convert the time domain signal into frequency domain signal

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neamah al-naffakh 2016-9-6

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https://ww2.mathworks.cn/matlabcentral/answers/302011-convert-the-time-domain-signal-into-frequency-domain-signal

评论： neamah al-naffakh 2017-5-5

采纳的回答： Star Strider

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hi guys, this is the second part of this topic ,

I have divided into two part in order to make the topic readable and useful and I'd like to thank Mr Star Strider for his useful answer and support

Ok, let carry on

I have the acceleration data of 3 axes(x, y, and z) and it's represented in time domain signal.

There are about 10500 records (data points or samples)in the file for each axis and I have divided these records into segments ( each segment contains 256 data points.

now, I'd like to convert each segment in the time domain into frequency domain .

As we know this can be done using FFT function

One of the limitations of using the FFT function is that the number of data points in the segment must be a power of two. and I have already fixed the size of each segment into 256( 2 to the power 8)

i have used this code,

% FD_Signal_X{nn,1}=fft(X_Segments_256{nn});

Note, NN is the number of segments, X_Segments_256 contains the data of X axes of each segment, which is 256

my question is

1- I have used this code to calculate the Energy of the frequency domain signal,

FD_Signal_X{nn,1}=fft(X_Segments_256{nn});
Energy_X{nn,1} = (FD_Signal_X{nn}).^2;

or this one is correct?

FD_Signal_X{nn,1}=fft(X_Segments_256{nn});
Magnitude_X {nn,1} = abs(FD_Signal_X{nn}); 
Energy_X{nn,1} = (Magnitude_X{nn}).^2;

With my respect

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Star Strider 2016-9-6

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https://ww2.mathworks.cn/matlabcentral/answers/302011-convert-the-time-domain-signal-into-frequency-domain-signal#answer_233885

The second is correct.

The first squares a complex signal, so both the real an imaginary parts of the signal are squared, producing a complex result. I do not believe that is what you want. I would not use it.

The second squares the absolute value of the complex signal, producing a real result. That calculates the power in your signal, essentially the power spectral density of your signal.

The energy of your signal at each frequency is the absolute value of the Fourier transform of your signal. The power at each frequency is the square of the energy.

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neamah al-naffakh 2016-9-22

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Hi sir,

I have N number of users, each one has set of samples (features) that are going to be used for authentication.

However, as we know not all features that have been calculated are useful as some of them might be influenced the accuracy. Hence, I want to select the best features that are discriminative (unique) for each user.

For example, each feature belongs to User 1(i.e. ' Muna-SD.mat'), I have calculated the Standard deviation and the mean value; and the procedure has repeated for User2 (' Aisa-SD.mat'). i have written this code.

load('Muna-SD.mat' );
stdev_Acc_Max_X_U1=std(feature_vector (:,1));
stdev_Acc_Max_Y_U1=std(feature_vector (:,2));
stdev_Acc_Max_Z_U1=std(feature_vector (:,3));
Avg_Acc_X_U1=mean(feature_vector (:,1));
Avg_Acc_Y_U1=mean(feature_vector (:,2));
Avg_Acc_Z_U1=mean(feature_vector (:,3));
load('Aisa-SD.mat' );
stdev_Acc_Max_X_U2=std(feature_vector (:,1));
stdev_Acc_Max_Y_U2=std(feature_vector (:,2));
stdev_Acc_Max_Z_U2=std(feature_vector (:,3));
Avg_Acc_X_U2=mean(feature_vector (:,1));
Avg_Acc_Y_U2=mean(feature_vector (:,2));
Avg_Acc_Z_U2=mean(feature_vector (:,3));

I have attached the Muna-SD.mat and Aisa-SD.mat*

in order to see which feature are useful, I want to draw features in a graph

could you help me to draw the standard deviation of each single feature for all users in one graph?

x-axis represents users and Y-axis represents the mean.

kind regards.

neamah al-naffakh 2016-9-23

编辑：neamah al-naffakh 2016-9-23

Hi Sir,

ok let me explain it in more details.

suppose we have 100 features for each user ( e.g. Max, Min, etc)

For each one of the above features, i have 35 values (e.g. 35 samples or values of Max Feature ).

Therefore, before sending all features to any classification algorithem, I need to identify which feature is useful.

in order to select the optimal features, each single feature should go through two tests ( similarity of the user's samples (ideally the similarity score should be small as much as possible), and the dissimilarity (uniqueness) of the user's samples from imposters (ideally the dissimilarity score should be large as much as possible) .

1- the first test ( similarity test) is make sure that the multi-samples of one feature (e.g. Max) for the same user (e.g. user1) are very close to each other.

This can be achieved by calculating the standard deviation for the user's samples in order to see how similar the user's samples of that feature is ( e.g. calculate the standard deviation of the 35 samples of Max feature and as i meantioned above the , ideally the output should be small.

2- the second test ( dissimilarity test ) is to make sure that the (Max feature) of other users (i.e. Imposters or user2, user3, etc) are far enough from the ( Max) feature of user1.

This can be acheived by calcuting the Mean (e.g. mean of 35 samples of the Max feature), if the Mean output of other users (imposters) are far enough from user1, that means this feature (i.e. max ) is good to be used for authentication because it meet the requirments of the first and second tests.

After i calculted the standard deviation of ( 35 Max samples) and the Mean of ( 35 Max samples) for each user, my advisor suggested to represent them in graph to check if there is overlap between the feature of User1 and the remaining users.

I hope you get what i mean !

kind regards.