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How to apply windowing technique in frequency Domine using Convolution Technique

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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

Accepted Answer

Wayne King
Wayne King on 30 Mar 2013
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)
  4 Comments
Thulasi Durai Durai Samy
Thulasi Durai Durai Samy on 31 Mar 2013
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:
Output
Thulasi Durai Durai Samy
Thulasi Durai Durai Samy on 1 Apr 2013
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.

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