# Need explanation on plotting frequency response of a causal discrete-time LTI system implemented using the difference equation.

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Evelio Excellenta on 16 May 2022
Commented: Star Strider on 18 May 2022
So....
i have a program like this
RH_coeff=[0.1 -0.1176 0.1];% Coefficient of x on RHS of difference equation
LH_coeff=[1 -1.7119 0.81]; % Coefficient of y on LHS of difference equation
%% Frequency response of the filter
[H,w]=freqz(RH_coeff,LH_coeff); % Frequency response
plot(w/(2*pi),20*log10(abs(H)),'LineWidth',1.5); % Plot Frequency response
xlabel('Normalized frequency (f/fs)Hz');
ylabel('Magnitude');
title('Frequency response');
grid;
%% Generating response y[n] due to input x[n]
n=0:100;% X axis
xn=cos(0.1*n*pi);% x[n]
yn=filter(RH_coeff,LH_coeff,xn); %y[n]
figure;
subplot(2,1,1);
stem(n,xn); %Plot input
xlabel('n');
ylabel('x(n)');
title('Input sequence');
subplot(2,1,2);
stem(n,yn);% Plot output
xlabel('n');
ylabel('y(n)');
title('Output sequence');
grid;
1. Can someone explain to me what [H,w]=freqz(RH_coeff,LH_coeff); means? does it mean H=RH_coeff, w=LH_coeff?
2. what does this function (plot(w/(2*pi),20*log10(abs(H)),'LineWidth',1.5);) means? why does this function exist? i thought for plotting frequency responce i just stopped at freqz(RH_coeff,LH_coeff);

Star Strider on 16 May 2022
does it mean H=RH_coeff, w=LH_coeff?
No. The first argument are the numerator coefficients of the filter transfer function, and the second argument are the denominator coefficients.
what does this function (plot(w/(2*pi),20*log10(abs(H)),'LineWidth',1.5);) means?
It plots the magnitude section of the Bode plot created by freqz as the frequency in Hz and magnitude in dB.
.
Star Strider on 18 May 2022
The ‘H’ output is the complex transfer function, and ‘w’ are the associated radian frequencies.

R2019a

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