How to change value of a signal's range in Mat

Question

Let's say that I have a signal in Matlab like this

x = cos(2*pi*10*t) + cos(2*pi*20*t) + cos(2*pi*50*t);

And I want to change the values between 20 and 30 hz into 0. How can I do that? I mean, those values generated from the x formula, I want to change them a little bit.

Answer 1

You can either use a filter, or you can filter it by yourself by going into Fourier space and explicitly setting the signal on the frequencies you need to zero. After that, you need to go back to the time domain. Here is a code:

t=0:0.01:0.99;  % time
x = cos(2*pi*10*t) + cos(2*pi*20*t) + cos(2*pi*50*t); %signal
xf=fftshift(fft(x)); %Fourier signal 
N=size(x,2); % Size of the signal
frequency=2*pi*[-N/2:N/2-1]; %frequency range
frequencyrangeplus=find(frequency/(2*pi)>=20 & frequency/(2*pi)<=30); %find     positive frequencies in the required range
frequencyrangeminus=find(frequency/(2*pi)<=-20 & frequency/(2*pi)>=-30);     %find negative frequencies in the required range
xf(frequencyrangeplus)=0; %set signal to zero at positive frequencies range
xf(frequencyrangeminus)=0; %set signal to zero at nagative frequencies range
xnew=ifft(ifftshift(xf)); %get the new signal in time domain
xcheck= cos(2*pi*10*t) + cos(2*pi*50*t); % to check the code
max(abs(xcheck-xnew)) % maximum difference

Answer 2

You can do it by performing FFT over x and setting to zero those values that are between 20 and 30 Hz then applying the FFT inverse on the previous values and you should get the signal without those frequencies. However, you may lose valuable information or the signal might just not look as you wish. Therefore, I recommend you to use a "Bandstop filter". The band stop filter will receive the cutoff frequencies (the limit frequencies you want to work with) and some other parameters. The bandstop filter basically removes from the signal the frequencies that you specify. And the good part is that it can be done as easy as doing what follows:

1. First you have to build the filter. To do so, you need to indicate the filter order which can be defined as you wish. Usually a second order works good. Also, you have to be aware of your sampling rate Fs.

   d = designfilt('bandstopiir','FilterOrder',2, ... 'HalfPowerFrequency1',20,'HalfPowerFrequency2',30, ... 'SampleRate',Fs);

2. Now you only need to apply the filter to your desired signal.

   filtered_signal_x = filtfilt(d, x)

Now, filtered_signal_x should not have the frequencies you wanted to delete. By using the bandstop you don't have to mess with the FFT and that kind of stuff and is a way faster so I think its the best option.