i);
+ 
+ end
+end
+j=sqrt(-1);
+Wnkm(k,m) = exp((-j*4*pi*k*m)/N);
+Wnk(k) = exp((-j*2*pi*k)/N);
+F1 = (zeros(1,round(N/2)));
+F2 = (zeros(1,round(N/2)));
+%F1(k)
+for k=1:(round(N/2))
+ for m=1:(round(N/2))
+ F1(k) = F1(k) + f1(m)*Wnkm(k-1,m-1);
+ end
+end
+%F2(k)
+for k=1:(round(N/2))
+ for m=1:(round(N/2))
+ F2(k) = F2(k) + f2(m)*Wnkm(k-1,m-1);
+ end
+end
+y1 = (zeros(1,round(N/2)));
+y2 = (zeros(1,round(N/2)));
+%X1(k) = X(k) and X2(k) = X(k+N/2)
+for k=1:(round(N/2))
+ y1(k) = (F1(k) + Wnk(k-1)*F2(k))/N;
+ y2(k) = (F1(k) - Wnk(k-1)*F2(k))/N;
+end
+y_linear_convolved = [y1,y2]
\ No newline at end of file
diff --git a/linear_convolution.m b/linear_convolution.m
new file mode 100644
index 0000000..38a6e3f
--- /dev/null
+++ b/linear_convolution.m
@@ -0,0 +1,41 @@
+x = [1,2,3];
+h = [3,4,5,6];
+x_length = length(x);
+h_length = length(h);
+N = x_length + h_length -1;
+x = [x,zeros(1,N-x_length)];
+h = [h,zeros(1,N-h_length)];
+y = zeros(1,N);
+
+%Without inbuilt function
+for n=1:N
+for m=1:n
+y(n) = y(n)+x(m)*h(n-m+1);
+end
+end
+figure("Name","without-Inbuilt")
+ny = (0:N-1);
+subplot(2,2,1);
+stem(ny,x,"LineWidth",3);
+xlabel("n");
+ylabel("x(n)");
+title("First sequence");
+subplot(2,2,2);
+stem(ny,h,"LineWidth",3);
+xlabel("n");
+ylabel("h(n)");
+title("Second sequence");
+subplot(2,2,3);
+stem(ny,y,"LineWidth",3);
+xlabel("n");
+ylabel("y(n)");
+title("Convoluted signal");
+
+%With inbuilt function
+x = [1,2,3];
+h = [3,4,5,6];
+y = conv(x,h);
+ny = (0:N-1);
+subplot(2,2,4)
+stem(ny,y,"LineWidth",3);
+title('Inbuilt Function')
diff --git a/sampling_func.m b/sampling_func.m
new file mode 100644
index 0000000..b9c99cb
--- /dev/null
+++ b/sampling_func.m
@@ -0,0 +1,49 @@
+%To Demonstrate sampling theorm
+f=2;
+fs1=1.2*f;
+fs2=2*f;
+fs3=8*f;
+t=0:0.01:3;
+t1=0:1/fs1:3;
+t2=0:1/fs2:3;
+t3=0:1/fs3:3;
+x=sin(2*pi*f*t);
+subplot(2,2,1);
+plot(t,x);
+xlabel('Time');
+ylabel('Amplitude');
+title('Continuous sine wave');
+
+%Under sampling
+% for fs<2fm
+y1=sin(2*pi*f*t1);
+subplot(2,2,2);
+stem(t1,y1);
+hold on
+plot(t1,y1)
+xlabel('Time');
+ylabel('Amplitude');
+title('Sampled output fs<2fm');
+hold off
+
+%Critical sampling    for fs=2fm
+y2=sin(2*pi*f*t2);
+subplot(2,2,3);
+stem(t2,y2);
+hold on
+plot(t2,y2);
+xlabel('Time');
+ylabel('Amplitude');
+title('Sampled output fs=2fm');
+hold off
+
+%Over sampling   for fs>2fm
+y3=sin(2*pi*f*t3);
+subplot(2,2,4);
+stem(t3,y3);
+hold on
+plot(t3,y3);
+xlabel('Time');
+ylabel('Amplitude');
+title('Sampled output fs>2fm');
+hold off
\ No newline at end of file
diff --git a/signals.m b/signals.m
new file mode 100644
index 0000000..765e810
--- /dev/null
+++ b/signals.m
@@ -0,0 +1,54 @@
+t = (-1: .01 : 1)';
+impulse = t == 0;
+unitStep = t >= 0;
+ramp = t .* unitStep;
+exponential_inc = exp(1 * t);
+exponential_dec = exp(-1 * t);
+
+% Impulse unitStep Ramp
+plot(t,[impulse unitStep ramp],"LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
+legend("Impulse","Unit step","Ramp")
+hold off
+
+% Exponential 
+plot(t,exponential_inc,"LineWidth",3)
+hold on
+plot(t,exponential_dec,"LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
+legend("Rise","Fall")
+hold off
+
+% Sinc And sa
+x = linspace(-5,5); 
+sc = sinc(x);
+sa = sin(x) ./ x;
+plot(x,sc,"k-","LineWidth",3)
+hold on
+plot(x,sa,"r-","LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
+legend("sinc","sa")
+hold off
+grid on
+
+% Rectangular pulse
+fs = 1000;
+T = 10*(1/50);
+t = -0.1:.01:T-1/fs;
+w = 20e-3;
+x = rectpuls(t,w);
+plot(t,x,"LineWidth",3)
+xlabel("Time")
+ylabel("Amplitude")
+title("Rectangular")
+grid on
+
+%Triangle 
+t = (0:0.001:0.4);
+f = 10;
+plot(t,sawtooth(2 * pi * f * t,1/2),"k-","LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
\ No newline at end of file
diff --git a/sine_func.m b/sine_func.m
new file mode 100644
index 0000000..59fb327
--- /dev/null
+++ b/sine_func.m
@@ -0,0 +1,15 @@
+t = (0:.01:2);
+f = 1;
+plot(t,sin(2 * pi * f * t),"k-","LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
+grid on
+
+%ct_dt sine
+fs = 40;
+t = linspace(0,2,fs*2);
+f = 1;
+stem(t,sin(2 * pi * f * t),"k-","LineWidth",3)
+xlabel("Time");
+ylabel("Amplitude");
+