{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 11: Multirate Digital Signal Processing"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.1: Time_Decimatio.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//Example 11.1\n",
"\n",
"clc;clear;close;\n",
"x=[0:6 0:6];\n",
"y=x(1:3:length(x));\n",
"disp(x,'Input signal x(n)=');\n",
"disp(y,'Output signal of decimation process by factor three y(n)');\n",
"subplot(2,1,1);\n",
"plot2d3(x);title('Input signal x(n)');\n",
"subplot(2,1,2);\n",
"plot2d3(y);title('Output signal y(n)');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.2: Interpolation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//Example 11.2\n",
"\n",
"clc;clear;close;\n",
"x=0:5;\n",
"y=[];\n",
"for i=1:length(x)\n",
"    y(1,2*i)=x(i);\n",
"end\n",
"disp(x,'Input signal x(n)=');\n",
"disp(y,'Output signal of interpolation process with factor two y(n)');\n",
"subplot(2,1,1);\n",
"plot2d3(x);title('Input signal x(n)');\n",
"subplot(2,1,2);\n",
"plot2d3(y);title('Output signal y(n)');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.4: Polyphase_Decompositio.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//Example 11.4\n",
"\n",
"clc;clear;\n",
"z=poly(0,'z');\n",
"num=1-4*z^-1;\n",
"den=1+5*z^-1;\n",
"H=num/den;\n",
"num1=num*(1-5*z^-1);\n",
"den1=den*(1-5*z^-1);\n",
"H1=num1/den1;\n",
"c=coeff(numer(num1));\n",
"clength=length(c);\n",
"c=[c zeros(1,pmodulo(clength,2))];      //make length of 'c' multiple of 2\n",
"c0=[];c1=[];\n",
"for n=1:ceil(clength/2)                 //loop to separate even and odd powers of z\n",
"    c0=[c0 c(2*n-1) 0];\n",
"    c1=[c1 c(2*n) 0];\n",
"end\n",
"E0=poly(c0,'z','coeff')/z^n/den1;\n",
"E1=poly(c1,'z','coeff')/z^(n-2)/den1;\n",
"disp('Polyphase Components')\n",
"disp(E0,'E0(z)');\n",
"disp(E1,'E1(z)');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.5: Decimator_implementation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//Example 11.5\n",
"\n",
"clc;clear;\n",
"\n",
"function [N,R]=func(Fs,Fp,Ft,Fti,dp,ds,M)\n",
"    dF=(Fs-Fp)/Ft;                                      //Normalised transition bandwidth\n",
"    N=round((-20*log10(sqroot(dp*ds))-13)/(14.6*dF));   //FIR Filter length\n",
"    R=N*Fti/M;                                          //Number of Multiplications per second\n",
"endfunction\n",
"\n",
"Ft=20000;         //Sampling rate of input signal\n",
"Fp=40;            //Passband frequency\n",
"Fs=50;            //Stopband frequency\n",
"dp=0.01;          //Passband ripple\n",
"ds=0.002;         //Stopband ripple\n",
"M=100;            //Decimation Factor\n",
"Fti=Ft;           //Input sampling rate\n",
"//Single stage implementation\n",
"[N1,R1]=func(Fs,Fp,Ft,Fti,dp,ds,M);\n",
"\n",
"//Two stage implementation\n",
"//Stage 1 F(z) with decimation factor 50\n",
"Fpf=Fp;            //Passband frequency\n",
"Fsf=190;           //Stopband frequency\n",
"dpf=0.005;         //Passband ripple\n",
"dsf=0.002;         //Stopband ripple\n",
"Mf=50;             //Decimation Factor\n",
"Fti=Ft;            //Input sampling rate\n",
"[N2f,R2f]=func(Fsf,Fpf,Ft,Fti,dpf,dsf,Mf);\n",
"\n",
"//Stage 2 G(z) with decimation factor 2\n",
"Fpg=50*Fp;         //Passband frequency\n",
"Fsg=50*Fs;         //Stopband frequency\n",
"dpg=0.005;         //Passband ripple\n",
"dsg=0.002;         //Stopband ripple\n",
"Mg=2;              //Decimation Factor\n",
"Fti=Ft/50;         //Input sampling rate\n",
"[N2g,R2g]=func(Fsg,Fpg,Ft,Fti,dpg,dsg,Mg);\n",
"N2=N2f+50*N2g+2;    //Total filter length\n",
"R2=R2f+R2g;         //Total Number of Multiplications per second\n",
"disp(R1,'Number of Multiplications per second =',N1,'FIR filter length =','For Single stage implementation:');\n",
"disp('For Two stage implementation:');\n",
"disp(R2f,'Number of Multiplications per second =',N2f,'FIR filter length =','For F(z):');\n",
"disp(R2g,'Number of Multiplications per second =',N2g,'FIR filter length =','For G(z):');\n",
"disp(R2,'Total Number of Multiplications per second =',N2,'Overall FIR filter length =');\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.6: Decimator_implementation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//Example 11.6\n",
"\n",
"clc;clear;\n",
"\n",
"\n",
"function [N,R]=func(Fs,Fp,Ft,Fti,dp,ds,M)\n",
"    dF=(Fs-Fp)/Ft;                                      //Normalised transition bandwidth\n",
"    N=round((-20*log10(sqroot(dp*ds))-13)/(14.6*dF));   //FIR Filter length\n",
"    R=N*Fti/M;                                          //Number of Multiplications per second\n",
"endfunction\n",
"\n",
"Ft=10000;         //Sampling rate of input signal\n",
"Fp=150;            //Passband frequency\n",
"Fs=180;            //Stopband frequency\n",
"dp=0.002;          //Passband ripple\n",
"ds=0.001;         //Stopband ripple\n",
"M=20;            //Decimation Factor\n",
"Fti=Ft;           //Input sampling rate\n",
"//Single stage implementation\n",
"[N1,R1]=func(Fs,Fp,Ft,Fti,dp,ds,M);\n",
"\n",
"//Two stage implementation\n",
"//Stage 1 F(z) with decimation factor 50\n",
"Fpf=Fp;            //Passband frequency\n",
"Fsf=720;           //Stopband frequency\n",
"dpf=0.001;         //Passband ripple\n",
"dsf=0.001;         //Stopband ripple\n",
"Mf=10;             //Decimation Factor\n",
"Fti=Ft;            //Input sampling rate\n",
"[N2f,R2f]=func(Fsf,Fpf,Ft,Fti,dpf,dsf,Mf);\n",
"\n",
"//Stage 2 G(z) with decimation factor 2\n",
"Fpg=10*Fp;         //Passband frequency\n",
"Fsg=10*Fs;         //Stopband frequency\n",
"dpg=0.001;         //Passband ripple\n",
"dsg=0.001;         //Stopband ripple\n",
"Mg=2;              //Decimation Factor\n",
"Fti=Ft/10;         //Input sampling rate\n",
"[N2g,R2g]=func(Fsg,Fpg,Ft,Fti,dpg,dsg,Mg);\n",
"N2=N2f+10*N2g+2;    //Total filter length\n",
"R2=R2f+R2g;         //Total Number of Multiplications per second\n",
"\n",
"disp(R1,'Number of Multiplications per second =',N1,'FIR filter length =','For Single stage implementation:');\n",
"disp('For Two stage implementation:');\n",
"disp(R2f,'Number of Multiplications per second =',N2f,'FIR filter length =','For F(z):');\n",
"disp(R2g,'Number of Multiplications per second =',N2g,'FIR filter length =','For G(z):');\n",
"disp(R2,'Total Number of Multiplications per second =',N2,'Overall FIR filter length =');"
   ]
   }
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