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Amplitude of input wave is massively different to Fourier coefficient amplitude
Plotting FFT on octaveAre real and imaginary parts of fft ouput correlated?Signal analysis: amplitude estimation in MATLABCan you compute the amplitude/power of original signal from Fourier transform?How do I match lomb-scargle and FFT plots of same dataset?How to calculate efficiently and accurately the Fourier transform of a radial function in FortranAutocorrelation of multiple time series in Matlab using FFTExtract Fourier coeffients from fft() in RIssue with Discrete Double Fourier Series in MATLABModeling a Fourier Series from Discrete Fourier Transform for ExtrapolationAmplitude for each day of daily time series
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The series of waves I input into the fft() function in R all have an RMS in the order of 10E-2, however the Fourier coefficient is massively different for all the waves (anywhere from 0.3-15).
I've looked at other fft functions such as the periodogram() and the coefficients remain the same.
Nothing fancy, just importing a series of y values into the fft function then taking the modulus.
result <- abs(fft(df))
An example of the input data and output transform is seen here:
Am I incorrect in assuming that there is a direct correlation between the RMS/Amplitude of the sin wave and the magnitude of the fourier coefficient?
Thanks in advance.
r signal-processing fft frequency-analysis
asked Mar 24 at 16:20
Jkind9Jkind9
5711
add a comment |
The series of waves I input into the fft() function in R all have an RMS in the order of 10E-2, however the Fourier coefficient is massively different for all the waves (anywhere from 0.3-15).
I've looked at other fft functions such as the periodogram() and the coefficients remain the same.
Nothing fancy, just importing a series of y values into the fft function then taking the modulus.
result <- abs(fft(df))
An example of the input data and output transform is seen here:
Am I incorrect in assuming that there is a direct correlation between the RMS/Amplitude of the sin wave and the magnitude of the fourier coefficient?
Thanks in advance.
r signal-processing fft frequency-analysis
asked Mar 24 at 16:20
Jkind9Jkind9
5711
2
I don't know about R's FFT implementation, but for most FFTs you need to divide the magnitude by the FFT size, as there is an implicit scaling factor.
– Paul R
Mar 24 at 17:00
add a comment |
The series of waves I input into the fft() function in R all have an RMS in the order of 10E-2, however the Fourier coefficient is massively different for all the waves (anywhere from 0.3-15).
I've looked at other fft functions such as the periodogram() and the coefficients remain the same.
Nothing fancy, just importing a series of y values into the fft function then taking the modulus.
result <- abs(fft(df))
An example of the input data and output transform is seen here:
Am I incorrect in assuming that there is a direct correlation between the RMS/Amplitude of the sin wave and the magnitude of the fourier coefficient?
Thanks in advance.
r signal-processing fft frequency-analysis
asked Mar 24 at 16:20
Jkind9Jkind9
5711
The series of waves I input into the fft() function in R all have an RMS in the order of 10E-2, however the Fourier coefficient is massively different for all the waves (anywhere from 0.3-15).
I've looked at other fft functions such as the periodogram() and the coefficients remain the same.
Nothing fancy, just importing a series of y values into the fft function then taking the modulus.
result <- abs(fft(df))
An example of the input data and output transform is seen here:
Am I incorrect in assuming that there is a direct correlation between the RMS/Amplitude of the sin wave and the magnitude of the fourier coefficient?
Thanks in advance.
r signal-processing fft frequency-analysis
r signal-processing fft frequency-analysis
asked Mar 24 at 16:20
Jkind9Jkind9
5711
asked Mar 24 at 16:20
Jkind9Jkind9
5711
asked Mar 24 at 16:20
Jkind9Jkind9
5711
asked Mar 24 at 16:20
Jkind9Jkind9
5711
asked Mar 24 at 16:20
Jkind9Jkind9
5711
5711
2
I don't know about R's FFT implementation, but for most FFTs you need to divide the magnitude by the FFT size, as there is an implicit scaling factor.
– Paul R
Mar 24 at 17:00
add a comment |
2
I don't know about R's FFT implementation, but for most FFTs you need to divide the magnitude by the FFT size, as there is an implicit scaling factor.
– Paul R
Mar 24 at 17:00
2
2
I don't know about R's FFT implementation, but for most FFTs you need to divide the magnitude by the FFT size, as there is an implicit scaling factor.
– Paul R
Mar 24 at 17:00
I don't know about R's FFT implementation, but for most FFTs you need to divide the magnitude by the FFT size, as there is an implicit scaling factor.
– Paul R
Mar 24 at 17:00
add a comment |
1 Answer
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As I described in another answer, there is an approximate relationship between the amplitude in the time-domain and the frequency-domain, which I stated under the usual Discrete Fourier Transform definition. Since R's fft follows the same definition (see the documentation), you may expect a similar approximate 0.5*N scaling of the amplitude when going from the time-domain to the frequency-domain.
Note that since you clearly do not have a pure sinusoidal signal, the different frequency component may start to interfere and make the relationship more approximate than absolute truth, but it should still be in the right order of magnitude.
answered Mar 26 at 1:42
SleuthEyeSleuthEye
11.1k22047
add a comment |
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As I described in another answer, there is an approximate relationship between the amplitude in the time-domain and the frequency-domain, which I stated under the usual Discrete Fourier Transform definition. Since R's fft follows the same definition (see the documentation), you may expect a similar approximate 0.5*N scaling of the amplitude when going from the time-domain to the frequency-domain.
Note that since you clearly do not have a pure sinusoidal signal, the different frequency component may start to interfere and make the relationship more approximate than absolute truth, but it should still be in the right order of magnitude.
answered Mar 26 at 1:42
SleuthEyeSleuthEye
11.1k22047
add a comment |
As I described in another answer, there is an approximate relationship between the amplitude in the time-domain and the frequency-domain, which I stated under the usual Discrete Fourier Transform definition. Since R's fft follows the same definition (see the documentation), you may expect a similar approximate 0.5*N scaling of the amplitude when going from the time-domain to the frequency-domain.
Note that since you clearly do not have a pure sinusoidal signal, the different frequency component may start to interfere and make the relationship more approximate than absolute truth, but it should still be in the right order of magnitude.
answered Mar 26 at 1:42
SleuthEyeSleuthEye
11.1k22047
add a comment |
As I described in another answer, there is an approximate relationship between the amplitude in the time-domain and the frequency-domain, which I stated under the usual Discrete Fourier Transform definition. Since R's fft follows the same definition (see the documentation), you may expect a similar approximate 0.5*N scaling of the amplitude when going from the time-domain to the frequency-domain.
Note that since you clearly do not have a pure sinusoidal signal, the different frequency component may start to interfere and make the relationship more approximate than absolute truth, but it should still be in the right order of magnitude.
answered Mar 26 at 1:42
SleuthEyeSleuthEye
11.1k22047
As I described in another answer, there is an approximate relationship between the amplitude in the time-domain and the frequency-domain, which I stated under the usual Discrete Fourier Transform definition. Since R's fft follows the same definition (see the documentation), you may expect a similar approximate 0.5*N scaling of the amplitude when going from the time-domain to the frequency-domain.
Note that since you clearly do not have a pure sinusoidal signal, the different frequency component may start to interfere and make the relationship more approximate than absolute truth, but it should still be in the right order of magnitude.
answered Mar 26 at 1:42
SleuthEyeSleuthEye
11.1k22047
answered Mar 26 at 1:42
SleuthEyeSleuthEye
11.1k22047
answered Mar 26 at 1:42
SleuthEyeSleuthEye
11.1k22047
answered Mar 26 at 1:42
SleuthEyeSleuthEye
11.1k22047
11.1k22047
add a comment |
add a comment |
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I don't know about R's FFT implementation, but for most FFTs you need to divide the magnitude by the FFT size, as there is an implicit scaling factor.
– Paul R
Mar 24 at 17:00