# Calculate the stop band energy of a filter by its Power spectral density graph

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Sara Nasir on 26 Dec 2020
Commented: Sara Nasir on 23 Feb 2021
I want to find the stop band energy of a filter by its Power spectral density graph. Stop band energy is calculated with normalized total energy.
I can not find the command for it. Below is the correct code of a rectangular filter.
%% Rectangular Filter
Ts = 0.01; % sampling time
time = -20:0.01:20; % time axis
NFFT = 2048; % number of samples
freq = linspace(-0.5,0.5,NFFT); % frequency axis
ht_Rectangular = zeros(size(time));
%% In Time Domain
for n = 1:length(time)
if time(n)>=-0.5 && time(n)<=0.5
ht_Rectangular(n) = 1;
end
end
figure(1);
plot(time,ht_Rectangular);
xlabel('t/T_s');
ylabel('h(t)');
title('Impulse Response of Rectangular Filter');
grid on,
%% In Frequency Domain
Hf_Rectangular = fftshift(fft(ht_Rectangular,NFFT)); % FFT with FFTshift for both negative & positive frequencies
figure(2);
plot(freq, (Hf_Rectangular(1:length(freq)))/max(Hf_Rectangular));
xlabel('f/F');
ylabel('H(F)');
title('Frequency Response of Rectangular Filter');
grid on,
%% Power Spectral Density
[PSD_Rectangular, F_Rectangular] = periodogram (ht_Rectangular, [], length (ht_Rectangular));
figure(3);
plot (F_Rectangular, 10 * log10 (PSD_Rectangular));
xlabel('f/F');
ylabel('PSD (dB)');
title('Power Spectral Density of Rectangular Filter');
grid on,
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### Answers (1)

Nitin Kapgate on 13 Jan 2021
You can use the "bandpower" function to calculate the stop band energy from PSD as illustrated in this example.
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Sara Nasir on 23 Feb 2021
It is for calculating the average power, not the sub-band energy

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