How to apply windowing technique in frequency Domine using Convolution Technique

Hello

Sample Rate: 500 Hz, L = 4500(Total Block Size)

%I applied a windowing technique with following command

wd = window(@tukeywin,L,1/1.7);

New_Signal = Time_Domine_Data * wd; %(Scalar Multiplication)

Freq = fft(New_Signal);

Multiplication in time domine is convolution in frequency domine, How do I apply windowing object 'wd' in frequency Domine using Convolution Technique

-- Thanks

Answer 1

[Wayne King]

Like this:

 x = randn(8,1);
 win = hamming(8);
 y = x.*win;
 ydft = fft(y);

Now compare ydft to the following:

N = length(x);
xdft = fft(x);
windft = fft(win);
1/N*cconv(xdft,windft,N)

[Thulasi Durai Durai Samy]

Thans for your Reply,

Please let me now the signification of taking reciprocal

1/N*cconv(xdft,windft,N)

I would like to read more on convolution theory specific to my case pls suggest any link.

[Wayne King]

Because the way the DFT is implemented in MATLAB (and in many other software packages) the Fourier transform is not unitary, there is a factor of 1/N in the inverse Fourier transform.

[Thulasi Durai Durai Samy]

Need to Apply Windowing Technique to Remove Intial Spike with the following codes, but it not happening

clear all;
clc;

load expt3b.txt;
Input_Data = expt3b;

S_rate = 500;
T = 1/S_rate;

Impulse(:,2) = Input_Data(:,1);
Response(:,2)= Input_Data(:,2);

%Conversion From Voltage to Accleration
Impulse(:,2)  = Impulse(:,2)  * (1/0.0225);
Response(:,2) = Response(:,2) *  31.64557;

L                       =   length(Input_Data(:,2));
F_L                     =   2^nextpow2(L);
t(:,1)                  =   (1:L)*T;
Freq                    =   (S_rate/2*linspace(0,1,F_L/2+1))';
Impulse(:,1)            =   t';
Response(:,1)           =   t';
Response_FF(:,1)        =   t';
Response_Time_Filt(:,1) =   t';
Dc_Bias                 =   mean(Response(:,2));
Response(:,2)           =   Response(:,2) - Dc_Bias;

%Applying Exponential Window
for i=1:L

      temp(i)             =   exp(-i/(2*S_rate));
      Response_FF(i,2)    =   temp(i) * Response(i,2);

end

Response_FF(:,1) =  Response(:,1);
Response_Time_Filt(:,1) =  Response(:,1);

%Apply Tukey Window in Time Domine
Tukeywin_Obj     = window(@tukeywin,numel(Response(:,2)),1/1.7);
Response_FF(:,2) = Response_FF(:,2).* Tukeywin_Obj; 

% % Design of Low Pass Flter 
[B, A]                   =  butter(5,35/250);
Response_Time_Filt(:,2)  =  filter(B,A,Response_FF(:,2));

%Apply FFT For Response Data
Response_FF_Freq(:,1)    =  fft(Response_Time_Filt(:,2),F_L)/F_L;
Output_Data_Response     =  abs(Response_FF_Freq(1:F_L/2+1,1)); 

%Applyin FFT For Windowng Object "Tukeywin_Obj"
Tukeywin_Obj_Freq_Domine = window(@tukeywin,numel(Response(:,2)),1/1.7);
Response_FF_Freq_2(:,1)  =  fft(Tukeywin_Obj_Freq_Domine,F_L)/F_L;
Output_Data_Window       =  abs(Response_FF_Freq_2(1:F_L/2+1,1)); 

%Applying Convolution
Freq_Data_Windowing      =  1/F_L*cconv(Output_Data_Response,Output_Data_Window,F_L);

plot(Freq,2*abs(Freq_Data_Windowing(1:F_L/2+1)));
grid on;

Input Time vs Response Data Link:

https://www.dropbox.com/s/8481khjriqm9hq9/expt3b.txt

Output

https://www.dropbox.com/s/rl6enzb3rosxroy/Output.tif

[Thulasi Durai Durai Samy]

Hi Wayne King,

Thanks for your reply, I hope, I tried to understand the principals. But still I am unable to get rid of initial spike, Which is a mandatory operation, pls help.