# Finding the frequency value of a signal

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Ramo on 25 Oct 2014
Commented: Image Analyst on 26 Oct 2021
How can I find the frequency of this signal?
Thanks, ##### 2 CommentsShowHide 1 older comment
Image Analyst on 26 Oct 2021
@Yasemin G try this:
% Initialization steps.
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
imtool close all; % Close all imtool figures if you have the Image Processing Toolbox.
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 18;
%==================================================================================
% Image Analyst's code below:
period = 0.57e5
originalFrequency = 1/period
x = linspace(0, 2e5, 2000);
signalAmplitude = 0.85;
perfectSineWave = signalAmplitude * sin(2 * pi * (x - 0.08e5) / period);
subplot(2,1,1);
plot(x, perfectSineWave, 'b-');
grid on;
noiseAmplitude = 0.05;
yNoisy = perfectSineWave + noiseAmplitude * (2 * rand(1, length(x)) - 1);
hold on;
darkGreen = [0, 0.5, 0];
plot(x, yNoisy, '-', 'Color', darkGreen)
yline(0, 'Color', 'b', 'LineWidth', 2)
xlabel('Time or x', 'FontSize',fontSize);
ylabel('Signal', 'FontSize',fontSize);
title('Original Signal', 'FontSize',fontSize);
%==================================================================================
% Harry's code below:
% Assume we capture 8192 samples at 1kHz sample rate
Nsamps = 8192;
fsamp = 1000;
Tsamp = 1/fsamp;
t = (0:Nsamps-1)*Tsamp;
% Choose FFT size and calculate spectrum
Nfft = 1024;
[Pxx,f] = pwelch(yNoisy, gausswin(Nfft), Nfft/2, Nfft,fsamp);
% Plot frequency spectrum
subplot(2,1,2);
plot(f, Pxx, 'b-', 'LineWidth', 2);
ylabel('PSD', 'FontSize',fontSize);
xlabel('Frequency (Hz)', 'FontSize',fontSize);
grid on;
% Get frequency estimate (spectral peak)
[~,loc] = max(Pxx);
FREQ_ESTIMATE = f(loc)
caption = sprintf('Frequency estimate = %f Hz', FREQ_ESTIMATE);
title(caption, 'FontSize',fontSize);
g = gcf;
g.WindowState = 'maximized' Harry on 26 Oct 2014
Edited: Harry on 26 Oct 2014
Whenever you're interested in frequency content of a signal, the Fast Fourier Transform is often an excellent tool to use (see help fft). More specifically, Matlab's PWELCH function will provide a Power Spectral Density estimate using Welch's method:
[Pxx,F] = pwelch(X,WINDOW,NOVERLAP,NFFT,Fs)
Here is an example of how to use it to estimate frequency:
close all; clear all; clc;
% Assume we capture 8192 samples at 1kHz sample rate
Nsamps = 8192;
fsamp = 1000;
Tsamp = 1/fsamp;
t = (0:Nsamps-1)*Tsamp;
% Assume the noisy signal is exactly 123Hz
fsig = 123;
signal = sin(2*pi*fsig*t);
noise = 1*randn(1,Nsamps);
x = signal + noise;
% Plot time-domain signal
subplot(2,1,1);
plot(t, x);
ylabel('Amplitude'); xlabel('Time (secs)');
axis tight;
title('Noisy Input Signal');
% Choose FFT size and calculate spectrum
Nfft = 1024;
[Pxx,f] = pwelch(x,gausswin(Nfft),Nfft/2,Nfft,fsamp);
% Plot frequency spectrum
subplot(2,1,2);
plot(f,Pxx);
ylabel('PSD'); xlabel('Frequency (Hz)');
grid on;
% Get frequency estimate (spectral peak)
[~,loc] = max(Pxx);
FREQ_ESTIMATE = f(loc)
title(['Frequency estimate = ',num2str(FREQ_ESTIMATE),' Hz']); Souarv De on 24 Sep 2019
From where NFFT = 1024 value came?

Image Analyst on 25 Oct 2014
I'd smooth it a bit with a 3rd order Savitzky-Golay filter, sgolayfilt() in the Signal Processing Toolbox, then I'd use findpeaks to get the period and 1/period is the frequency. Attached is a Savitzky-Golay filter demo. Image Analyst on 27 Mar 2020
Ramo, You chose a frame length, 41, that was far too small. It should be hundreds or thousands because you have 200 thousand data points (which is far too many to see on a single screen without zooming, by the way). Here is corrected code:
x = data(:, 1);
y = data(:, 2);
% Plot original noisy data.
subplot(1, 3, 2);
plot(x, y, '-');
title('Noisy Data', 'FontSize', 15);
grid on;
% Smooth the data
smoothedY = sgolayfilt(y, 4, 2001);
% Plot smoothed data.
subplot(1, 3, 3);
plot(x, smoothedY, 'r-', 'LineWidth', 2);
grid on;
title('Smoothed Data', 'FontSize', 15);
% Plot both original and smoothed data.
subplot(1, 3, 1);
plot(x, y, '-');
title('Noisy Data', 'FontSize', 15);
grid on;
hold on;
plot(x, smoothedY, 'r-', 'LineWidth', 2);
title('Both Noisy and Smoothed Data', 'FontSize', 15);
% Maximize the window.
g = gcf;
g.WindowState = 'maximized' Ramo on 26 Oct 2014
I got 20000 points (i.e. x and y) which i load from a txt file. then I plot them using plot(x,y).. what is the next step? Thanks
Rodrigo Picos on 27 Mar 2020
Many years later.....
You should use 'sin3' or 'sin4', and check if you need to use the third or fourth component.
Hint: call F=fit( ) without the ending ;

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