Converting frequency domain to Time Domain using IFFT.

Hello Experts,

I got a force data w.r.t frequency I want to convert it into force vs time. Can anyone please help with how to take sample rate, length and the plot with time of 0 to 10 secs

Thanks

[Star Strider]

That depends on what the data are. If you have the amplitude and phase data, or the complex Fourier transform, and the lowest frequency is 0 Hz and the highest frequency is the Nyquist frequency, inverting it, even if you only have half of it, is straightforward. If you only have the amplitude or power, then inverting it is not possible.

[Lokesh Katari]

Hi, thanks for your time.PFA of excel which contains forces vs fre data.

This dataI want to convert it into time domain. Can you please help. I am very new to this

[Star Strider]

Unfortunately, I cannot help. The data contain only frequency and magnitude, so it cannot be inverted.

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/755579/Force_Freq.xlsx', 'VariableNamingRule','preserve')

T1 = 60×2 table
    Frequency    Force Signal
    _________    ____________

         39         151.21   
      78.22         16.765   
     117.44         15.478   
     156.66          15.68   
     195.88         12.711   
      235.1         17.673   
     274.32         13.923   
     313.54         14.618   
     352.76         31.821   
     391.98         12.614   
      431.2         13.436   
     470.42         11.195   
     509.64         14.014   
     548.86          15.86   
     588.08         13.473   
      627.3         14.609   

figure
plot(T1.Frequency, T1.('Force Signal'))
grid

.

[Lokesh Katari]

Hi @Star Strider

Now I got magnitude and phase data w.r.t frequency. Can you please help me with the code.

[Yashika Chauhan]

@Star Strider I also have same issue can you please help me with the code?

Answer 1

[Star Strider]

I made some assumptions and managed to invert the frequency-domain signal —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/758601/Freq_to_timedomain.xlsx','VariableNamingRule','preserve')

T1 = 51×3 table
    Frequency    Compressor Signal     Phase  
    _________    _________________    ________

         39            0.44633          2.1385
      78.22            0.22602          1.0094
     117.44          0.0073646        -0.11463
     156.66           0.010899          1.4285
     195.88          0.0023688          1.1573
      235.1          0.0063101         0.60217
     274.32          0.0082103           0.948
     313.54           0.010135          0.1509
     352.76          0.0026814          1.9953
     391.98          0.0021176         -2.2674
      431.2          0.0012498        0.021459
     470.42         0.00044738         -1.8534
     509.64         0.00037295         -1.6413
     548.86         0.00064796           1.326
     588.08         0.00067373          2.2295
      627.3         0.00083095         0.72299

% Check = [mean(diff(T1.Frequency))  std(diff(T1.Frequency))*1E15]                    % Check Frequency Spacing % Regularity

Check = 1×2

39.2200 59.1180

FT1 = T1.('Compressor Signal') .* exp(1j*deg2rad(T1.Phase))                         % Complex Vector — Assumes Frequency In Hz & Phase In Degrees

FT1 = 
   0.4460 + 0.0167i
   0.2260 + 0.0040i
   0.0074 - 0.0000i
   0.0109 + 0.0003i
   0.0024 + 0.0000i
   0.0063 + 0.0001i
   0.0082 + 0.0001i
   0.0101 + 0.0000i
   0.0027 + 0.0001i
   0.0021 - 0.0001i
   0.0012 + 0.0000i
   0.0004 - 0.0000i
   0.0004 - 0.0000i
   0.0006 + 0.0000i
   0.0007 + 0.0000i
   0.0008 + 0.0000i
   0.0021 + 0.0001i
   0.0006 - 0.0000i
   0.0111 + 0.0003i
   0.0054 - 0.0001i
   0.0013 + 0.0001i
   0.0010 - 0.0000i
   0.0014 + 0.0000i
   0.0016 - 0.0000i
   0.0025 - 0.0000i
   0.0006 + 0.0000i
   0.0019 - 0.0000i
   0.0016 + 0.0001i
   0.0014 + 0.0000i
   0.0022 - 0.0000i
   0.0016 + 0.0000i
   0.0008 - 0.0000i
   0.0015 + 0.0001i
   0.0054 + 0.0001i
   0.0017 + 0.0001i
   0.0032 + 0.0000i
   0.0156 - 0.0002i
   0.0092 + 0.0001i
   0.0045 - 0.0001i
   0.0039 - 0.0000i
   0.0051 - 0.0001i
   0.0032 + 0.0001i
   0.0021 + 0.0001i
   0.0037 + 0.0000i
   0.0036 - 0.0000i
   0.0044 + 0.0001i
   0.0019 + 0.0001i
   0.0030 + 0.0001i
   0.0014 - 0.0000i
   0.0014 + 0.0000i
   0.0001 + 0.0000i

FT1 = [0;FT1];                                                                      % Create % Concatenate DC Component
Fn = T1.Frequency(end);                                                             % Nyquist Frequency (Hz Assumed)
Fs = 2*Fn;                                                                          % Sampling Frequency (Hz Assumed)
Ts = 1/Fs;                                                                          % Sampling Interval (Sampling Period) (Seconds Assumed)

FT2 = [FT1; flip(conj(FT1))];                                                       % Concatenate Flipped Complex Conjugate To End 
Time = linspace(0, 1, numel(FT2))*Ts;                                               % Create Time Vector (Assumes Highest Frequency Is The Nyquist Frequency)
IFT2 = ifft(FT2)

IFT2 = 
   0.0161 - 0.0000i
   0.0128 - 0.0004i
   0.0128 - 0.0008i
   0.0125 - 0.0011i
   0.0108 - 0.0013i
   0.0109 - 0.0017i
   0.0093 - 0.0017i
   0.0076 - 0.0016i
   0.0069 - 0.0017i
   0.0058 - 0.0016i
   0.0046 - 0.0014i
   0.0042 - 0.0015i
   0.0021 - 0.0008i
   0.0010 - 0.0004i
  -0.0000 + 0.0000i
  -0.0014 + 0.0007i
  -0.0021 + 0.0011i
  -0.0033 + 0.0019i
  -0.0046 + 0.0028i
  -0.0050 + 0.0033i
  -0.0055 + 0.0038i
  -0.0059 + 0.0043i
  -0.0061 + 0.0048i
  -0.0067 + 0.0056i
  -0.0067 + 0.0059i
  -0.0062 + 0.0059i
  -0.0065 + 0.0065i
  -0.0060 + 0.0064i
  -0.0059 + 0.0067i
  -0.0060 + 0.0072i
  -0.0052 + 0.0066i
  -0.0049 + 0.0066i
  -0.0045 + 0.0066i
  -0.0039 + 0.0060i
  -0.0037 + 0.0061i
  -0.0032 + 0.0057i
  -0.0025 + 0.0047i
  -0.0022 + 0.0044i
  -0.0018 + 0.0040i
  -0.0015 + 0.0036i
  -0.0013 + 0.0033i
  -0.0009 + 0.0026i
  -0.0006 + 0.0020i
  -0.0005 + 0.0018i
  -0.0004 + 0.0015i
  -0.0002 + 0.0010i
  -0.0002 + 0.0010i
  -0.0000 + 0.0002i
  -0.0000 + 0.0001i
   0.0000 - 0.0000i
   0.0000 - 0.0000i
   0.0000 - 0.0000i
   0.0000 - 0.0002i
  -0.0000 - 0.0005i
  -0.0000 - 0.0004i
  -0.0000 - 0.0004i
  -0.0001 - 0.0006i
  -0.0001 - 0.0007i
  -0.0003 - 0.0014i
  -0.0003 - 0.0015i
  -0.0005 - 0.0019i
  -0.0006 - 0.0022i
  -0.0007 - 0.0024i
  -0.0010 - 0.0030i
  -0.0014 - 0.0037i
  -0.0016 - 0.0039i
  -0.0019 - 0.0043i
  -0.0023 - 0.0047i
  -0.0026 - 0.0049i
  -0.0033 - 0.0058i
  -0.0037 - 0.0062i
  -0.0039 - 0.0060i
  -0.0045 - 0.0066i
  -0.0048 - 0.0066i
  -0.0051 - 0.0065i
  -0.0059 - 0.0070i
  -0.0058 - 0.0065i
  -0.0058 - 0.0061i
  -0.0062 - 0.0062i
  -0.0059 - 0.0056i
  -0.0063 - 0.0056i
  -0.0063 - 0.0053i
  -0.0056 - 0.0044i
  -0.0054 - 0.0040i
  -0.0050 - 0.0035i
  -0.0045 - 0.0029i
  -0.0040 - 0.0024i
  -0.0027 - 0.0015i
  -0.0014 - 0.0008i
  -0.0007 - 0.0003i
   0.0007 + 0.0003i
   0.0016 + 0.0007i
   0.0028 + 0.0011i
   0.0048 + 0.0017i
   0.0053 + 0.0016i
   0.0064 + 0.0018i
   0.0075 + 0.0018i
   0.0082 + 0.0018i
   0.0098 + 0.0018i
   0.0113 + 0.0017i
   0.0111 + 0.0013i
   0.0128 + 0.0012i
   0.0130 + 0.0008i
   0.0129 + 0.0004i

figure
yyaxis left
plot(T1.Frequency, T1.('Compressor Signal'))
ylabel('Amplitude')
yyaxis right
plot(T1.Frequency, T1.Phase)
ylabel('Phase (°)')
grid
title('Original One-Sided Fourier Transform')

figure
yyaxis left
plot(Time, real(IFT2))
ylabel('Real Component')
yyaxis right
plot(Time, imag(IFT2))
ylabel('Imaginary Componnent')
grid
title('Time-Domain Reconstruction')
xlim([min(Time) max(Time)])

There is something wrong with either the original data, or my interpretation of it (most likely the units, and that the omitted DC component is 0) and that the highest frequency in the data is the Nyquist frequency, because the imaginary component of the ifft should be essentially zero. (If the DC component is not 0, correct that in the ‘FT1’ creation assignment.)

I am confident that the code is correct, so it may be necessary to experiment with the unit conversions (if necessary) to produce a time-domain result with an essentially zero imaginary component. I have no idea what the original time-domain data look like, so I have nothing to compare it to.

.