What are high frequencies and low frequencies in a signal?

Question

I'm new to signal processing. I'm plotting a signal in the time-domain in matlab. I don't understand which parts of the signal are high frequencies and low frequencies, can someone explain what a high and low frequency is, and how to see high frequencies and low frequencies on a graph?

Answer 1

The high frequencies contribute to the fast varying parts of the signal(the sharp transitions), while the low frequencies contribute to the slow variations of the signal in the time domain.

You might want to take a look over here: http://cns-alumni.bu.edu/~slehar/fourier/fourier.html

Also, if you have the time you might want to take a look at this online course: http://academicearth.org/courses/the-fourier-transform-and-its-applications You won't regret it.

Answer 2

High and low frequencies are dependent on the application. A low frequency for wifi would be 2.4GHz, while a high frequency would be 5GHz. For human speech a low frequency is 300Hz, while a high frequency is 3000Hz.

A graph of a fft (Fast Fourier Transform) allows us to visualize different frequencies. This example is adapted from Matlab's fft help. The following figure shows the first 100 out of $2^{20}$ samples of a time signal with two frequencies. Note how it is difficult to see the 1Hz component in this figure.

To see the frequency content we plot the spectrum as show in the following figure. Here we can clearly see the two frequencies - one at 1Hz and the other at 50Hz.

Here is the code I used to generate these plots.

fs = 2^10;        %sample frequency in Hz
T  = 1/fs;        %sample period in s
L  = 2^20;        %signal length
t  = (0:L-1) * T; %time vector

A1 = 0.2; %amplitude of x1 (first signal)
A2 = 1.0; %amplitude of x2 (second signal)
f1 = 1;   %frequency of x1
f2 = 50;  %frequency of x2

x1 = A1*sin(2*pi*f1 * t); %sinusoid 1
x2 = A2*sin(2*pi*f2 * t); %sinusoid 2
y  = x1 + x2;

%Plot signal
figure;
set(gcf,'Color','w'); %Make the figure background white
plot(fs*t(1:100), y(1:100));
set(gca,'Box','off'); %Axes on left and bottom only
str = sprintf('Signal with %dHz and %dHz components',f1,f2);
title(str);
xlabel('time (milliseconds)');
ylabel('Amplitude');

%Calculate spectrum
Y = fft(y)/L;
ampY = 2*abs(Y(1:L/2+1));
f = fs/2*linspace(0,1,L/2+1);
i = L/fs * (max(f1,f2)) + 1; %show only part of the spectrum

%Plot spectrum.
figure;
set(gcf,'Color','w');  %Make the figure background white
plot(f(1:i), ampY(1:i));
set(gca,'Box','off');  %Axes on left and bottom only
title('Single-Sided Amplitude Spectrum of y(t)');
xlabel('Frequency (Hz)');
ylabel('|Y(f)|');

Answer 3

It really depends on what kind of time-domain signal at which you are looking, and how you are looking at it. Sometimes it's easy to see. Sometimes it is not.

If you are plotting something like amplitude (voltage, pressure, height, etc.) against time, and you see lots of up and down action in a relatively short distance, those may be due to higher frequency spectral content. If you see some up and down trends over a much larger span those may represent some lower frequencies. The two may be mixed (added or summed) together over the same span. If you see repeated repetitions of a waveform, that may represent it's own kind of frequency. Of course this all depends on picking a time scale factor relative to the contextual meaning of your "high" and "low". You may need to play with the scale factors to see something of interest.

An FFT may or may not be useful, and might even be wildly misleading. The FFT is more about spectral content in a given aperture width than either high or low frequencies in a signal. For instance it's possible for a sharp-edged low frequency periodic signal to show lot of high frequency content in an FFT, even for a very low frequency of repitition of the actual signal phenomena. People looking for musical pitch too often mistake the two. And FFTs of slices of a longer signal which is absolutely not periodic in the FFT aperture width will misleadingly show up as periodic frequencies in a naive interpretation of the FFT results.