# Python fft amplitude

It only takes a minute to sign up. I have to use FFT to determine the period of waves inside a signal. After applying FFT on a window of point from a signal, I get something like this:. What I don't understand is that FFT is supposed to return frequencies, but if the input is a longer signal with the same frequencies, the values of frequencies returned by FFT will change. Some answers pointed out the sampling frequency. I don't understand what the number of samples per second has to do with the size of the periodic pattern, the FFT returns frequencies right?

That means we have a repeating pattern every point, I'm not sure about this. To summaries I have a periodic signal and I need to identify the period T0. This is simply how Discrete Fourier Transform i.

Fourier Transform theory applied on sampled signal works. All these bins correspond to how many cycles, or ckgs continue my application you might have between each samples.

You can measure at best half a cycle between each sample for real signals. This is usually converted back into frequency simply by knowing the sampling rate. So indeed if your signal is longer, you will have a longer output.

So basically, the longer you record, for whatever sampling rate, the finer resolution you get in the frequency domain. Since you are using Python, you can do it by using the fftfreq function it returns negative frequencies instead of ones above the Nyquist.

However, here is an example how to do it manually:. Where T is the period length in samples, N is the FFT length in samples, and k is the FFT result bin index of interest, for instance a result bin where there is a local or nearby magnitude amplitude peak. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Calculating values of frequency bins in Python Ask Question. Asked 2 years, 11 months ago. Active 7 months ago. Viewed 25k times.

After applying FFT on a window of point from a signal, I get something like this: What I don't understand is that FFT is supposed to return frequencies, but if the input is a longer signal with the same frequencies, the values of frequencies returned by FFT will change. I use the fft function provided by scipy in python. Edit: Some answers pointed out the sampling frequency.

### How to plot FFT in Python – FFT of basic signals : Sine and Cosine waves

Sunit Gautam 4 4 bronze badges. Hamza Tahiri Hamza Tahiri 88 1 1 gold badge 1 1 silver badge 5 5 bronze badges. Looking for periodicity in spectrum is done via cepstrum analysis. But if I now understand you correctly, based on the spectrum, you want to know if there is a periodicity in signal every N samples. Why not to use the autocorrelation instead? It returns magnitudes and phases of correlation to a limited basis set of sinusoidal frequencies.

Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. However, I find that to obtain this result I need to multiply the result of FFT by a factor dtwhich is the time interval between two sample points on my function.

I don't understand why. Can anybody help? Be careful, you are not computing the continuous time Fourier transform, computers work with discrete data, so does Numpy, if you take a look to numpy.

FFT: Filtering Noise from Signals, Waveform and Amplitude Spectrum Matlab Code

Asked 6 years, 4 months ago. Active 6 years, 4 months ago. Viewed 12k times. Active Oldest Votes. Also, you're missing a j in the initial definition. Otherwise, great answer! You are right Henry, I don't even know how I passed my signal processing course at uni with those mistakes! I will correct them. Thank you very much. It should have been quite obvious indeed. By the way, do you know why the factor is not taken into account in standard fft routines?

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Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up. I don't understand why FFT return different maximum amplitude as the signal length increase. I would except that with a large signal length according to the frequency, detected amplitude will be very accurate.

Your code is bit unclear, especially generation of your signal. Python allows for vectorized operations so it is good to use it. What's more, it is good to clearly specify the sampling frequency of your signal and use it then. Also please remember to normalize your FFT by length of your signal in this particular case and multiply by 2 half of spectrum is removed so energy must be preserved.

Phenomena you are facing is connected with fact that your frequency is not matching exactly frequency bin for it. Because of that energy is leaking into other frequency bins. This is due to fact that you don't have integer amount of cycles of your sinusoid. Please search for spectral leakage. Easy way to check that is to use the equation for frequency spacing in frequency domain, that is:.

If frequency you are analysing matches exactly one in your frequency vector, then amplitude will be correctly estimated, otherwise - leakage. In order to minimize this effect, you might want to apply window to your signal. Here is small modification of your code to help you visualize that.

The red curve is ideal spectrum and blue one is for given number of frequency bins strictly connected to your signal length. Two intermediate steps. Signal is 10 Hz sinusoid with an amplitude of 0. The maximum magnitude has to be interpolated for any sinusoid that is not exactly periodic by an exact integer number of periods in the FFT length.

Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up. I have a sinusoidal current that I am sampling at about k SPS. The current signal is about 3A pk-pk hz top figure. I have a sample size of so I divided the fft by and multiplied by 2 to get the results below. Yet there is a discrepancy between your expectation and the obsevred DFT result? There are a few reasons.

Your assumptions on the sampling rate or the signal frequency could be wrong. Indeed as it seems from your figures, the signal is not a pure sine wave. In that case the amplitude looses its crisp definition and spectral leakage and main lobe width smearing becomes an issue. For details please search the site for spectral estimation, spectral display etc I'm getting exactly what is expected.

So this suggests me that your signal is not a pure sine wave. It's either modulated, or your sampling rate and frequency information is not consistent.

Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 1 year, 8 months ago. Active 1 year, 8 months ago. Viewed 2k times.

Where's your problem with this? I expect 3 however am getting a peak of around 1. I assumed my scaling was correct as well since I've gotten the correct amplitudes with other frequencies I have measured. Unfortunately, this shows otherwise! Active Oldest Votes. Fat32 Fat32 I got the same results as you after I generated an ideal sine wave in python too. Since my measured sinusoid isn't exactly pure, are there any methods to compensate for the spectral leakage and retrieve an accurate amplitude?

Hence you cannot find the exact individual amplitudes. There is a resolution limit to every spectral estimation technique. Some error is unavoidable. I've used a sampling rate of Hz but I can't retrieve the correct amplitude. Post as a guest Name.Often we are confronted with the need to generate simple, standard signals sine, cosine, Gaussian pulse, squarewave, isolated rectangular pulse, exponential decay, chirp signal for simulation purpose.

If you are inclined towards Matlab programming, visit here. In order to generate a sine wave, the first step is to fix the frequency f of the sine wave. Given the frequency of the sinewave, the next step is to determine the sampling rate.

For baseband signals, the sampling is straight forward. By Nyquist Shannon sampling theoremfor faithful reproduction of a continuous signal in discrete domain, one has to sample the signal at a rate higher than at-least twice the maximum frequency contained in the signal actually, it is twice the one-sided bandwidth occupied by a real signal.

For a baseband signal bandwidth to and maximum frequency in a given band are equivalent. Numpy is a fundamental library for scientific computations in Python. In order to use the numpy package, it needs to be imported. Here, we are importing the numpy package and renaming it as a shorter alias np. We note that the function sine wave is defined inside a file named signalgen. We will add more such similar functions in the same file. The intent is to hold all the related signal generation functions, in a single file. This approach can be extended to object oriented programming. Now that we have defined the sine wave function in signalgen.

Python is an interpreter based software language that processes everything in digital. In order to obtain a smooth sine wave, the sampling rate must be far higher than the prescribed minimum required sampling rate, that is at least twice the frequency — as per Nyquist-Shannon theorem.

Hence, we need to sample the input signal at a rate significantly higher than what the Nyquist criterion dictates.

Higher oversampling rate requires more memory for signal storage. It is advisable to keep the oversampling factor to an acceptable value. An oversampling factor of is chosen in the previous function. This is to plot a smooth continuous like sine wave. Thus, the sampling rate becomes. If a phase shift is desired for the sine wave, specify it too. The FFT, implemented in Scipy. Cooley and J.Fourier analysis is fundamentally a method for expressing a function as a sum of periodic components, and for recovering the function from those components.

When both the function and its Fourier transform are replaced with discretized counterparts, it is called the discrete Fourier transform DFT. The DFT has become a mainstay of numerical computing in part because of a very fast algorithm for computing it, called the Fast Fourier Transform FFTwhich was known to Gauss and was brought to light in its current form by Cooley and Tukey [CT].

Press et al. Because the discrete Fourier transform separates its input into components that contribute at discrete frequencies, it has a great number of applications in digital signal processing, e. The output is called a spectrum or transform and exists in the frequency domain. There are many ways to define the DFT, varying in the sign of the exponent, normalization, etc.

In this implementation, the DFT is defined as. The DFT is in general defined for complex inputs and outputs, and a single-frequency component at linear frequency is represented by a complex exponentialwhere is the sampling interval. The routine np. The phase spectrum is obtained by np. It differs from the forward transform by the sign of the exponential argument and the default normalization by.

The default normalization has the direct transforms unscaled and the inverse transforms are scaled by. It is possible to obtain unitary transforms by setting the keyword argument norm to "ortho" default is None so that both direct and inverse transforms will be scaled by.

When the input is purely real, its transform is Hermitian, i. The family of rfft functions is designed to operate on real inputs, and exploits this symmetry by computing only the positive frequency components, up to and including the Nyquist frequency. Correspondingly, when the spectrum is purely real, the signal is Hermitian.

In higher dimensions, FFTs are used, e. The computational efficiency of the FFT means that it can also be a faster way to compute large convolutions, using the property that a convolution in the time domain is equivalent to a point-by-point multiplication in the frequency domain.

Discrete Fourier Transform numpy. Cambridge Univ. Press, Cambridge, UK. Table of Contents Discrete Fourier Transform numpy. Last updated on Jul 26, Created using Sphinx 1. The inverse of fftshift. Cooley, James W.

### How can I find the amplitude of a real signal using "fft" function in Matlab?

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For further information, including about cookie settings, please read our Cookie Policy. By continuing to use this site, you consent to the use of cookies. We value your privacy. Asked 12th Dec, Fernanda Catelani. How can I find the amplitude of a real signal using "fft" function in Matlab? I would like to get the same amplitude in the frequency domain with fft and in the time domain.

I've read about some methods:. Can anybody help me? Thank you. Frequency Modulation. Most recent answer. Suresh Babu. Kamaraj College of Engineering and Technology. Dear Madam. In both time domain and frequency damain, energy of the signal should be the same. It is the statement of Parseval's theorem. It is easily proved by using matlab. Popular Answers 1. Tariq Abuhamdia. So you should divide by N, then take the absolute value.