Converting frequency domain to Time Domain using IFFT.

Question

Lokesh Katari 2021-10-1

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1464454-converting-frequency-domain-to-time-domain-using-ifft

评论： Yashika Chauhan 2022-12-4

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

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Lokesh Katari 2021-10-5

Freq_to_timedomain.xlsx

Hi @Star Strider

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

Yashika Chauhan 2022-12-4

Untitled spreadsheet - UWB_CPWfreespace (1).csv

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

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Answer 1

Star Strider 2021-10-5

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1464454-converting-frequency-domain-to-time-domain-using-ifft#answer_801856

在 MATLAB Online 中打开

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.

.