# FFT OF A SIGNAL

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I have a signal data set that i have to analyse but i cant get my code to work can anyonbe help me? Am i forgetting to include something or add something

thats the error that im getting

Error: File: fft_fun.m Line: 39 Column: 1

This statement is not inside any function.

(It follows the END that terminates the definition of the function "fft_fun".)

The code is as follows

function [PN, df] = fft_fun(fs, input_signal)

function [PN, df] = fft_fun(fs, input_signal)

%% Fast Fourier Transform (FFT); Powerline Noise (tut1)

% Function to compute and plot the fft (fast fourier transform) of an input

% signal.

% Input_signal = signal to compute the fft on. fs = sample rate of

% the input signal. If sample rate is unknown, it can be found using:

% fs = 1/(max(tm)/length(tm)-1).

% A fft plots the signal in the frequency spectrum, allowing for the easy

% recognition of power line noise, usually shown at either 50Hz or 60Hz in

% the plotted frequency transform.

%% create FFT

% Detrend of Input Signal

n = detrend(input_signal);

% FFT

N = fft(n);

% Power Spectrum

spect = 2*abs(N)/length(N);

PN = spect.^2;

% Frequency Axis

df = fs/length(n); %% fs << fc

f = 0:df:fs-df; %% fs << fc

indf = (1:floor(length(f)/2));

figure

plot(f(indf),PN(indf));

xlabel('Hz')

ylabel('(Input Units)^2 / Hz')

end % end of function fft_fun

Appendix 2b - Power-line Nose & High-Frequency Noise Removal (notch_fun.m)

function [signal] = notch_fun(input_signal)

%% Powerline Noise and High Frequency Noise Removal (tut3)

% Function to apply a 50Hz notch filter and low and high pass filters.

% Notch filter removes powerline noise at specified frequency (50Hz).

% Low pass filter removes high frequency noise

% input_signal = signal to apply filters to.

% [signal] = output signal with applied filters (noise removed).

%% Notch Filter @ 50Hz

fc = 1000;

fQf = 35;

NOf0 = 0;

bw = 0;

signal = input_signal;

while NOf0<fc/2-50,

% Apply a 50Hz and harmonics notch filters:

% notch frequency

NOf0 = NOf0+50;

% normalise frequency in 'pi radiant per sample'

wNO = NOf0/(fc/2);

bw = wNO/fQf;

[bNO,aNO] = iirnotch(wNO,bw);

% Apply filter

signal = filter(bNO,aNO,signal);

end;

%% Build a 40 Hz low pass filter against the HF noise

% normalise frequency in 'pi radiant per sample'

order = 50; % Order 50

NOf0 = 40;

wNO = NOf0/(fc/2);

bNO = fir1(order,wNO); % defaults to lowpass filter

% Apply low pass filter

signal = filter(bNO,1,signal);

%% Apply High-Pass Filter at 1Hz

order = 50;

NOf0 = 1;

wNO = NOf0/(fc/2);

bNO = fir1(order,wNO,'high');

% Apply high pass filter

signal = filtfilt(bNO,1,signal);

%% Plot Signals

% Plot original signal and signal of notch filtered signal for comparison

figure

% Plot of original signal

subplot(2,1,1)

plot(input_signal)

title('Input ECG Signal')

% Plot of output signal

subplot(2,1,2)

plot(signal)

title('Notch Filtered Signal')

end % end of function notch_fun

Appendix 2c - Baseline Wandering Removal (blw_fun.m)

function [filtsignal] = blw_fun(tm,input_signal)

%% Low-Pass Filter; DC Removal Filter; Baseline Wandering (tut3)

% Function to remove the baseline wandering of an input signal.

% Takes a signal, input_signal, and applies a low-pass filter to remove DC

% noise, as such removes baseline wandering. Allows for easier analysis of

% mutiple-lead ECG signals (typically 12-Lead ECGs) by removing overlap of

% individual lead signals.

%% Low-Pass Filter

% create the DC removal filter coefficient

lamda = 0.98; % as close to but not equalling 1

b = [1 -1];

a = [1 -lamda];

figure

freqz(b,a); % plot the freqency response of the low-pass filter

title('Filter Frequency Response')

% filter input signal using DC removal filter

filtsignal = filtfilt(b,a,input_signal);

%% Comparison of Signals

% plot filtsignal; filtered signal using filtfilt

figure

subplot(2,1,2)

plot(tm,filtsignal);

title('Baseline Wandering Corrected ECG Signal')

% plot original signal

subplot(2,1,1)

plot(tm,input_signal);

title('Input ECG Signal')

end % end of function blw_fun

Appendix 2d - Calculate SNR (snr_fun.m)

function [Pnoise, Psignal, SNR] = snr_fun(PN,df)

%% Signal to Noise Ratio (SNR) (tut4)

% Function to calculate and display the signal to noise ratio of an ECG

% signal. Also displays the values of the noise and signals individually.

% Takes PN and df input obtained from the completion of the fft function

% (fft_fun.m) to calculate the noise of a signal and determine a numeric

% value of the signal to compute the SNR.

% Pnoise = amount of noise in the signal

% Psignal = numeric value of signal

% SNR = calucated Signal to Noise Ratio

% Power of the noise

Pnoise = sum(PN(1:round(5/df)))/round(5/df) + sum(PN(1+round(15/df):end))/(round(500/df)-(1+round(15/df))) + PN(round(50/df));

% Power of the signal

Psignal = sum(PN(1+round(5/df):round(15/df)));

% Calculate the signal to noise ratio (SNR)

SNR = 10*log10(Psignal/Pnoise);

end % end of snr_fun

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### Answers (1)

Subhadeep Koley
on 17 Dec 2020

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