Respiration belt signal example: LPF filter

We illustrate the usage of butterworth LPF on respiration data in resp_noisy.txt.

ELEC-C5211 - Johdatus signaalien tilastolliseen mallintamiseen ja paattelyyn

Load the data
plot the noisy respiration belt signal
Apply the (butterworth) LPF to the signal
Plot the filtered signal
Question

Load the data

sampling frequency is

$f_s = \frac{1}{T_s}$

where $T_s$ is the sampling interval

Ts = 0.001; % sampling interval (in seconds)
fs = 1/Ts;  % sampling frequency (sampling at 1000 Hz )
respiration_n = load('resp_noisy.txt');

plot the noisy respiration belt signal

ind = 1:100:20000; % plot 20 seconds
figure(1); clf
plot(ind*Ts,respiration_n(ind),'b','linewidth',2.5)
xlabel('Time [s]');
set(gca,'LineWidth',2.0,'FontSize',18);
grid on; ylim([-3 3]);
set(gca,'YTick',-3:1:3,'FontSize',12,'FontSize',16)
set(gca,'XTick',0:2:20,'FontSize',12,'FontSize',16)
ax = axis;

Apply the (butterworth) LPF to the signal

fc = 2; % cut off frequency is 2 Hz
fc_n = fc/(fs/2); % normalized by the Nyquist rate
[b,a] = butter(4,fc_n,'low');
[H,f] = freqz(b,a,10000,fs); % The frequency response H for samling frequency 1000 Hz
ind = find(f < 10);

% Plot the gain (the amplitude of frequency response)
figure(2); clf
plot(f(ind),abs(H(ind)),'b-','LineWidth',2.5);
axis tight; axis on;
grid on;
xlim([0 10])
xlabel('Frequency $f$ [Hz]','Interpreter','Latex');
ylabel('$|H(\mathrm{exp}(j 2 \pi f/f_s))|$','Interpreter','Latex');
set(gca,'LineWidth',2.0,'FontSize',20);

Plot the filtered signal

respiration_f = filter(b,a,respiration_n); % filtered signal
ind = 1:100:20000;
figure(3); clf
plot(ind*Ts,respiration_f(ind),'b-','LineWidth',2.5)
xlabel('Time [s]');
set(gca,'YTick',-3:1:3,'FontSize',12,'FontSize',16)
set(gca,'XTick',0:2:20,'FontSize',12,'FontSize',16)
grid on; ylim([-3 3]);
set(gca,'LineWidth',2.0,'FontSize',18);

Question